Physics

with a High Intensity Proton Source

at Fermilab

Draft Version 1.0

February 3, 2008

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### Contributors to this document

(under construction)

If there is anyone missing, e-mail <ykkim@fnal.gov>, or your working
group conveners.

Please contribute (read it, send your comments etc.) or in other forms,
and join the contributor list.

Jeffrey Appel (Fermilab)

David Asner (Carleton University)

Ikaros Bigi (University of Notre Dame)

Douglas Bryman (University of British Columbia)

Andrjez Buras (Technical University of Munich)

Marcela Carena (Fermilab)

Roberto Carosi (INFN, Pisa)

Dave Christian (Fermilab)

Janet Conrad (Columbia University)

Milind Diwan (Brookhaven National Laboratory)

Craig Dukes (University of Virginia)

Estia Eichten (Fermilab)

David Finley (Fermilab)

Peter Fisher (MIT)

Bonnie Fleming (Yale University)

Steve Geer (Fermilab)

Andre de Gouvea (Northwestern University)

Keith Gollwitzer (Fermilab)

Deborah Harris (Fermilab)

David Hertzog (University of Illinois, Urbana-Champaign)

Christopher Hill (Fermilab)

Stephen Holmes (Fermilab)

Gino Isidori (INFN, Frascati)

David E. Jaffe (Brookhaven National Laboratory)

Boris Kayser (Fermilab)

Edward Kearns (Boston University)\
Young-Kee Kim (Fermilab and University of Chicago)

Andreas Kronfeld (Fermilab)

Kenneth Lande (University of Pennsylvania)

Kevin Lesko (Lawrence Berkeley National Laboratory)

Laurence Littenberg (Brookhaven National Laboratory)

Byron Lundberg (Fermilab)

Joseph Lykken (Fermilab)

Michelangelo Mangano (CERN)

David McGinnis (Fermilab)

Mark Messier (Indiana University)

James Miller (Boston University)

Sanjib Mishra (University of South Carolina)

William Molzon (University of California, Irvine)

Pier Oddone (Fermilab)

Vaia Papadimitriou (Fermilab)

Stephen Parke (Fermilab)

Klaus Peters (GSI)

Roberto Petti (CERN)

Kevin Pitts (University of Illinois, Urbana-Champaign)

Stephen Pordes (Fermilab)

Chris Quigg (Fermilab)

Thomas Phillips (Duke University)

Regina Rameika (Fermilab)

Lee Roberts (Boston University)

Jonathan Rosner (Univerwity of Chicago)

Alan Schwartz (University of Cincinnati)

Niki Saoulidou (Fermilab)

James Siegrist (UC Berkeley and Lawrence Berkeley National Laboratory)

Giulio Stancari of INFN Ferrara

Rex Tayloe (Indiana University)

Robert Tschirhart (Fermilab)

Taku Yamanaka (Osaka University)

Peter Yamin (Brookhaven National Laboratory)

**[Contents]{.underline}**

0\. Executive Summary (to be done)

1\. Introduction 5

2\. The Proton Source Roadmap for Fermilab 9

3\. Neutrinos 13

4\. Muons 35

5\. Kaons 57

6\. Charms 79

7\. Antiprotons 82

8\. Conclusions 96

**1 Introduction**

**Perspective**

Within the next ten years the Standard Model will likely have to be
modified to encompass a wide range of newly discovered phenomena, new
elementary particles, new symmetries, and new dynamics. These phenomena
will be revealed through experiment with high energy particle
accelerators, mainly the LHC. This will represent a revolution in our
understanding of nature, and will either bring us closer to an
understanding of all phenomena, through existing ideas such as
supersymmetry to superstrings, or will cause us to scramble to find new
ideas and a new sense of direction. We are thus entering a dramatic and
important time in the quest to understand the fundamental laws of nature
and their role in shaping the universe.

The energy scales now probed by the Tevatron, of order hundreds of GeV,
will soon be subsumed by the LHC and extended up to a few TeV. We expect
the unknown structure of the mysterious symmetry breaking of the
Standard Model to be revealed. We will then learn the answer to a
question that has a fundamental bearing upon our own existence: \"What
is the origin of mass?\"

All modern theories of \"electroweak symmetry breaking\" involve many
new particles, mainly to provide a \"naturalness\" rationale for the
weak scale. Supersymmetry (SUSY) represents extra (fermionic) dimensions
of space, leading to a doubling of the number of known elementary
particles and ushering in many additional new particles and phenomena
associated with the various symmetry breaking sectors. The possibility
of additional bosonic dimensions of space would likewise usher in an
even greater multitude of new states and new phenomena. Alternatively,
any new spectroscopy may indicate new principles we have not yet
anticipated, and we may see new strong forces and/or a dynamical origin
of mass. The wealth of new particles, parameters, *CP*-phases, and other
phenomena carries important implications for precision quark flavor
physics experiments that are uniquely sensitive probes of new phenomena.

We have already begun to see the enlargement of the Standard Model in
the leptonic sector. Neutrino masses and mixing angles, which in the
early 1990\'s were unknown, must now be incorporated into our full
description of nature. In a minimal scenario of Majorana masses and
mixings amongst the three known left-handed neutrinos, we see a strong
hint of a new and very large mass scale, possibly associated with grand
unification or the scale of quantum gravity, the Planck mass. We are not
yet sure what the proper description of neutrino masses and mixing
angles will be. Experiments may reveal additional unexpected particles
coupled to the neutrino sector. New phenomena, such as leptonic
*CP*-violation, will be major focal points of our expanding
understanding of the lepton sector. There is much to be done with
experiment to attack the issues that neutrinos now present.

Already, developments in neutrino physics and the possibility of a novel
source of *CP*-violation in the lepton sector have spawned hopes that
the cosmic matter-antimatter asymmetry may be explained through
*leptogenesis.* Neutrino physics, together with the search for new
energy frontier physics, offers the possibility of experimental handles
on the questions of dark matter and dark energy. Without the discovery
of new particles in accelerator experiments, the telescope-based
cosmological observations of the early universe would remain unexplained
puzzles. The process of understanding the laws of physics in greater
detail through accelerator-based high energy physics will potentially
have incisive impact on our understanding of dark matter and dark
energy.

Precision flavor physics in both the quark and the lepton sectors offers
a window on the sensitive entanglement of beyond-the-Standard-Model
physics with rare processes, through quantum loop effects involving
known or new states. Flavor physics offers sensitive indirect probes and
may be the first place to reveal additional key components of the
post-Standard Model physics. The main arenas for quark flavor physics
include strange, charm and beauty, hence kaons, *D*-mesons, *B*-mesons
and heavy baryons. A remarkable historical paradigm for the importance
of flavor physics is the well known suppression of flavor-changing
neutral currents. The analysis of the *K~L~--K~S~* mass difference by
Gaillard and Lee, 35 years ago in the Fermilab Theory Group, led to the
confirmation of the GIM mechanism and predicted the mass of the charm
quark, *m~c~* \~ 1.5 GeV, definitively and prior to its discovery. This,
today, implies an astonishing constraint on SUSY models, e.g., that the
down and strange squarks are mass degenerate to 1:10^5^. This, in turn,
has spawned a new working hypothesis called \"Minimal Flavor Violation\"
(MFV). But is MFV really a true principle operating in nature and, if
so, where does it come from? Such questions can only be addressed in
precision flavor physics experiments.

Modes in rare *K* and *B* decays have been calculated to a high degree
of precision within the framework of the Standard Model. Hypothetical
new phenomena coming from physics beyond the Standard Model can lead to
departures from these precise predictions. In the lepton sector there
remains a large unexplored territory in rare muon decays accessible to
modern experiments with similar sensitivity to new physics. The spirit
of the approach remains very much the same as in the era of Gaillard and
Lee.

Flavor dynamics and the origin of quark and lepton masses and mixings
are amongst the least understood topics in elementary particle physics,
representing the darkest corner of the Standard Model. There is a
plausible \"string-inspired\" view that the ultimate understanding of
flavor dynamics will come only from a more fundamental theory at the
inaccessible GUT or Planck scale. Yet, we do not know definitively the
scale of and origin of these phenomena. Plausible theories abound in
which flavor dynamics could be rich at scales of order hundreds of TeV
and accessible to *K*, *B*, *D*, and rare muon transition experiments.
In fact, rare decays provide a method to address the ultra high energy
\> 100 TeV scale in nature. The discovery of new physics in the study of
*CP*-violating and rare decay processes would play a fundamental role in
sculpting a revolutionary new view of the physical world.

**Creating Opportunities**

Experimental particle physics advances by synthesizing insights won by
many techniques. Collider experiments have taken us to the energy
frontier with proton-antiproton collisions at the Tevatron and
electron-positron interactions at LEP and SLC. Colliders have enabled
measurements of great delicacy at the *B* factories and CLEO.
Fixed-target experiments have been major contributors to flavor physics,
our knowledge of nucleon structure, and our understanding of neutrino
properties and interactions. However, many of the accelerator
experiments that have helped define the diversity and scale of our
program, and have helped drive the past decades of discovery, are coming
to an end.

Beyond the Tevatron Collider program, we look forward to the Large
Hadron Collider, which will place experiment squarely in the heart of
the TeV scale essential to the understanding of electroweak symmetry
breaking. Fermilab is a key player in the LHC program, as a developer of
superconducting magnets, the headquarters of U.S. CMS, and the site of
the LHC Physics Center. The high-energy frontier is part of Fermilab's
heritage, and remains an essential element of its future.

Doing good science and making new scientific tools available is critical
to our challenging future. This requires the broadband energy frontier
assault that the LHC provides, followed by the incisiveness of the ILC.
We must also explore the energy frontier beyond the ILC via a multi-TeV
scale lepton collider, such as CLIC or the muon collider. Both of these
machines pose extreme technical challenges and have comparable degrees
of unproven technological viability. Bold new concepts in overcoming
some of these challenges have evolved in recent years and need to be
tested.

This document describes a framework for constructing an adaptable
program that will bring world-class science in the short term, can
evolve toward world-leading experiments in the medium term, and prepares
the technological ground for ambitious energy frontier accelerator
initiatives in the future. While providing views of more than one
possible long-term future, the program develops in stages, allowing for
multiple decision points that refine and optimize the ultimate path and
destinations. Scientific opportunities and the state of technology will
inform each decision. Our overarching goal is to create a diversity of
possibilities as we continue our tradition of discovery.

Above all, it is imperative that we adopt a realistic view and
understanding of what can be done now, as well as a strong vision of
regaining the energy frontier in the future. A new high-luminosity
proton source, Project X (a national project with international
collaboration), could provide a diverse interim physics program, and
could potentially drive long range future accelerator initiatives. This
would form the basis for the U.S. leadership in neutrino physics, and a
parallel program of world-class kaon and muon experiments. The first
phase could be developed with some of these experiments prior to the
availability of Project X, using enhanced, existing facilities at
Fermilab. As Project X becomes available, these experiments could enter
a next phase in which the ultimate capabilities are achieved.

Project X calls for the development of the same superconducting
radio-frequency technology as will be used in the ILC.   Thus the
pursuit of Project X would spur U.S. industrialization in this vital
area while also providing a system test for key ILC components. The
expertise gained through this work would position the U.S. and Fermilab
to contribute significantly to the global ILC effort and would
help position Fermilab to host the ILC.[^1]

We focus here on a menu of experiments at the sensitivity frontier that
work coherently with the laboratory's committed program in neutrino
physics (MINOS through NOvA) to opportunities of next-generation
neutrino experiments of great sensitivity to leptonic *CP* violation
that would require a multi-MW proton source and a very large, longer
baseline detector. Prominent examples are studies of the charged and
neutral rare kaon decays *K* and the search for lepton-flavor violation
in muon-electron conversion. These experiments, each with the capability
to affect dramatically our understanding of the fundamental
interactions, can produce world-class results with modest
reconfiguration and improvement of the existing accelerator complex.
Enhanced by a new bright proton source, Project X, they would become
world-leading experiments. The superconducting linac would demonstrate
the superconducting RF technology of the ILC and may ultimately provide
a platform for developing an evolutionary path to a muon-storage-ring
neutrino factory and a multi-TeV muon collider.

Not every item on the experimental menu will be chosen. The possibility
of mounting some experiments early will be explored and R&D resource
needs to investigate these possibilities are modest. The resource scope
of a new high intensity proton source that drives this research program
into the future is comparable to the Main Injector project
(http://projectx.fnal.gov/RnDplan/).With the flexibility to construct a
coherent program, we can deliver discovery science, renew the user
community by encouraging young scientists to bring new ideas, and create
possibilities for the future of particle physics.

**2 The Proton Source Roadmap for Fermilab**

Fermilab is embarked upon a program of continuous performance
improvements to the proton complex in support of the ongoing needs of
the neutrino program. This program is being implemented in phases, with
the "Proton Plan" currently underway, to be followed by accelerator
upgrades implemented as part of the NOA project. The Proton Plan aims to
deliver roughly 340 kW of beam power to the NuMI target, coincident with
70 kW to the antiproton production target in early FY 2009. Following
completion of Run II the total, 410 kW, would be available on the NuMI
target. The NOA Project includes accelerator and NuMI target station
upgrades aimed at delivery of 700 kW of beam power to the NuMI target.

Following completion of the Proton Plan there are several paths to
further increase the proton beam power available at Fermilab that have
been considered. These paths include evolution and further upgrade of
the existing complex to "Super-NuMI" (SNuMI), construction of a new
rapid cycling synchrotron, and construction of a high-power linac based
on Superconducting RF technology (SCRF) developed for the ILC. The path
based on a new SCRF linac is referred to as "Project-X" and has been
identified by the Fermilab Steering Group as the most compelling path
forward. The Project-X path described below provides the greatest
flexibility toward a very high power facility while simulataneously
advancing energy-frontier accelerator technology.

The table below compares performance of the present complex with the
SNuMI path forward and the Project-X path forward. The first three
columns represent current performance and improvements now underway. The
last two columns list SNuMI and Project X parameters. All columns are
based on injecting beam from the existing 8 GeV Booster, except for
Project X, which eliminates the need for the Booster. While the table
does not list any beam power availability at 8 GeV in SNuMI, protons
could be made available at this energy at the expense of availability at
120 GeV.

  ---------------------- --------- --------- -------- -------- --------- ---------------
                         Current   Proton    NOvA     SNuMI    Project X Unit
                                   Plan                                  

  Batch intensity (8     3.0E12    4.3E12    4.1E12   4.5E12   5.6E13    protons/pulse
  GeV)                                                                   

  Rep rate               9         9         12       13.5     5         Hz

  Protons / hour         9.7E16    1.4E17    1.8E17   2.2E17   1.0E18    

  Main Injector batches  11        11        12       18       3         

  MI batches to pbar     2         2         0        0        0         
  target                                                                 

  MI cycle time          2.4       2.2       1.33     1.33     1.4       Second

  NuMI beam power (120   216       338       710      1169     2304      kW
  GeV)                                                                   

  8 GeV beam power       14        17        16       0        205       kW
  (available)                                                            

  Injection energy       400       400       400      400      8000      MeV
  (1^st^ synch)                                                          

  y^2^                   1.45      1.45      1.45     1.45     90.30     

  Injection emittance    10        10        10       10       20        mm-mr

  Injection space charge 0.15      0.22      0.21     0.23     0.07      
  tune shift                                                             
  ---------------------- --------- --------- -------- -------- --------- ---------------

**Table 1 Proton sources at Fermilab. NOvA column includes a potential
upgrade of the Booster repetition rate to support simultaneous delivery
of 2×10^20^ protons / year at 8 GeV. NOvA itself requires Booster
operations at 9 Hz.**

**2.1 Project X**

Project X is identified in the Fermilab Roadmap as described in the
Fermilab Steering Group Report as the preferred route forward for the
proton based program at Fermilab.

(<http://www.fnal.gov/pub/directorate/steering/index.shtml>).

![](media/image1.wmf){width="5.997222222222222in"
height="2.1909722222222223in"}

**Figure 2.1: Schematic view of Project X**

Project X is based on an 8 GeV superconducting *H^-^* linac, paired with
the existing (but modified) Main Injector and Recycler rings, to provide
in excess of 2 MW of beam power throughout the energy range 60 -- 120
GeV, simultaneous with at least 100 kW of beam power at 8 GeV. The linac
utilizes technology in common with the ILC over the energy range 0.6 --
8.0 GeV. Beam current parameters can be made identical to those of ILC
resulting in identical RF generation and distribution systems. This
alignment of ILC and Project X technologies allows for a shared
development effort. The initial 0.6 GeV of the linac draws heavily on
technology developed by Argonne National Laboratory for a facility for
rare isotope beams. It is anticipated that the exact configuration and
operating parameters of the linac will be defined through the R&D
program and will retain alignment with the ILC plan as it evolves over
this period.

Utilization of the Recycler Ring as an H^-^ stripper and accumulator
ring is the key element that provides the flexibility to operate the
linac with the same beam parameters as the ILC. The linac operates at 5
Hz with a total of 5.6×10^13^ *H^-^* ions delivered per pulse. *H^-^*'s
are stripped at injection into the Recycler in a manner that "paints"
the beam both transversely and longitudinally to reduce space charge
forces. Following the 1 ms injection, the orbit moves off the stripping
foil and circulates for 200 msec, awaiting the next injection. Following
three such injections a total of 1.7×10^14^ protons are transferred in a
single turn to the Main Injector. These protons are then accelerated to
120 GeV and fast extracted to a neutrino target. The Main Injector cycle
takes 1.4 seconds, producing approximately 2.3 MW of beam power at 120
GeV. At lower proton energies Main Injector cycle times can be shorter,
allowing a beam power above 2 MW in the range of proton energy between
60 GeV and 120 GeV. In parallel, because the loading of the Recycler
only requires 0.6 seconds, up to four linac cycles are available for
accumulation and distribution of 8 GeV protons from the Recycler. Total
available 8 GeV beam power lies in the range of 100-200 kW, depending on
the energy in the Main Injector.

It is anticipated that Project X configured as described above would
initially support high intensity neutrino beams to the NOA experiment,
in parallel with a rare-decay research program driven with the intense 8
GeV proton source. Depending upon future directions, flexibility is
retained for delivering neutrinos toward the DUSEL site and/or protons
into the Tevatron.

**2.2 Rare Decay Experiment Requirements of the 8 GeV Proton Complex**

The next generation of rare-decay experiments requires kaon and muon
beams of extraordinary quality. These experiments operate at the
intensity frontier, where conventional decay and interaction processes
can conspire in a high-rate environment to mimic the sought-after rare
decay signatures. The principal weapon to control these backgrounds is
the partnership of detectors that deliver excellent time resolution with
high duty-factor beams which minimize the instantaneous rates that the
detectors must face. Project-X is an exceptional opportunity to build a
high intensity 8-GeV proton beam complex with nearly 100% duty factor
and high availability (nominally 5000 hours per year). This complex
could be realized with the intrinsically high duty factor SCRF 8-GeV
linear accelerator driving a series of stacking and stretcher rings
configured to deliver the RF structure required by the experiments. The
joint potential of high duty factor and high availability would make the
Fermilab complex a unique resource for rare-decay experiments.

Both the muon and kaon rare decay programs could have Phase I operation
before the high-power Project X era (Phase II). A conceptual scheme has
been developed to establish the required RF structure for Phase-I
operation for both programs with an evolution of the existing
Accumulator and Debuncher complex into an 8-GeV "stretcher ring". The
scheme is described in some detail in the Fermilab Steering Group
report. The proton beam RF train requirements for the kaon and muon
programs are listed below in Table 2.

+---------------------------+---------------+-------------+----------+
|                           | Train         | Pulse Width | Int      |
|                           | Frequency     |             | er-Pulse |
|                           |               | (n          |          |
|                           | (MHz)         | anoseconds) | Ex       |
|                           |               |             | tinction |
+---------------------------+---------------+-------------+----------+
| Kaon experiments          | 20-30         | 0.1-0.2     | 10^-3^   |
+---------------------------+---------------+-------------+----------+
| Muon conversion           | 0.5-1.0       | 50          | 10^-9\*^ |
| experiment                |               |             |          |
+---------------------------+---------------+-------------+----------+
| Muon g-2 experiment       | 30-100        | 50          | \-\--    |
+---------------------------+---------------+-------------+----------+

\*muon conversion extinction is achieved by a combination of extinction
in the circulating beam/extraction and in an external device in the
proton beam transport

**Table 2: RF train requirements for the kaon and muon rare decay
programs.**

The average Phase-I beam current in an Accumuator/Debuncher stretcher
ring would be about two amperes, comparable to B-factory currents and
manageable with now standard accelerator instrumentation and techniques.
Phase-II operation with the Accumulator / Debuncher stretcher complex
would lead to an order of magnitude higher circulating current which may
lead to beam instabilities (driven by electron cloud effects for
example) that could compromise the integrity of the RF train or the high
duty factor required by the experiments. This can be mitigated by more
rapid cycling of the 8 GeV Recycler/Debuncher/Accumulator complex, more
sophisticated beam instrumentation and feedback, or evolution and
construction of another stretcher ring in the complex for Phase-II
operation. More rapid cycling of the 8 GeV complex would come at the
expense of duty factor, but is relatively straightforward. Advanced
instrumentation and feedback is possibly a solution but does not scale
well to even higher power in the complex. A larger stretcher ring based
on the Recycler or Tevatron infrastructure would reduce the circulating
beam current by a factor of six and twelve, respectively. It has the
best scaling properties for the complex, thereby reducing technical risk
but comes with a greater initial capital cost. A larger stretcher ring
also preserves the Fermilab antiproton complex for possible future
experiments. A study group of experimenters and accelerator physicists
is now actively reviewing these options to determine the best path
forward for a Phase-II stretcher ring complex.

**2.3 Comparison to Other Facilities.**

The intensity frontier physics potential has motivated investments
world-wide in next generation proton facilities. How the evolution of
the Fermilab proton complex fits in this context is summarized here.

For long-baseline neutrino physics the principal metric is high-energy
beam power where the Fermilab Main Injector and the new JPARC proton
facility in Japan will be leading the next decade. The JPARC facility
has a near term goal of \>400 kW, comparable to the NOvA-era Proton
Plan. JPARC is considering upgrades to 1.6 MW with 50 GeV protons by the
end of the next decade. Project X would be able to deliver over 2 MW in
the wide range of proton energy between 50 and 120 GeV in a similar time
scale.

For rare-muon and rare-kaon decay physics the facility metric is more
nuanced than neutrino facility metrics. Beam power, duty factor, beam
availability and the ease of implementing necessary RF beam structures
are all important elements. After the Tevatron collider program is
complete, the existing multiple rings in the Fermilab accelerator
complex can be redeployed as elements of a unique high duty factor and
high availability facility with an order of magnitude higher sensitivity
than other facilities world-wide. As an example, the comparative power
of Project X among world-wide facilities for kaon physics is tabulated
in Section 4.

For physics driven by antiproton beams, the existing Fermilab facility
already exceeds the intensity goals of the GSI antiproton facility
projected to come online late in the next decade. With the construction
of a new accelerator ring dedicated for experiments, the current
antiproton source will then be able to drive an antiproton based
research program with an expected yearly antiproton yield of an order of
magnitude higher than the one at GSI. In Section 5 the
existing/projected Fermilab and projected GSI antiproton facilities are
compared.

**3 Neutrinos**

3.1 Introduction

**3.1.1 Neutrino Oscillations**

During the past decade, we have found compelling evidence that neutrinos
oscillate between flavors, which implies that they have nonzero masses.
Laboratory and astrophysical data indicate that these masses are
extremely small. Their small size suggests, through the "see-saw"
mechanism, that new physics occurs at an ultra-high mass scale very
close to the grand unification scale. Thus, neutrino masses provide a
tantalizing window on physics way beyond the purview of the Standard
Model.

Neutrino oscillation also implies that leptons mix, just as quarks do.
As with quark mixing, leptonic mixing can lead to *CP* violation, which
is a key requirement of theories that try to explain the
baryon-antibaryon asymmetry of the universe. While *CP* violation in the
CKM quark mixing matrix cannot explain this asymmetry, there is the
remarkable prospect that, through "leptogenesis," leptonic *CP*
violation can explain it.

To learn more about the new physics to which neutrino masses point and
about the possibility of leptogenesis, we need to answer two qualitative
questions:

*1. Is the neutrino mass hierarchy normal (i.e., quark-like) or
inverted?*

*2. Do neutrino interactions violate CP?*

Also important is a quantitative third question:

*3. What is the approximate size of the small leptonic mixing angle
~13~?*

In the past decade, dramatic insights into the nature of neutrinos have
been gained from experiments with naturally-occurring neutrinos.
However, answering these new questions will require experiments with
man-made neutrinos, from accelerators and reactors. In particular,
answering the qualitative questions *1* and *2* will almost certainly
require intense neutrino beams from accelerators. An important first
step in this direction will be made by the NOvA experiment, using a beam
from Fermilab.

In this section, we briefly review what has been learned so far about
the neutrinos, discuss the importance of the open questions *1--3*, and
consider how these questions can be answered, while recognizing that as
in the past, neutrinos may bring us unexpected surprises in the future.

***What we have learned so far***

Neutrinos come in three "flavors": *~e~*, , and . Each of these is
coupled only to the charged lepton of the same flavor: *~e~* to the *e*,
to the , and to the . If there are additional neutrino flavors, they
must be very massive or have non-Standard-Model couplings. Neutrino
oscillation is the remarkable morphing of a neutrino of one flavor into
that of another. The leptonic mixing implied by this oscillation means
that each neutrino of definite flavor, , is not a neutrino of definite
mass, *~i~* , but a superposition of such neutrinos. This superposition
is given by $\nu_{\alpha} = \sum_{}^{}{U_{\alpha i}^{}\nu_{i}}$, where
*U* is the unitary *leptonic mixing matrix*. Conversely, each neutrino
of definite mass is a superposition of the neutrinos of definite flavor,
given by $\nu_{i} = \sum_{}^{}{U_{\alpha\ i}\nu_{\alpha}}$.

![](media/image2.jpeg){width="5.125in" height="3.4611111111111112in"}

**Figure 3.1 The neutrino (Mass)^2^ spectrum.**

Since there are three neutrinos of definite flavor, there must be at
least three of definite mass: *~1~*, ~2~, and ~3~. Oscillation data tell
us that the (Mass)^2^ spectrum of these neutrinos is one of the two
spectra shown in Figure 3.1. The spectrum on the left, with the
closely-spaced pair at the bottom, resembles the charged lepton and
quark spectra, and so is referred to as a "normal" spectrum or
hierarchy, while the very unusual one on the right, with the
closely-spaced pair at the top, is referred to as an "inverted" spectrum
or hierarchy.

The atmospheric (Mass)^2^ splitting in Figure 3.1, *m*^2^~atm~ 2.4 10^3^
eV^2^, drives the observed behavior of atmospheric neutrinos, while the
thirty-times smaller solar (Mass)^2^ splitting, *m*^2^~sol~ 7.6 10^5^
eV^2^, drives the behavior of solar neutrinos. The approximate *~e~*, ,
and fractions of each neutrino are shown by different color/hatching.
However, the *~e~* fraction shown for the isolated neutrino *~3~* is
just an illustration of the possibilities. At present, we know only
that, at 2, this fraction, whose size is the mixing parameter
sin^2^~13~, is no larger than 0.032.

Neglecting phases irrelevant to neutrino oscillation, the leptonic
mixing matrix can be written in the form

![](media/image3.png){width="4.3909722222222225in"
height="1.0944444444444446in"} **(1)**

Here, *c~ij~* cos*~ij~* and *s~ij~* sin*~ij~*. The first, "Atmospheric,"
matrix factor dominates atmospheric neutrino oscillation, and from the
atmospheric neutrino data, 37º ~23~ 53º at 90% CL. The last, "Solar,"
factor dominates solar neutrino flavor change, and from the solar (and
to some extent the KamLAND reactor) data, ~12~ =
($\text{33}\text{.}9_{- 2\text{.}2}^{+ 2\text{.}4}$)º. In striking
contrast to the small quark-mixing angles, the atmospheric and solar
neutrino mixing angles, ~23~ and ~12~, are both very large. Indeed, the
value of ~23~ that fits the data best is 45º --- maximal mixing. The
middle, "Cross-Mixing," factor involves the mixing angle ~13~, which is
constrained by upper limits from reactor data to 10º, corresponding to
sin^2^2~13~ 0.12. The Cross-Mixing factor also contains the
*CP*-violating phase , which, if not 0º or 180º, leads to a
*CP*-violating difference between the probabilities for corresponding
neutrino and antineutrino oscillations. However, as the expression above
for *U* makes clear, enters leptonic mixing only in the (~13,~ )
combination sin~13~ exp(--i). Thus, the size of any -induced
*CP*-violating difference between neutrino and antineutrino oscillation
will depend on the value of ~13~. In addition, our ability to tell
whether the neutrino mass spectrum is normal or inverted will depend on
~13~. Consequently, it is important to know for how small a value of
~13~ any proposed experimental facility can still show that neutrino and
antineutrino oscillations violate *CP*, and still determine the nature
of the neutrino mass spectrum.

***The importance of the open questions***

*1. Is the neutrino mass spectrum normal or inverted?*

The most plausible explanation for the extreme lightness of neutrinos is
the "see-saw mechanism." Given this lightness, the see-saw mechanism
suggests that neutrino masses come from physics near the grand
unification energy scale, 10^16^ GeV. Needless to say, physics from
10^16^ GeV is far beyond the scope of the Standard Model. From the
standpoint of the Grand Unified Theories (GUTs) that describe physics at
this scale, we expect the neutrino spectrum (or "hierarchy") to resemble
the charged lepton and quark spectra. The reason is simply that, in
GUTs, the neutrinos, charged leptons, and quarks are all related -- they
belong to common multiplets of the theory. On the other hand, some
classes of string theories lead one to expect an inverted neutrino
spectrum. Thus, in working toward a theoretical understanding of the
origin of neutrino mass, we would certainly like to know whether the
mass spectrum is normal or inverted.

The nature of the spectrum can also help us determine whether, as is
widely expected, neutrinos are their own antiparticles. The only known
practical approach to confirming this expectation is to show that
neutrinoless double beta decay occurs. The rate for this process is
proportional to the square of an effective neutrino mass, *m*. If the
mass spectrum is inverted, then *m* must be larger than 10--15
millielectron volts (meV). Thus, if the spectrum should be found to be
inverted, and a search for neutrinoless double beta decay can establish
that the rate for this process is less than the rate that would
correspond to *m* = 10 meV, then we will have learned that, contrary to
prejudice, neutrinos are distinct from their antiparticles. Looking at
the matter in another way, if the spectrum should be found to be
inverted, and neutrinos are their own antiparticles, then an
experimental search for neutrinoless double beta decay is guaranteed to
see a signal if its reach extends to *m* = 10 meV.

The question of the character of the spectrum may involve more than the
issue of whether it is normal or inverted. The LSND experiment reported
an antineutrino oscillation whose short wavelength calls for a (Mass)^2^
splitting much larger than either of those in the three-neutrino spectra
of Fig. 3.1.1. Confirmation of the reported oscillation would require
that the neutrino spectrum be revised altogether to include one or more
additional states. The MiniBooNE experiment, aimed at testing LSND, does
not confirm the LSND oscillation in neutrino running. However, it is
possible that the LSND signal may still be confirmed in antineutrino
running. Furthermore, MiniBooNE has observed an excess of events at low
energies which could suggest new physics. The interpretation of this
excess may be addressed through future precision low energy neutrino
experiments. In this report, we have assumed a three-neutrino spectrum
in making our plans, but with a watchful eye on future developments.

*2. Do neutrino interactions violate CP?*

We would like to know why the universe contains baryons, of which we are
made, but almost no antibaryons, which, had they been present, would
have annihilated us. An explanation for this crucial feature of the
universe is suggested by the see-saw mechanism. This mechanism gives the
light neutrinos ultra-heavy (perhaps GUT-scale) neutrino "see-saw
partners." Both the light neutrinos, , and their heavy see-saw partners,
*N*, are their own antiparticles. The heavier the *N* are, the lighter
the are. The heavy neutrinos *N* would have been created in the hot Big
Bang, and would then have decayed via the modes $N \rightarrow l + H$
and $N \rightarrow \overline{l} + \overline{H}$, where $l$ is a lepton,
and *H* is the Standard-Model Higgs boson. If today's light neutrinos
violate *CP*, then quite likely so do their heavy see-saw partners,
since both *CP* violations arise from the same matrix of Yukawa coupling
constants. With *CP* violated, the *CP*-mirror-image decays
$N \rightarrow l + H$ and $N \rightarrow \overline{l} + \overline{H}$
have different rates, so that *N* decays in the early universe would
have produced a world with different numbers of leptons and antileptons.
Standard-Model processes would then have converted some of this
lepton-antilepton asymmetry into a baryon-antibaryon asymmetry,
producing the matter-antimatter asymmetric world that we see today.
Clearly, to explore the possibility that this scenario, known as
leptogenesis, was indeed the origin of the matter-antimatter asymmetry
of the universe, we must find out whether the light neutrinos violate
*CP*.

*3. What is the approximate size of ~13~?*

While we know that the mixing angle ~13~ is small, we do not know *how*
small. A compilation of the ~13~ predictions of 63 models of neutrino
masses and leptonic mixing shows very wide variation, with predictions
for sin^2^2~13~ ranging from values slightly above the present upper
bound all the way down to 10^--5^. Thus, learning the actual size of
~13~ will discriminate among the models. Quite apart from specific
models, from the mathematics of mixing it can easily be shown that it is
highly unlikely for ~13~ to be very different from the other, large
mixing angles unless there is some physical mechanism making it so.
Hence, should we find that sin^2^2~13~ is less than, say, 10^--2^, there
will be strong motivation to seek a reason, such as a new symmetry, for
this behavior. Clearly, learning the size of ~13~ will be important to
our quest for an understanding of the origin of neutrino mass.

As we have already noted, and will see in greater detail shortly, the
size of leptonic *CP* violation and our ability to determine whether the
neutrino mass spectrum is normal or inverted both depend on the value of
~13~. Thus, knowledge of this value would be of help in the planning of
experiments to probe *CP* violation and the nature of the mass spectrum.
However, this knowledge is not essential if, as here, the approach being
contemplated is appropriate for any value of sin^2^2~13~ within a broad
range covering several orders of magnitude.

***How the questions can be answered***

The determination of ~13~ will be a major focus of accelerator and
reactor experiments already under construction. Here we shall
concentrate on the determination of the neutrino mass hierarchy and the
search for *CP* violation -- objectives of a longer- term program.

The mass hierarchy and *CP* violation can both be probed via accelerator
neutrino experiments that study the oscillations
$\nu_{m} \rightarrow \nu_{e}$ and
${\overline{\nu}}_{m} \rightarrow {\overline{\nu}}_{e}$. The appearance
probability for *~e~* in a beam that is initially can be written for
sin^2^2~13~ \< 0.2

$P\left\lbrack \nu_{m} \rightarrow \nu_{e} \right\rbrack@\text{sin}^{2}2q_{\text{13}}T_{1} - \alpha\text{sin}2q_{\text{13}}T_{2} + \alpha\text{sin}2q_{\text{13}}T_{3} + \alpha^{2}T_{4}$

Here, $\alpha º{Dm}_{\text{21}}^{2}/{Dm}_{\text{31}}^{2}$is the small (
1/30) ratio between the solar and atmospheric (Mass)^2^ splittings, and

$T_{1} = \text{sin}^{2}q_{\text{23}}\frac{\text{sin}^{2}\left\lbrack (1 - x)D \right\rbrack}{(1 - x)^{2}}$$T_{2} = \text{sin}d\text{sin}2q_{\text{12}}\text{sin}2q_{\text{23}}\text{sin}D\frac{\text{sin}(xD)}{x}\frac{\text{sin}\left\lbrack (1 - x)D \right\rbrack}{(1 - x)}$$T_{3} = \text{cos}d\text{sin}2q_{\text{12}}\text{sin}2q_{\text{23}}\text{cos}D\frac{\text{sin}(xD)}{x}\frac{\text{sin}\left\lbrack (1 - x)D \right\rbrack}{(1 - x)}$

$T_{4} = \text{cos}^{2}q_{\text{23}}\text{sin}^{2}2q_{\text{12}}\frac{\text{sin}^{2}(xD)}{x^{2}}$

In these expressions ${Dm}_{\text{31}}^{2}$*L/*4*E*, with *L* the
distance between the neutrino source and the detector and $E$ the
neutrino energy, is the kinematical phase of the oscillation. The
quantity $xº2\sqrt{2}G_{F}N_{e}E/{Dm}_{\text{31}}^{2}$, with *G~F~* the
Fermi coupling constant and *N~e~* the electron number density, is a
measure of the importance of the matter effect resulting from coherent
forward scattering of electron neutrinos from ambient electrons as the
neutrinos travel through the earth from the source to the detector.

In the appearance probability $P(\nu_{m} \rightarrow \nu_{e})$, the
*T~1~* term represents the oscillation due to the atmospheric mass
scale, the *T~4~* term represents the oscillation due to the solar mass
scale, and the *T~2~* and *T~3~* terms are the *CP*-violating and
*CP*-conserving interference terms, respectively. At the first
atmospheric oscillation maximum,
$\left\lbrack (1 - x)D \right\rbrack = p/2$ , the atmospheric
*T~1\ ~*term and the solar *T~4\ ~*term are equal when sin^2^2~13~ =
0.002. The solar term leads to *~e~* appearance even if sin^2^2~13~ = 0.

The probability for the corresponding antineutrino oscillation,
$P\left( {\overline{\nu}}_{m} \rightarrow {\overline{\nu}}_{e} \right)$,
is the same as the probability $P(\nu_{m} \rightarrow \nu_{e})$ given by
the equations above, but with the signs in front of both *x* and sin
reversed: both the matter effect and *CP* violation lead to a difference
between the $\nu_{m} \rightarrow \nu_{e}$ and
${\overline{\nu}}_{m} \rightarrow {\overline{\nu}}_{e}$ oscillation
probabilities. In view of the dependence of *x* on
${Dm}_{\text{31}}^{2}$, and in particular on the sign of
${Dm}_{\text{31}}^{2}$, the matter effect can reveal whether the
neutrino mass hierarchy is normal or inverted. However, to determine the
nature of the hierarchy via the matter effect, and to establish the
presence of *CP* violation in neutrino oscillation, it obviously will be
necessary to disentangle the matter effect from *CP* violation in the
neutrino-antineutrino probability difference that is actually observed.
To this end, complementary measurements will be extremely important.
These can take advantage of the differing dependences on the matter
effect and on *CP* violation in $P(\nu_{m} \rightarrow \nu_{e})$.

Given that
$\left| {Dm}_{\text{31}}^{2} \right|@2\text{.}4´\text{10}^{- 3}\text{eV}^{2}$,
the matter-effect parameter $|x|@E/\left( \text{12}\text{GeV} \right)$.
With this in mind, we imagine, as one illustration, measurements made at
accelerator neutrino energies of 1 GeV, and at the
$\frac{L}{E}$corresponding to the first maximum of the atmospheric
oscillation term, $\text{sin}^{2}2q_{\text{13}}T_{1}$, of
$P(\nu_{m} \rightarrow \nu_{e})$. Then, from the equations for
$P(\nu_{m} \rightarrow \nu_{e})$, we see that --- at this given
$\frac{L}{E}$ --- the effect of matter on the *T~1~* term,
$1/(1 - x)^{2}@1 \pm \left( E/6\text{GeV} \right)$, grows with energy,
enhancing (suppressing) the term if the mass hierarchy is normal
(inverted). In contrast, at this same fixed $\frac{L}{E}$, the
*CP*-violating *T~2~* term in $P(\nu_{m} \rightarrow \nu_{e})$ is
approximately proportional to $D$, hence to $\frac{L}{E}$, so that it
grows with *L* and decreases with *E*. At fixed $\frac{L}{E}$, it does
not vary with energy or distance. Hence, two detectors, at two different
distances *L* and two different energies *E*, but at the same
$\frac{L}{E}$, will see the same *CP* violation but different matter
effects.

As a second illustration, if we go from the first atmospheric
oscillation maximum to the second one by reducing the energy a factor of
three with *L* fixed, the effect of matter on the
$\text{sin}^{2}2q_{\text{13}}T_{1}$ term is reduced by a factor of
three, while the *CP*-violating term propor­tional to $\text{sin}d$ is
tripled. In a broadband neutrino beam, the required reduction of *E* by
a factor of three can be achieved by simply probing a lower-energy part
of the neutrino spectrum. In a narrowband off-axis beam, the reduction
can be achieved by going further off axis at a given *L*.

The violation of *CP* can either enhance $\nu_{m} \rightarrow \nu_{e}$
and suppress ${\overline{\nu}}_{m} \rightarrow {\overline{\nu}}_{e}$, or
*vice versa*, depending on the value of the phase . Similarly, the
matter effect can either enhance\
$\nu_{m} \rightarrow \nu_{e}$ and suppress
${\overline{\nu}}_{m} \rightarrow {\overline{\nu}}_{e}$, or *vice
versa*, depending on the sign of ${Dm}_{\text{31}}^{2}$. For a given
$q_{\text{13}}$, the neutrino-antineutrino asymmetry obviously is
easiest to observe when *CP* violation and the matter effect happen to
add together in the same direction.

In Section 3.1.2 (A) we outline an experimental program to address these
important measurements.

**3.1.2 Neutrino Scattering Physics**

Measurements of neutrino scattering have played an important role in
both the development of the Standard Model as know it, and in providing
evidence that the Standard Model does not suffice. The first
measurements of the weak neutral current were made with neutrino
scattering measurements on both electrons and nuclei, and neutrinos have
probed the quark structure of the nucleon and provided measurements of
the strong coupling constant across a range of momentum transfers. More
recently, the discovery that neutrinos change flavor and therefore have
mass has forced the field to rethink completely the notion of mass and
its origin.

The previous section discusses how oscillation measurements will need to
be made at hundreds of kilometers from the neutrino production location.
This section will discuss the questions that can be answered with
neutrino scattering measurements at short distances. A clear need for
scattering measurements comes from the fact that neutrino oscillation
experiments rely on precise knowledge of neutrino scattering cross
sections. The 2004 *APS Multidivisional Neutrino Study Report* which set
a roadmap for neutrino physics predicated its recommendations on a set
of assumptions about current and future programs including:
"determination of the neutrino reaction and production cross sections
required for a precise understanding of neutrino-oscillation physics and
the neutrino astronomy of astrophysical and cosmological sources. Our
broad and exacting program of neutrino physics is built upon precise
knowledge of how neutrinos interact with matter."

*Neutrino Scattering Measurements from Low to High Energy*

At neutrino energies below about 1GeV, the quasi-elastic process
dominates the cross section. With a current uncertainty of 15-20%, this
process is one of the best measured cross sections in neutrino physics.
The upcoming generation of cross section experiments will make
significant inroads in understanding the form factor for this process as
a function of momentum transfer, and make first measurements of possible
nuclear effects of this cross section. However, a whole new suite of
measurements would be possible with additional proton power in the
beamline. This process will dominate any signal of muon to electron
neutrino oscillations, and recent studies have shown that for the long
term oscillation experiments, not only the cross section itself must be
known but eventually, uncertainties on the ratio between electron and
muon neutrino cross sections will become important, and the field must
measure that ratio accurately.

At higher energies, deep inelastic scattering processes dominate,
offering the opportunity to probe the quark distributions in the nuclei
themselves. Using the high statistics samples that would be accessible
in the Project X era as well as with special attention to minimizing
neutrino beam uncertainties, it should be possible to measure separately
the four different structure functions *F*~2~, *F*~2~^bar^, *F*~3~ and
*F*~3~ ^bar^.

At energies above 10's of GeV, on shell charm can be produced, which can
result in new precise measurements of the strange sea. Although we know
that the net strangeness in the proton and neutron must be equal to 0,
neutrino scattering measurements provide our best knowledge of whether
or not the strange quark distribution equals that of the strange
anti-quark distribution as a function of momentum transfer. These
measurements will require high statistics of both neutrino and
antineutrino data, and at the current time only a very small number of
nuclei have been probed.

At neutrino energies above about 30 GeV, the neutrino electron
scattering cross section becomes large enough to provide a suite of new
measurements. One exciting possibility with the advent of a high energy
high statistics neutrino and antineutrino run would be that of a new
measurement of sin^2^~W~, the weak mixing angle, using neutrino-electron
scattering. There is currently a 3 sigma discrepancy between the most
precise measurement in neutrino nucleon scattering and the value coming
from precision electroweak observables at the *Z* mass.

With the advent of neutrinos obtaining a mass comes the possibility that
neutrinos have magnetic moments. If the neutrino mass were 1 eV, the
resulting magnetic moment would be about 3e^-19^ *~b~*, where *~b~* =
*e*/2*m~e~*~.~ This value is too small to be detected, but that means
that any measurement of a non-zero magnetic moment would be a striking
signal of new physics. By measuring the elastic scattering rate as a
function of recoil energy, in the Project X era one can probe well past
current experimental limits. In the next section we outline the Fermilab
experiments, current and future, that can contribute to this important
area of neutrino physics.

**3.1.3 Proton Decay and Related Deep Underground Physics**

One of the central consequences of grand unification is the prediction
of proton decay. Its observation would lend credence to the general
picture of coupling constant unification and the merging of the standard
gauge interactions into a common simple gauge group, such as SU(3) x
SU(2) x U(1) SU(5), with a telescoping pathway to SO(10) E6 \... E8 x
E8. This phenomenon is central to SUSY, and Superstring Theory, and we
may already be seeing hints of the effects of unification in the tiny
nonzero neutrino masses as anticipated by the neutrino seesaw mechanism.

Very large detectors future are being contemplated for neutrino
oscillation physics, with accelerator neutrinos and atmospheric
neutrinos, supernova neutrino detection, dark matter searches and a
renaissance of searches for nucleon decay. One possibility is a water
Cherenkov detector, similar to Super-Kamiokande, with mass in the range
of 1000 kton. Another is a liquid Argon detector, similar to the ICARUS
liquid Argon TPC for the Gran Sasso Laboratory. Both have various
advantages, the water Cherenkov detector mass providing great fiducial
volme sensitivity, and the liquid Argon detector providing resolution
through tracking similar to a bubble chamber. Both are being
contemplated in a deep underground facility, such as DUSEL, to operate
in the very low cosmic ray background at depths as great as 6000 feet.

Very large detectors would be extremely sensitive to nucleon decay. Such
detectors would extend the limits on proton decay into modes such as *p
e^+^* to sensitivities of 10^35^ yr or beyond and will have
complimentary sensitivity to the scalar mediated mode p *K^+^* at a
sensitivity of a few 10^34^ yr. Although the kaon is too slow to produce
Cherenkov radiation in a water detector, the 2 decay modes can be
reconstructed in low background environment. This level is suggested by
gauge boson mediated proton decay in super-symmetric GUTs.

The complementarity to the neutrino long baseline program and the study
of leptonic CP-violation suggests that these programs should operate in
tandem in a common detector. In addition, there is sensitivity to the
neutrinos produced from galactic supernovae. A supernova event is
expected on a 40 year time scale within the galaxy and could produce of
order 10^5^ detectable neutrinos. Large, isotropically sensitive,
general-purpose detectors can also probe many other physics targets.
This includes exploration of subjects ranging from the temporal
variation of the solar neutrino flux, searches for neutrinos from
individual or aggregate sum over all supernovae and other cataclysmic
events, to cosmic ray composition (where the depth is advantageous),
dark matter searches annihilation neutrinos, searches for cosmic exotic
particles (e.g., quark nuggets, monopoles, monopolonium, etc.), and
point source neutrino astronomy. In all instances, the capability
potentially exceeds Super-Kamiokande by virtue of lower energy
thresholds, better energy loss rate resolution, momentum, angle, sign
and event topology resolution.

#### 3.2 Experimental Program

The compelling questions in neutrino physics today drive a worldwide
program of forefront neutrino experiments. The operating, approved, and
proposed experiments constitute a program such that Fermilab is, and
will continue to be, a leader in this exciting field. The experiments
which comprise this program are described below and the strategy to
realize it is described in the "The Neutrino Strategy" section.

**3.2.1 Neutrino Oscillation Measurements**

######## 

Fermilab is home to two operating neutrino beamlines, the Booster
Neutrino Beam and the NuMI Neutrino Beam. An exciting program of short
and long baseline neutrino oscillation experiments is presently
underway. With experiments using these beams, together with upgrades
such as Project X, we envision a vibrant future in neutrino oscillation
physics at Fermilab.

The Booster Neutrino Beamline (BNB) produces a narrow band, 800 MeV peak
energy, primarily muon neutrino beam, from 8 GeV protons from the
Fermilab Booster. The MiniBooNE short baseline neutrino oscillation
experiment, running since 2002 on the BNB, has ruled out a two neutrino
interpretation of the LSND neutrino oscillation signal in neutrino mode.
However, a low energy excess observed by MiniBooNE is still not
understood. Results in anti-neutrino mode may provide an important clue
both to oscillations across a broad range of energies, and to the low
energy excess. A proposed new liquid Argon TPC experiment, MicroBooNE,
will definitively address this low energy excess, measure low energy
neutrino cross sections on Argon, and perform important R&D necessary
for larger liquid Argon detectors.

Fermilab is presently operating the world's highest intensity neutrino
beam for long baseline neutrino oscillation physics, the NuMI beam. In
the near term, the MINOS experiment is NuMI's flagship long baseline
program, providing definitive evidence for the oscillatory behavior of
neutrinos as well as the best measurement of *m*^2^~23~. Although not
optimized for $\nu_{e}$appearance, MINOS has sensitivity to ~13~ that
reaches beyond the benchmark limit by CHOOZ. As such, it will provide
valuable input, positive or negative~~,~~ in the search for ~13~.

After 2011, the NuMI beamline will have the main objective of delivering
neutrinos to the NOvA detector. In recent studies and reviews NOvA has
been classified as one of the Phase I experiments which are searching
for the small mixing angle ~13~. The other experiments are the reactor
neutrino experiments Double CHOOZ and Daya Bay, as well as the T2K
experiment which will use the new neutrino beam from JPARC and the
Super-Kamiokande detector. While the Double CHOOZ experiment will
achieve a maximum sensitivity to sin^2^2~13~ \~ 0.03 (90% CL), the Daya
Bay and T2K experiments hope to reach a sensitivity of sin^2^2~13~ \~
0.01 (90% CL) after several years of running.

NOvA was recommended for CD-2 approval in October 2007 based on a
schedule that has 15 kilotons of detector mass complete by January of
2013. The project scope includes an accelerator upgrade to take the NuMI
intensity to 700 kW. NOvA plans to run for six years, three using
neutrinos and three using anti-neutrinos. NOvA will extend the search
for $\nu_{m} \rightarrow \nu_{e}$ oscillations down to
$\text{sin}^{2}2q_{\text{13}} = 0\text{.}\text{02}$ (3) and obtain
information about the sign of ${Dm}_{\text{23}}^{2}$ and
$d_{\text{CP}}$. For favorable values of the phase $d_{\text{CP}}$, NOvA
can determine the mass hierarchy for values of
$\text{sin}^{2}2q_{\text{13}} > 0\text{.}\text{06}$ (at the 95% C.L.).
In addition, NOvA will improve on the measurements of
$\nu_{m} \rightarrow \nu_{t}$, measuring
$\left| {Dm}_{\text{23}}^{2} \right|$ to roughly 3% and
$\text{sin}^{2}2q_{\text{23}}$ to roughly 2-3 %, providing a sensitive
test of - symmetry in neutrinos.

######## **Project X Neutrino Physics**

A flagship neutrino program for Project X could be a new long baseline
beam directed toward a very large detector. The physics motivations and
experimental strategies have been previously outlined in detail in the
report by NuSAG to NSAC/HEPAP and the accompanying study by the joint
BNL/FNAL working group \[arXiv:0705.4396 hep-ph\].

Here we recapitulate the essential points that relate to the
experimental strategy for long baseline neutrino oscillation physics. In
all cases, an intense neutrino beam based on 2.3 MW proton beam power
driven by Project X is assumed. That leaves the following fundamental
experimental choices to be determined: the choice of detector
technologies, the baseline of the neutrino beam, and the neutrino beam
configuration (wide band vs. off-axis, narrow band). Connected to these
choices are scientific and practical considerations. The scientific
considerations are mainly related to how the choice of detector
technologies will influence a broader program that includes proton
decay, astrophysics, and other non-accelerator opportunities. Another
important scientific consideration will be the evolving knowledge of
~13~ as the experimental program advances. The practical considerations
are driven by cost, schedule, and risk. Phase II accelerator based
programs have also been proposed for neutrino beams from JPARC (T2KK)
and CNGS (ModuLAr). In all programs major improvements in proton
intensity and detector mass are required.

######## **Project X Neutrino Detectors**

For the massive detectors required for *CP* violation searches the
choice of detector technology has been narrowed to three possible
configurations: a 100 kiloton liquid argon TPC (LAr100), a 300 kiloton
water Cherenkov detector (WC300), or some combination of the two. These
detector configurations are estimated to be roughly comparable in
sensitivity, where the larger mass of the WC300 compensates for lower
efficiency and higher background compared to the assumptions made for
LAr100. An advantage of the water Cherenkov option is that it is a known
and tested technology on large scales, though several R&D issues remain.

The liquid argon option shows great promise for reach in accelerator and
non-accelerator physics, but the technology has not yet been
demonstrated for a large mass (\>100 ton) in a physics experiment. There
is necessary R&D to accomplish in order to realize detectors on this
mass scale. For both technologies, if sited below ground. This includes
R&D on construction of large caverns.

######## Water Cherenkov Detectors

The long and successful history of the operation of the Super-Kamiokande
detector makes the water Cherenkov detector technology an excellent
candidate for scaling to even larger sizes. The critical technical
issues that need to be studied for construction of such a detector are
discussed below.

First, since the detector needs to be sited underground, there are two
concepts for constructing a water Cherenkov detector in the 300-500 kton
scale. These can be classified as single horizontal chamber (the
concepts for the proposed Hyper-Kamiokande and the UNO detectors), and
multiple vertical cylinders (the concepts for MEMPHIS in Frejus or the
Multi-Modular, 3M, detector in Homestake). In either case, the
feasibility of the chamber is determined by the span -- the width of the
horizontal chamber or the diameter of the vertical cylinder. The cavern
stability and feasibility must be examined at the specific proposed
location, depth, and rock type. Detailed geo-technical measurements and
modeling should be carried out so that questions about cavern
configurations can be resolved.

The second issue in regard to water detectors is the choice of
phototube. Recent developments have led to the option of selecting
smaller diameter (10 -- 12 inch) but more efficient tubes than used in
Super-Kamiokande (20 inch). The smaller PMTs are also mechanically
stronger than the larger PMTs and, in case of implosion, have only 1/8
the stored energy of the larger PMTs. The smaller tubes are also shorter
allowing for a larger fraction of the water volume to be fiducial.

Because the water detectors do not need to be prototyped on a small
scale they do not feature prominently in the near term plans for the
Fermilab accelerator complex. Nevertheless, if they are to be part of
the long term neutrino program, attention to the specific R&D needs of
this technology must be considered in planning the future program.

*Liquid Argon TPC Detectors*

Liquid argon detectors show great promise with excellent efficiencies
and background rejection for a variety of physics goals. An extensive
R&D program culminating in the success of the ICARUS T600 program has
illustrated the capabilities of the detector. However, further R&D is
necessary to consider massive detectors, on the scale of tens of
kilotons.

For several years there have been efforts both in the U.S. and Europe to
carry out an R&D plan for large detectors and several different design
ideas for massive detectors have emerged. These include a modularized
detector, a single detector but with modularized drift regions, and a
single open volume, very long drift detector combining charge and light
collection. In addition to conceptual designs for massive detectors,
small scale test stands have been constructed to address the technical
issues of liquid argon purity and electronics.

Regardless of the configuration, the major challenges for running a
liquid argon detector include:

-   Achieving and maintaining argon purity adequate to support electron
    drift times on the order of 10 msec in industrially built vessels

-   Achieving a high signal to noise ratio with wires of lengths up to
    10 meters

-   Optimizing the detector size, configuration, and internal detectors
    for constructability and cost scaling

-   Developing fully automated simulation, reconstruction and particle
    identification techniques, and data reduction algorithms for liquid
    argon detectors

In recent months, progress on how to bridge the gap between test stands
and the ultimate massive detector has emerged. A staged evolution of the
liquid argon detector technology for use in neutrino experiments, as
suggested by the NuSAG committee, has come into focus.

Detectors ranging in mass from the ton to kiloton scale can be deployed
in existing Fermilab neutrino beams. At each stage, key issues in
detector development will be addressed at the relevant scale, as well as
producing physics results. The shift from R&D to physics will evolve
with the size of the detector. The R&D goal of the program is to develop
a clear concept of how to construct a detector with total mass in the
one hundred kiloton range. Along the way, exciting and timely physics
questions will be addressed.

The R&D strategy of developing a series of liquid argon TPCs for
neutrino experiments is already underway, with the 0.3 ton ArgoNeuT
detector being installed in the NuMI-MINOS near detector hall. This
small detector will be able to record more than 150 neutrino
interactions per day, providing a valuable data set for developing
reconstruction and particle ID algorithms.

The next detector in the series would be a 170 ton total volume,
installed in the Booster Neutrino beam as has been proposed for the
MicroBooNE experiment. This detector will insure that progress in the
program continues smoothly by developing components needed for a larger
detector. At the same time the MicroBooNE experiment addresses the
MiniBooNE low energy excess and measures neutrino cross sections on
argon.

For the next step, installation of liquid argon detector modules in the
Soudan Laboratory (LAr5 at Soudan) on the NuMI beam (\~5000 ton) is
being explored. This effort would address all of the issues related to
underground operation. At the same time, a detector of this mass has
sensitivity to measuring sin^2^2~13~ and the mass hierarchy with reach
comparable to that of the NOvA experiment. Combination of the results
from both detectors would maximize the investment made in the NuMI beam.
A simple analysis to determine the physics reach of an evolving NuMI
program with the NOvA and liquid argon detectors has been done. The
results show this detector combination to be very advantageous. The NOvA
experiment will have sensitivity down to sin^2^2~13~ \~ 0.02. The
addition of the LAr5 detector will double that sensitivity. Operation of
these detectors with Project X intensity will extend the reach to
observing sin^2^2~13~ to well below 0.01.The actual limit achievable
will depend on the knowledge of the intrinsic and neutral current
backgrounds. Using both detectors and Project X, ultimate sensitivity to
the mass hierarchy for a large region of phase space can extend down to
well below sin^2^2~13~ \~0.04. A full simulation of the liquid argon
detector including measured efficiencies and background measurements
from the ArgoNeuT detector will be done in the near future. Preliminary
considerations also indicate that the underground liquid argon detector
may also have competitive sensitivity to the proton decay in the *K*
channel.

The above outlined program makes progress in both the R&D and physics
phases continuously throughout this and the next decade, leading to a
flagship program with excellent reach in the exploration of neutrino
mass and mixing. The sensitivities for the above scenarios are shown in
Figure 3.2.

***Building on Project X: A Neutrino Factory***

The next-to-next generation of neutrino physics, clearly an uncertain
extrapolation from our current state of knowledge, is typically
envisioned to be based on a radically different neutrino source, either
on muon decay in a storage ring (neutrino factory), or radioactive
nuclear decay in a storage ring (beta beam). It is worth noting that
Project X ties into the development plans for a neutrino factory. As one
illustrative example, consider a 4 GeV Neutrino Factory. This facility
could be developed by (i) upgrading the Project X beam power at 8 GeV to
2 MW, (ii) adding an intense muon source that could also serve as a Muon
Collider front end test facility, and (iii) adding acceleration to 4 GeV
and a racetrack shaped muon storage ring. The costs associated with the
Muon Collider test facility is believed to be of the same scale as the
Project X cost, as is the cost of the additional upgrade to a Neutrino
Factory. Hence, Project X offers a potentially attractive path to a
facility which, in principle, could determine the neutrino mass
hierarchy even if ~13~ was exactly zero, or if ~13~ were large, could
determine the oscillation parameters with unprecedented precision. To
keep this option open, it is important that the Project X beam power at
8 GeV be upgradeable to 2 MW or more.

***DUSEL***

The proposed Deep Underground Science and Engineering Laboratory (DUSEL)
at the Homestake Mine in Lead, South Dakota offers an option for the
neutrino community to plan for the next generation of long baseline
neutrino oscillation detectors to be located deep underground. The
DUSEL-Homestake site is located at a distance of 1300 km from Fermilab.
Over this baseline, a beam of neutrinos in the energy range of a few GeV
is well suited to extend the sensitivity to measurement of neutrino mass
and mixing parameters, including the search for *CP* violation. Proton
intensities envisioned for the Project X era will be essential for such
a program.

DUSEL also offers the opportunity to construct large caverns at a depth
suitable for placement of multiple detectors, each on the scale of
10-100 kton. A program of constructing and deploying these detectors
such that the ultimate mass will approach one megaton can give an
ultimate sensitivity to nucleon decay of order 10^35^ years in the *p*
*e^+^* mode and for *p* *K^+^* at a sensitivity of a few 10^34^ years. A
combination of detectors, water Cherenkov and liquid argon may be an
appropriate way to maximize discovery potential.

In addition, there is sensitivity to the neutrinos produced from
galactic supernovae. A supernova event is expected on a 40 year time
scale within the galaxy and could produce of order 10^5^ detectable
neutrinos. Large, isotropically sensitive, general-purpose detectors can
also probe many other physics targets. This includes exploration of
subjects ranging from the temporal variation of the solar neutrino flux,
searches for neutrinos from individual or aggregate sum over all
supernovae and other cataclysmic events, to cosmic ray composition
(where the depth is advantageous), dark matter searches annihilation
neutrinos, searches for cosmic exotic particles (e.g., quark nuggets,
monopoles, monopolonium, etc.), and point source neutrino astronomy. In
all instances, the capability potentially exceeds Super-Kamiokande by
virtue of lower energy thresholds, better energy loss rate resolution,
momentum, angle, sign and event topology resolution.

Such a program would be a significant achievement for the scientific
community. Exploring the synergy that can be achieved by constructing a
multi-purpose detector which can lead to the accomplishment of multiple
science goals is an important element in planning the DUSEL facility.

![](media/image4.png){width="5.989583333333333in"
height="3.1694444444444443in"}

**Figure 3.2 Sensitivities as a function of the *CP* violating phase for
discovering sin^2^2~13~, neutrino mass hierarchy and *CP* violation for
a staged evolution of the neutrino program, starting with the NOvA
experiment (Phase I) and culminating with a neutrino beam to very
massive detectors (Phase II). As examples we show the potential of two
massive detectors in the NuMI off-axis location, and the reach of a
single massive detector at a 1300 km baseline with a wide band neutrino
beam. (Note : The reactor experiments, Double CHOOZ and Daya Bay aim to
achieve sensitivity to sin^2^2~13~ to the 90% CL of 0.03 and 0.01
respectively, but have no sensitivity to the mass ordering or *CP*
violation.)**

**3.2.2 Neutrino Scattering Measurements**

The intense neutrino beams currently running at Fermilab (BNB, NuMI) and
possible additional near-future scenarios (e.g., the Tevatron neutrino
beam) offer the possibility for exciting on-site neutrino scattering
experiments in these beams. These experiments could provide insight into
electroweak and strong-interaction physics via the use of electrons,
quarks, nucleons, and nuclear targets.

######## **The BNB and NuMI Neutrino Scattering Programs**

The MiniBooNE experiment, located 500 meters from the BNB target, has
produced an important physics result on neutrino oscillations. In
addition, neutrino charged- and neutral-current scattering has been
investigated in the 1 GeV energy with world-record sized data samples.
Results from these measurements are providing better understanding of
neutrino interactions on carbon which will greatly help with extracting
precise neutrino oscillation parameters from future experiments such as
T2K and NOvA. More data on antineutrino interactions is currently being
collected by MiniBooNE in order to understand the antineutrino sector.

The SciBooNE experiment is located at a near location on the BNB 100
meters from the BNB neutrino beam target. This neutrino scattering
experiment uses a fine-grained tracking detector and was commissioned in
2007. It will collect 1 x 10^20^ protons on target in both neutrino and
antineutrino modes. The data collected by SciBooNE will enable more
precise measurements of multiple neutrino and antineutrino scattering
processes, furthering the understanding of the underlying physics at 1
GeV. Upgrades and further running with the SciBooNE detector are
currently being considered in order to extend the physics reach of the
detector and BNB. One possibility is a precise measurement of neutrino
neutral current elastic scattering. This process is uniquely sensitive
to the spin of the nucleon carried by an isoscalar component in the
nucleon (such as strange quarks) and can provide an answer to part of
the nucleon spin puzzle.

The MINERvA experiment will be located on axis on the NuMI beamline, and
will run concurrently with both MINOS with a low energy beam (peaked at
about 3.5 GeV) and also with NOvA with a medium energy beam (peaked at
about 7 GeV). The goal of the MINERvA experiment is to study neutrino
interactions in this broad energy range in unprecedented detail by
constructing a fine-grained hermetic detector with several different
nuclear targets.

The aforementioned MicroBooNE experiment, with excellent tracking
capabilities and low energy sensitivity will also provide rich neutrino
scattering data from both the BNB and NuMI neutrino spectra.

Although the intense neutrino beam from Project X is driven by the
requirements for long baseline neutrino oscillations, there is also a
relatively new proposal for an on-site experiment that would build on
the cross section measurements made by SciBooNE and MINERvA. The
proposal, HiResM, is to build a high-resolution neutrino detector within
a dipole magnetic field (B \~ 0.4T) and a fiducial mass of 7.4 tons. The
experiment could run with long-baseline neutrino oscillation experiments
in the Medium-Energy configuration of the NuMI-beam. In addition to
contributing to the understanding of the systematic limits of the
neutrino oscillation experiments, such an experiment can address a broad
range of measurements ranging from measurement of the weak mixing angle
to searches for weakly interacting massive particles with electronic,
muonic and hadronic decay modes with unprecedented sensitivity.

######## **Tevatron Neutrino Program**

Using the Tevatron, Fermilab can create a unique ultra-high-energy
neutrino facility. The facility would target 800 GeV protons on a target
and a dump. A very pure sign-selected high energy beam can be created
with 20 times the intensity of the previous NuTeV experiment. At the
same time, using the beam dump, a flux enriched in s which are above CC
threshold can be produced. This is the only practical source of s above
threshold, since long-baseline experiments, which produce neutrinos
through oscillations, must run at low energies. The flux in one year of
running will be 150 times that of the previous DoNuT Experiment. The
intensity goals, which are challenging, were developed in consultation
with the Tevatron Department.

This facility opens new opportunities for physics studies which
complement both LHC/ILC and the presently planned neutrino program, and
which cannot otherwise be done. Three possible experiments to use this
facility are:

-   A high-precision experiment, with two orders of magnitude more
    events than DoNuT. The sector is essentially unexplored physics
    territory. Many Beyond-Standard Model theories favor expression in
    the third family, making this an exciting sector to explore.

-   A dedicated search for 10 keV -- 5 GeV neutral heavy leptons (also
    called "neutrissimos") produced by mixing with light neutrinos in
    meson decays. This facility, with its 800 GeV protons-on-target,
    allow searches in the GeV range produced via B-decays which are not
    otherwise possible.

-   A high statistics experiment designed to obtain 40 times the world's
    sample of neutrino-electron scatters. This allows for studies of
    neutrino universality and unitarity not possible at collider
    experiments. The design for this experiment, NuSOnG, which could
    anchor the Tevatron neutrino program, is well underway and was
    endorsed by the Fermilab Steering Group for further consideration.

**3.3 Neutrino Strategy**

The neutrino strategy consists of developing a series of world-leading
experiments in a phased approach with ever increasing beam intensities
and ever increasing detector capabilities. A key element of the strategy
is the continuous operation of a neutrino beam facility at Fermilab such
that there would be no significant period without running experiments
and the acquisition of data with world competitive detectors.

[Phase I: Today to 2012]{.underline}

-   *Operation of MINOS, MiniBooNE, and SciBooNE;*

-   *Construction and operation of MINERVA*

-   *Construction of the NOvA detector and the Main Injector upgrades to
    700 kW (part of the NOvA project);*

-   *Liquid Argon Program: Operation of ArgoNeuT; Construction of
    MicroBooNE; Design of LAr5 at Soudan; R&D at test stands*

-   *Accelerator R&D (Project X)*

-   *Conceptual exploration of other neutrino experiments (NuSOnG,
    HiResNu)*

-   *Conceptual design of a second generation long (\>1000 km) baseline
    neutrino program including a beamline, caverns and detectors (LAr
    and Water Cherenkov detectors) -- coordinate efforts with the DUSEL
    planning process*

The initial phase of the program takes us to the early part of next
decade. It is based on the exploitation of the present neutrino beams at
Fermilab, the most powerful in the world now and for several years to
come. The NuMI beam has been recently upgraded with slip-stacking in the
Main Injector to deliver over 300 kW of power, about 40% more than the
most recent runs. During this period, MINOS will obtain the most
accurate values of oscillation parameters in the "atmospheric" neutrino
oscillation region. Also very importantly, MINOS has sensitivity to
$q_{\text{13}}$ that reaches beyond the benchmark limit by CHOOZ. As
such, it will provide early input into the search for ~13~.

A low energy neutrino beam operating from the Booster will feed
MiniBooNE and SciBooNE through the end of their respective runs. The
cross sections determined by SciBooNE will be important for the T2K
experiment and other long baseline experiments. There remain a lot of
physics to be understood in low energy neutrino interactions, including
the excess of low energy neutrino events in MiniBooNE, and low energy
neutrino cross sections. The MicroBooNE experiment has proposed to study
low energy neutrino interactions, in particular, the intriguing low
energy excess, while advancing liquid argon TPC R&D, as described below.

While producing physics with existing detectors, we will be building the
NOvA detector, including an upgrade of the Main Injector to deliver a
total power of 700 kW maintaining Fermilab's leadership in neutrino beam
intensity. Both the detector and the upgrades of the Main Injector have
been built into the funding profiles provided by the DOE.

During this phase we are building a small detector, MINERvA, to study
neutrino cross sections for different materials as well as nuclear
scattering models. The construction of this detector has already started
and would commence operations towards the end of this period.

The ultimate program in neutrino physics depends on the product of beam
intensity, detector mass and detector efficiency. Great gains can be
made in all of these. The beam intensity can be increased several fold
by upgrades of the Fermilab complex. In particular, during this phase we
would complete the design of Project X to greatly increase the neutrino
flux, adding flexibility and reliability to the future program.

The second important R&D effort will be the staged program of scalable
liquid argon TPC detectors for neutrino physics as described previously.
The R&D program scales from small to large detectors, at each step
addressing the most pressing R&D questions at the relevant scale, while
combining ever more physics with the R&D program.

After the termination of the Tevatron collider run, there will be a
possibility to have high energy neutrino beams for other experiments. A
proposal to study electro-weak physics with high energy neutrinos could
be carried out with the Tevatron in fixed target mode. This would be a
unique program with significant discovery potential. During this period
we will study what other possibilities in neutrino physics are opened up
with the re-use of parts of the Fermilab accelerator complex.

At present we do not know the time scale for the development of the
DUSEL laboratory. However, the excavation of a smaller cavern could
start early next decade, thus conceptual design for a beam aimed at
DUSEL and a detector could begin in this period in coordination with the
DUSEL planning process.

[Phase II: 2012 -- 2016]{.underline}

-   *Exploitation of NOvA at 700 kW; continued running of MINERvA with
    different materials and energies; dismantling of MINOS*

-   *Construction of Project X*

-   *Liquid Argon program: Continued running of MicroBooNE; construction
    of LAr5 at Soudan*

-   *Design of a second generation very large, longer (\> 1000 km)
    baseline neutrino experiment; coordinate efforts with the DUSEL
    planning process*

    -   *Beamline, caverns and detectors (LAr and Water Cherenkov)*

-   *Possible construction of DUSEL smaller caverns and smaller
    detectors*

-   *Scaled-up effort in neutrino factory R&D and design*

Project X could be constructed during this period.

This phase begins with the running of NOvA as soon as about 5 kton of
the detector is completed in the Minnesota site. The construction would
continue through 2013 when the entire 15 kton would be in place. The
beam power of 700 kW together with the long baseline and a totally
active detector insures a world leading program. The NOvA detector with
the NuMI beam offers quite different sensitivities to the neutrino
oscillation parameters than the T2K experiment. The energy of neutrinos
is higher and the baseline is longer, both giving greatly enhanced
sensitivity to matter effects. During this phase, NOvA is the only
experiment which provides information on the mass hierarchy and *CP*
violation. Results from the NOvA experiment, along with complimentary
results from T2K, will increase our understanding of the neutrino
parameters.

The MINERvA detector will begin operation before the start of this
period and will continue to operate through the first part of this
phase.

The NuMI neutrino physics program could be augmented with the totally
active LAr5 at Soudan detector, operating on axis in the Soudan mine, in
conjunction with NOvA. LAr5 at Soudan would serve not only to greatly
enhance the physics that can be achieved prior to a Phase II program,
but would also be a prototype for a large liquid Argon detector at the
100 kton mass scale. We consider it important to build such a detector
whether Project X is already under construction or not.

There is considerable interest in Italy to develop 5 kton modules for a
massive 20 to 100 kton detector for long base-line experiment from CERN
to Grand Sasso. We are currently beginning discussions on how these
efforts could be joined with the U.S.'s liquid argon effort.

At present we do not know the time scale for the development of the
DUSEL laboratory. We expect that only around the middle of the next
decade it will be possible to start the excavation of a large cavern at
depth for a detector that would be used for a varied program from
neutrino oscillations using a Fermilab beam, to proton decay and
supernova neutrinos. We will need to have solid concepts for a beam
aimed at a DUSEL detector, which could be a liquid Argon detector, a
water Cherenkov detector, or some combination of the two. There is also
a possibility of constructing smaller caverns and smaller detectors
during this period.

Depending on the physics results over the next few years it may well be
time to seriously develop a neutrino factory. The R&D efforts on a
neutrino factory would be enhanced during this period. Project X will be
designed with the flexibility to serve as the front end of a neutrino
factory and/or a muon collider.

[Phase III: 2016 -- 2020]{.underline}

In this phase we work toward the goal of precision measurements of the
mass and mixing parameters, in particular *CP* violation. This program
requires massive detectors, high intensity proton source, and a new
world class neutrino beam.

-   *Exploitation of Project X with 2.3 MW and combined running of NOvA
    and LAr5 at Soudan*

-   *Design of ultra-massive detectors for the next generation of
    neutrino and proton decay experiments*

-   *Possible construction of DUSEL caverns and construction of neutrino
    and proton decay detectors*

-   *Possible construction start of a new beamline toward DUSEL*

-   *Completion of design for a neutrino factory.*

The initial running of Project X would greatly increase the power to
NOvA, which will have been running for several years at this time. If
prior to this period we have also built a 5 kton LAr detector in the
Soudan site, then the program has a remarkable reach on the neutrino
oscillation parameter space prior to the investment in a new beamline
and massive detectors. Even with only the 700 kW power prior to Project
X it would be the program with the greatest reach for
sin^2^2$q_{\text{13}}$ and the mass hierarchy.

Unless we are very fortunate and the neutrino parameters are measured by
this time, it will be important to develop the study of the lepton
sector further with the construction a more powerful detector and new
beamline to a detector at a long baseline. Our program is designed to
develop such a detector and beamline during this period. If the DUSEL
project is a part of the national program, the new caverns and detectors
located there will enable the commencent of a broad physics program that
will last for decades.

If more power and flexibility is required in the world's neutrino
program, and greater reach into the neutrino parameters is needed, then
a neutrino factory or beta beams could provide a solution in the long
term. Coupled with a neutrino factory it will be important to develop
detectors that can determine the sign of the final leptons, a great
challenge for large detectors. The design of the neutrino factory would
be accompanied by the design of a new class of detectors. In any case,
Project X would be designed with the flexibility to serve as the front
end of a neutrino factory.

**3.4 Neutrino Summary**

The current Fermilab neutrino program is the best in the world. The
MINOS experiment in the NuMI beam will make the most precise measurement
of *m*^2^~23~ and provide an early glimpse into the search for ~13~.
Using the Booster neutrino beam, MiniBooNE is probing the possibility
that neutrinos quite different from those in the standard paradigm
exist, and MiniBooNE and SciBooNE experiments are measuring neutrino
cross sections to high precision as well. The MINERvA experiment, which
is currently under construction, will use the existing NuMI beam to
measure neutrino cross sections to unprecedented precision.

The NOvA experiment, which will be located in Ash River, Minnesota in
the NuMI off-axis beam at an 810 km baseline, will be a world class
neutrino experiment with the only near-term sensitivity in the world to
the mass hierarch. NOvA will also have excellent sensitivity to ~13~.
The long term vision of building an experiment sensitive to measuring
neutrino *CP* violation will evolve by building on what is learned from
NOvA and other Phase I experiments.

A liquid Argon detector placed in the NuMI beam will complement and add
to the NOvA program, while at the same time advancing this potentially
excellent detector technology. The combination of NOvA, a liquid Argon
detector and Project X will be a powerful program maximizing the return
on the investment that has already been made in the NuMI project,
producing physics results from now through the next decade.

Project X could produce the world's most powerful neutrino beam.
Developing beam designs and technologies in which those neutrinos are
directed towards massive detectors at a very long baseline is an
important component of Fermilab's strategic plan. This detector, if
located at underground facilities such as the National Science
Foundation\'s DUSEL, would also be a world-class detector for proton
decay, addressing the question Do all the forces become one? This
detector could also perform high-statistics studies of atmospheric
neutrinos and carry out astrophysical searches including detection of
relic-supernova neutrinos and neutrino bursts from supernovae in our
galaxy and nearby.

In addition to experiments at the long baseline, smaller detectors
located in the neutrino beamlines on the Fermilab site can study
neutrino interactions over a wide energy range to make precise
measurements of neutrino properties and neutrino scattering parameters.

The neutrino strategy that we have outlined will fully exploit the
investments that have been made in existing facilities as well as those
being planned for the future. This broad based, multi-component neutrino
program would ensure that the United States remains a world leader in
particle physics throughout the next decade and beyond.

### 4 Muons

**4.1 Introduction**

**4.1.1 e Conversion in Nuclei**

With the discovery of neutrino masses and lepton mixing, the fact that
individual lepton-flavor numbers -- electron-number, muon-number, and
tau-number -- are not conserved has been established. All such violating
effects to date have been observed in the neutral lepton sector, through
the phenomenon of neutrino oscillations. Charged-lepton flavor-violation
(CLFV), on the other hand, has been the subject of intense experimental
searching since the discovery of the muon but, to this date, no evidence
for it has ever been uncovered.

The Standard Model augmented by new physics that leads to the
experimentally observed neutrino masses predicts a non-zero rate for
CLFV process, but expectations depend dramatically on the mechanism
responsible for neutrino mass generation. For example, if the physics
responsible for neutrino masses is very heavy (as in the case of a high
mass scale seesaw mechanism) or very weakly coupled (as in the case of
Dirac neutrinos), expectations for CLFV processes are around forty
orders of magnitude smaller than current experimental bounds. The reason
for this is that the active neutrino contribution is GIM suppressed,
such that the amplitude for CLFV is proportional to the tiny neutrino
mass-squared differences. For example, the massive neutrino contribution
(Figure 4.1) to →e is

> $\text{Br}(\mu \rightarrow e\gamma) = \frac{3\alpha}{\text{32}\pi}\left| \sum_{i = 2,3}^{}{U_{\mu i}^{}U_{\text{ei}}\frac{{\Delta m}_{1i}^{2}}{M_{W}^{2}}} \right|^{2} < \text{10}^{- \text{54}},$
> (1)

Here, *U~i~, =e,,* and *i*=1,2,3 are the elements of the neutrino mixing
matrix and *M~W~* is the W-boson mass.

![](media/image5.wmf){width="3.53125in" height="1.5729166666666667in"}

**Figure 4.1 Massive neutrino contribution to the charged lepton
flavor-violating muon decay →e. ~i~ are neutrino mass eigenstates, while
U, =e,, and k=1,2,3, are the elements of the lepton mixing matrix.**

On the other hand, certain neutrino mass generating mechanisms are
already disfavored due to the fact that CLFV has yet to be observed. It
is fair to say that searches for CLFV are bound to play a key role in
uncovering the origin of neutrino masses. Moreover, like other
flavor-changing neutral current processes, searches for CLFV are also
among the most powerful and promising probes of new physics at or even
above the TeV scale, regardless of its connection to neutrino masses.
Concrete examples will be discussed in the next subsection.

Among the different CLFV channels, three rare muon processes stand out,
thanks in part to the muon\'s small mass and long lifetime: →e, →eee,
and →e conversion in nuclei. Current experiments have been able to rule
out, at the 90% confidence level, →e with branching ratios above 1.2 x
10^-11^ and →eee with branching ratios above 10^-12^, while the rate for
Ti→eTi normalized to the capture rate →(conversion in titanium), is
constrained to be less than 4.3 x 10^-12^. The concurrent exploration of
all three rare muon processes is of the utmost importance given that
these are all state-of-the-art, extremely challenging experiments and
the fact that the three processes "feel" different types of new physics
in distinct ways. If CLFV is observed in any of these processes, results
from other searches will play a fundamental role in establishing the
nature of the lepton-flavor-violating new physics.

Depending on the nature of the CLFV physics, one of the three bounds
listed above turns out to be the most significant. For a particular
class of models, including several of the standard supersymmetric ones,
efforts to observe →eprove to be most promising currently and in the
immediate future. The MEG experiment, currently taking data at PSI, is
aiming to be sensitive to →e branching ratios larger than several times
10^-14^. However, given the existence of very intense future muon
sources, →e conversion will likely serve as the deepest probe of CLFV,
superior to →ein its new physics reach regardless of the nature of the
new physics. Among other factors, it is this feature (which will be
discussed in more detail in the next subsection) that drives us to
concentrate on the CLFV process where a nuclear-captured muon converts
into an electron -- →e conversion in nuclei.

Negatively charged muons that stop in matter are quickly trapped and
form muonic atoms, which undergo electromagnetic transitions until the
muon is in the 1S orbital. Trapped muons either Michel-decay or convert
into neutrinos in the field of the nucleus:

> →+ (A,Z-1). (2)

(A,Z) represents a nucleus with mass number A and atomic number Z.
Similarly, the →e conversion process is characterized by

> →e(A,Z). (3)

Instead of discussing the rate for this muon and electron number
violating process, it is convenient to define the normalized conversion
rate:

> $R_{\mu e} \equiv \frac{\Gamma(\mu^{-} + (A,Z) \rightarrow e^{-} + (A,Z))}{\Gamma(\mu^{-} + (A,Z) \rightarrow \nu_{\mu} + (A,Z - 1))}\text{.}$
> (4)

We will often refer to this as the *→e conversion rate*.

**4.1.2 Muon g-2**

Flavor-conserving muon properties are also expected to reveal
indispensable information concerning physics beyond the standard model.
Thanks to the muon small mass and long lifetime, some of these can be
measured with great precision. The muon anomalous magnetic moment
(*g-*2)/2 = *a* is worthy of special attention.

The muon magnetic moment is one of the most precisely measured and
calculated quantities in elementary particle physics. A significant
effort continues worldwide to improve the precision of the
standard-model prediction. Moreover, the current experimental
measurement of *a* shows one of the largest deviations of any observable
from the corresponding standard-model prediction, *a*^(E821)^ = 295(88)
x 10^-11^. Owing to this precision, *a* is not only a sensitive test of
all standard model interactions, but also of possible new physics at and
above the electroweak scale. If the precision of *a* is improved to 39 x
10^-11^, *a* will be a highly sensitive probe of physics beyond the
standard model up to the TeV-scale.

**4.2 Comparison to Current HEP Program**

It is important to place searches for CLFV in general and →e conversion
in particular in the larger context of the current and near future
developments of the high energy physics program. The same is true for
next-generation measurement of *a*We will assume that next-generation
neutrino oscillation experiments will take place and provide nontrivial
information regarding lepton mixing and other new *neutrino physics*. We
will also assume that the LHC experiments will have taken enough data to
provide a clearer picture of physics at the TeV scale. Finally, we
assume that one will either have observed →e or constrained its
branching ratio to be less than 10^-14^. It appears unlikely that a
future experiment will be able to significantly improve on this,
regardless of whether very intense muon sources are available. This is
*not* the case of future searches for →e conversion, as will be
discussed later.

*Model Independent Analysis: a*

One can estimate the sensitivity of precision measurements of *a*to new
physics in a model independent way by adding to the standard model
effective operators that contribute, at tree level, to the muon magnetic
moment. For example,

![](media/image6.png){width="1.5618055555555554in"
height="0.3770833333333333in"}

leads to *ame*. If the current discrepancy is due to new heavy physics,
the current data on the anomalous magnetic moment of the muon translates
into a measurement of the new physics scale = 7 TeV. As will be
discussed in more detail later, is not necessarily the mass of any new
degree of freedom. For example, if one is parameterizing the effect of
new heavy degrees of freedom with mass *M*~new~ that couple to the
standard model with a coupling *f* and contribute to *a*at the one-loop
level

![](media/image7.png){width="1.1479166666666667in"
height="0.4340277777777778in"}

*Model Independent Analysis: →e conversion vs. →e*

One can estimate the sensitivity of CLFV processes to new physics in a
model independent way by adding to the standard model effective
operators that violate lepton flavor. For concreteness, consider the
effect of the standard model augmented by the following CLFV effective
Lagrangian:

> $L_{\text{CLFV}} = \frac{m_{\mu}}{(\kappa + 1)\Lambda^{2}}\overline{\mu}R\sigma e_{L}F^{\text{μν}} + \frac{\kappa}{(1 + \kappa)\Lambda^{2}}{\overline{\mu}}_{L}\gamma_{\mu}e_{L}\left( \sum_{q = u,d}^{}{{\overline{q}}_{L}\gamma^{\mu}q_{L}} \right)\text{.}$
> (5)

is the scale of new physics and measures whether the dominant new
physics contribution to CLFV comes in the form of a dimension-five, CLFV
magnetic moment-type operator (1) or from a CLFV four-fermion
interaction (1). The effective Lagrangian above will mediate both →e and
→e conversion (and, at a less significant level, →eee, which will not be
discussed). While there is a handful of other effective operators that
may also contribute, the ones above contain qualitatively the
predictions of most distinct new physics scenarios as far as →eand →e
conversion are concerned. The sensitivity of different CLFV probes to as
a function is depicted in Figure 4.2. Note that, regardless of the value
of , a →e conversion experiment sensitive to capture rates above 10^-16^
probes values smaller than a few thousand TeV!

For \<\< 1, the normalized →e conversion is around several times10^-3^
of the branching ratio for →e, while for \>\> 1 the normalized capture
rate for →e conversion is many orders of magnitude larger than the
branching ratio for →e. Hence, a →e conversion experiment sensitive to
normalized rates above 10^-16^ is at least as sensitive to new physics
as a →e experiment sensitive to branching ratios above a few times
10^-14^, regardless of the nature of the new physics. It is important to
emphasize that while we are using Eq. (5) to make this point, this
conclusion is very general and applies to most new physics scenarios
that have been explored in the literature to date.

![](media/image8.wmf){width="3.0965277777777778in"
height="3.873611111111111in"}

**Figure 4.2 Sensitivity of a *→e* conversion in ^48^Ti experiment that
can probe a normalized capture rate of 10^-16^ and 10^-18^, and of a *→
e* search that is sensitive to a branching ratio of 10^-13^ and 10^-14^,
to the new physics scale as a function of** , **as defined in Eq. (5).
The dimensionless parameter interpolates between a flavor-violating
magnetic moment-type operator ( \<\<1) and a flavor-violating
four-fermion operator (\>\>1). Also depicted is the currently excluded
region of this parameter space.**

In the case of a positive CLFV signal in either→e or →e conversion,
combined results from different CLFV processes provide detailed
information regarding the new physics. For example, should the world be
properly described by Eq. (5), a measurement of→e and →e conversion
allows one to determine both and independently, while a single
measurement can only determine a combination of the two new physics
parameters. More generally, it is well known that a comparison of R~e~
and the branching fraction for →e (B~e~) helps distinguish among models
or even measure the value of new physics parameters. A concrete example
is depicted in Figure 4.3, where the ratio of branching ratios C =
B~e~/R~e~ is plotted as a function of tan in the case of the MSSM with
MSUGRA boundary conditions for the soft SUSY breaking parameters. One
can see that a precise measurement of C can determine the sign of the
MSSM -parameter, especially if tan is not too large.

The effective Lagrangian that describes →e conversion and →e contains,
in general, several dimension-six operators not included in Eq. (5),
including those with different muon and electron chiralities and
scalar-scalar four-fermion operators. Information regarding all the
different parameters that describe CLFV can be obtained from the CLFV
probes themselves. In the advent of a positive signal for →e conversion,
details of the effective Lagrangian can be obtained by comparing the
rate for →e conversion in different nuclei, since different nuclei are
sensitive to new physics in distinct ways, as depicted in Figure 4.4.
This flexibility is not shared by→e (where one can only hope to measure,
in principle, the final state photon or electron polarizations). In the
case of a positive signal in→eee, some detailed information regarding
the underlying physics can also be obtained by analyzing in detail the
kinematics of the three final state leptons.

*CLFV and new physics at the TeV scale*

By the end of 2008, we expect the LHC experiments to start accumulating
data that will reveal the mechanism of electroweak symmetry breaking and
explore the physics of the TeV scale. Several theoretically motivated
scenarios predict the existence of new degrees of freedom with masses at
or below 1 TeV and, if this is the case, one expects some of these new
states to be discovered at the LHC.

![](media/image9.wmf){width="4.756944444444445in"
height="2.9006944444444445in"}

**Figure 4.3 B~e~/R~e~ in the MSSM with MSUGRA boundary conditions for
the soft parameters and neutrino masses induced by the seesaw mechanism,
as a function of tan for different signs of the -parameter. From C. E.
Yaguna, Int. J. Mod. Phys. A21, 1283 (2006).**

![](media/image10.wmf){width="4.3902777777777775in"
height="2.5388888888888888in"}

**Figure 4.4 →e conversion rate for different nuclei, normalized to that
for →e conversion in aluminum. The different curves represent the
contribution of different types of higher dimensional operators. From R.
Kitano, M. Koike and Y. Okada, Phys. Rev. D66, 096002 (2002).**

New physics at the TeV scale is expected to mediate CLFV processes.
Expectations are model-dependent, but detailed computations in specific
models lead to CLFV rates very close to current experimental bounds, as
will be discussed in more detail shortly. We first conservatively assume
that the new physics will predominantly induce flavor-violating
magnetic-moment type effective interactions at the one-loop level. A
concrete example is depicted in Figure 4.5.

![](media/image11.wmf){width="2.225in" height="1.1916666666666667in"}

**Figure 4.5 MSSM slepton\--neutralino contribution to →e. m~e~^2^
stands for the insertion of an off-diagonal element of the slepton
mass-matrix. From Y. Kuno and Y. Okada, Rev. Mod. Phys. 73, 151
(2001).**

In this case, CLFV is given by Eq. (6) (potentially augmented by similar
operators where the electron and muon chiralities are reversed) with
\<\<1 and

> $\frac{1}{\Lambda^{2}}\text{\textasciitilde}\frac{\text{eg}^{2}}{\text{16}\pi^{2}}\frac{\theta_{e\mu}}{M_{\text{new}}^{2}}\text{.}$
> (6)

*M~new~* are the masses of the new states that couple to standard model
fields with coupling g and ~e~ is a flavor-violating factor, most likely
inaccessible to the LHC. If one assumes g (henceforth assumed to be of
order one) and *M~new~* to be known, failure to observe CLFV translates
into bounds on *~e~*.

As a concrete example, consider the possibility that the currently
observed three sigma discrepancy between the standard model prediction
and the measurement of the muon anomalous magnetic moment is due to new
electroweak scale physics. In this case, the new physics contribution to
the anomalous magnetic moment of the muon is capture by a
flavor-conserving version of the magnetic moment-type operator that
mediates CLFV. Current data on the muon anomalous magnetic moment
translates into a measurement of a combination of the new physics scale
*M~new~* and the new coupling g, in which case currents bounds on CLFV
are already quite severe and constrain ~e~\< 10^-3^.

Similarly, if the LHC discovers new states with masses *M~new~* around 1
TeV, current bounds from CLFV will already translate into ~e~ \< 10^-2^.
In this case, →e conversion experiments sensitive to conversion rates
greater than 10^-16^ will probe *~e~* \> 10^-4^.

What are the expected values for *~e~*? The answer to this is model
dependent, but one can identify general categories. Generic new physics
models predict *~e~* \~ 1, in which case searches for CLFV already rule
out *M~new~* \~ 1TeV. Hence searches for CLFV, along with other flavor
observables, already constrain any physics at the TeV scale to be flavor
conserving at the leading order. For this reason, one often assumes that
the only sources of lepton-flavor violation are the ones already present
in the standard model, *e.g.*, the charged-lepton Yukawa couplings and
the neutrino mass generating sector. In this case, ~e~ values can be
computed on a case-by-case basis, and its value may or may not depend on
the unknown new physics responsible for neutrino masses and lepton
mixing.

Several detailed analyses have been performed for the different
independently motivated new physics scenarios, including models with
weak scale supersymmetry, models with flat and warped extra-dimensions,
and little Higgs models. Some results depend on details of the physics
responsible for neutrino masses, about which we will discuss more
shortly, but tend to lead to ~e~ values such that →e conversion is
likely to happen with rates above 10^-17^ or so as long as the new
physics is observable at the LHC.

Two examples are depicted in Figures 4.6 and 4.7. Figure 4.6 depicts the
result of a scan of the MSSM parameter space for different SUSY-GUT
scenarios where neutrino masses are generated via the seesaw mechanism.
The GUT hypothesis fixes the values of the right-handed neutrino
Majorana masses, while there remains the freedom to choose the
off-diagonal structure of the neutrino Yukawa couplings. Here two
different choices are made: the neutrino Yukawa coupling matrix is
PMNS-like with all its mixing angles large as in the physically
observable lepton mixing matrix, or it is CKM-like with all its mixing
angles small as in the physically observable quark mixing matrix. While
the different choices lead to →e gamma rates that vary by more than four
orders of magnitude, it is clear that a →e conversion experiment
sensitive to normalized rates above 10^-17^ or so should cover the
majority of the LHC accessible parameter space.

Figure 4.7 depicts the result of a scan of the parameter space of the
littlest Higgs model with T-parity. The different colored (shaded)
points refer to different ansatze for the structure of the mirror lepton
mixing sector, not dissimilar from the choice of neutrino Yukawa
matrices made in the SUSY example discussed briefly above. Also here, a
→e conversion experiment sensitive to normalized conversion rates above
10^-16^ should cover the parameter space explored in the figure. This is
also true for a handful of points where the branching ratio for →e is
less than 10^-14^. Note that in this case results do not depend on the
mechanism responsible for neutrino masses, but do depend on the unknown
mirror fermion mixing matrix.

![](media/image12.wmf){width="3.591666666666667in"
height="2.341666666666667in"}

**Figure 4.6 →e conversion rate in Ti for different SUSY\--GUT
scenarios. The plots are obtained by scanning the LHC accessible
parameter space. The horizontal lines are the present (SINDRUM II) bound
and the planned (future) sensitivity to the process both at the proposed
PRIME experiment in JPARC and at the proposed mu2e experiment in FNAL.
From L. Calibbi, A. Faccia, A. Masiero and S. K. Vempati, Phys. Rev.
D74, 116002 (2006).**

![](media/image13.wmf){width="4.258333333333334in" height="2.375in"}

**Figure 4.7 →e conversion rate in Ti versus →e branching ratio for
different littlest Higgs scenarios. The light grey region is allowed by
current searches for CLFV. The different shaded points represent
different ansatze for the mirror fermion mixing matrix. From M. Blanke,
A. J. Buras, B. Duling, A. Poschenrieder and C. Tarantino, JHEP 0705,
013 (2007).**

It is also important to discuss the case where CLFV is generated by new
physics at the tree-level, i.e. it is a consequence of the simple
exchange of a heavy new physics particle. An example is depicted in
Figure 4.8. Other than SUSY with R-parity violation, depicted in Figure
4.8, several well-motivated new physics scenarios lead to similar CLFV
effects including the models with lepto-quarks, neutrino mass models
with Higgs triplets, and models with extra Z\' gauge bosons. In this
case, CLFV is described by Eq. (5) (potentially augmented by, say,
scalar-scalar four-fermion operators) with \>\>1 and

$\frac{1}{\Lambda^{2}}\text{\textasciitilde}\frac{\text{eg}^{2}}{\text{16}\pi^{2}}\frac{\theta_{e\mu}}{M_{\text{new}}^{2}},$
(7)

Here, if M~new~ is measured at the LHC, current bounds from →e
conversion constrain g^2^~e~ to be tiny. In the example depicted in
Figure 4.8, g^2^~e~\~^'^~221~/^'^~121~). Not surprisingly, this
parameter is most severely constrained by searches for →e conversion in
nuclei.

![](media/image14.wmf){width="2.2in" height="1.9784722222222222in"}

**Figure 4.8 MSSM tree-level R-parity violating contribution to →e
conversion. From A. de Gouvea, S. Lola and K. Tobe, Phys. Rev. D63,
035004 (2001).**

To summarize the discussion so far: if the LHC discovers new states at
the TeV scale, several distinct new physics scenarios predict CLFV
violating process to occur with rates that are close to current
experimental bounds. In this case, a positive →e conversion result
(which may or may not be accompanied by a positive →e or →eee result)
will tell us about the flavor structure of the new physics sector, and
may even help distinguish among different new physics scenarios. It is
important to emphasize that the information one will extract from the
CLFV sector is complementary to the information one can hope to extract
from LHC data.

Similarly, in the advent of new physics at the LHC, a negative →e
conversion result will also contribute to our understanding of the new
TeV scale physics. It would reveal that (i) the new physics is indeed
intrinsically lepton-flavor conserving and (ii) the flavor breaking
effects induced by the known sources of flavor violation are smaller
than naive expectations. Different physics may explain (ii). For
example, in the case of SUSY, low-energy gauge-mediated scenarios
usually lead to suppressed flavor-violating effects. Furthermore, as
will be discussed in more detail shortly, some of the estimates above
depend on the physics responsible for neutrino masses, which may be such
that TeV-scale CLFV effects are smaller than naive expectations.

There remains, of course, the possibility that the LHC discovers no new
degrees of freedom other than what appears to be a standard model Higgs
boson. This will indicate that the new physics beyond the standard model
is significantly heavier than the TeV scale. Under these circumstances,
searches for CLFV violation remain extremely valuable, especially
searches for →e conversion (and, to a lesser extent, searches for →eee).
The reason is that if the LHC fails to discover any
beyond-the-standard-model effect, the gauge hierarchy problem will, most
likely, prove to be a poor indicator for the new physics scale. In this
case, progress in fundamental particle physics, including the answers
for the open questions, will have to rely, at least for some time, on
indirect new physics probes, i.e. on the intensity frontier. These
include precision studies of neutrinos and their properties, precision
measurements of well-known standard model quantities (like the anomalous
magnetic moment of the muon), and searches for forbidden or extremely
suppressed processes, like CLFV muon processes. Under these
circumstances, the intensity frontier would be the only game in town. Of
the probes listed above, CLFV is the one capable of "directly" reaching
out to several thousand TeV, especially in the case of →e conversion, if
new flavor-violating effects are large (in the sense θ~eμ~ \~ 1) and
strongly coupled (g \~1) and occur at the tree-level (see Eq. (7) and
Figure 4.2). While there are, by no means, any guarantees that this is
the case, there are reasons to believe in such a scenario. Among other
plausibility arguments is the fact that the only palpable evidence for
new physics is the existence of non-zero neutrino masses. The tiny
neutrino masses are potentially due to new, heavy physics and the large
lepton mixing angles seem to indicate that flavor-numbers are not
conserved in the neutrino sector. Hence, as long as the neutrino mass
scale is not too heavy (above 10^4^ TeV), there remains the possibility
that *→e* conversion will directly teach us about the physics
responsible for non-zero neutrino masses.

*a* *and new physics at the TeV scale*

If there are new degrees of freedom at the TeV scale, it is widely
expected that the new physics that governs these new states and how they
interact with the standard model fields will help address many
fundamental questions and lead to qualitative progress in our
understanding of fundamental physics. Due to the expected importance and
complexity of physics at the TeV-scale, we need to combine and
cross-check information from the LHC with information from as many
complementary experiments as possible. The measurement of the muon
magnetic moment *a* is indispensable in this respect.

As an example, we discuss in more detail the example of supersymmetric
extensions of the standard model. A simple model with equal masses gives

![](media/image15.wmf){width="5.9944444444444445in" height="0.6125in"}

where tan is the ratio of the vacuum expectation values of the two Higgs
boson fields. In order to discuss the relative sensitivity of LHC and
*a* to tan, we reconsider the situation discussed in R. Lafaye, T. Plehn
and D. Zerwas, hep-ph/0404282. In this reference it has been assumed
that the MSSM reference point SPS1a is realized, and the potential of
the LHC to determine MSSM parameters has been worked out. By performing
a global fit of the MSSM to all available LHC data, a large set of MSSM
parameters can be determined to a precision of a few percent. Apart from
the sign of the parameter, which has been assumed to be positive, tan
could be determined only poorly: tan = 10.22 +/- 9.1. In such a
situation, an improved *a* measurement will be the perfect complement of
the LHC. One can simply study the MSSM-prediction for *a* as a function
of tan (all other parameters are known from the global fit to LHC data)
and compare it to the measured value. One can display the result in a
"blue band" plot, similar to the case of the LEP precision data, which
can be compared to the standard model predictions as a function of the
standard-model Higgs boson mass. The resulting possible future "blue
band" plot for tan determined by the measurement of the muon anomalous
magnetic moment is shown in Figure 4.9 (Left). As can be seen from the
plot, the improvement of the determination of tan from the *a*
measurement is excellent.

![](media/image16.png){width="3.001388888888889in"
height="3.001388888888889in"}![](media/image17.png){width="2.9409722222222223in"
height="3.0277777777777777in"}

**Figure 4.9 Left: A possible future \`\`blue band\'\' plot, where tan
is determined from the measurement of *a*. The white region between the
yellow vertical bars indicates the plus/minus one sigma region from the
LHC-determination of tan^LHC^= 10.22 +/- 9.1. The darker blue band is
with the present E821 restrictions. The lighter blue band corresponds to
*a*= 295(39) x 10^-11^. It is assumed that the MSSM reference point
SPS1a is realized and that the MSSM parameters have been determined by a
global fit to the values given in hep-ph/0404282, Table 5, and that the
measured value *a*^exp^ coincides with the actual value of the SPS1a
point. The plot shows ^2^ as a function of tan. All MSSM parameters
except for tan have been set to the values determined at the LHC. The
width of the blue curves results from the uncertainty on these
parameters. The plot indicates that the precision for tan that can be
obtained using *a* is limited by the precision of the other input
parameters, but is still better than 20% and thus much better than the
determination using LHC data alone. Right: The *m*~0~ -- *m~1/2~* plane
of the CMSSM parameter space for tan=10, *A*~0~=0, sign()=+1. The *a*=
295(39) x 10^-11^ between experiment and standard-model theory is from
J.P. Miller, E. de Rafael and B.L. Roberts, hep-ph/0703049, and Rep.
Prog. Phys. 70, 795-881 (2007), see text. The brown wedge on the lower
right is excluded by the requirement the dark matter be neutral. Direct
limits on the Higgs and chargino masses are indicated by vertical lines.
Restrictions from the WMAP satellite data are shown as a light-blue
line. The *g*-2 1 and 2-standard deviation boundaries are shown in
purple. The region \`\`allowed\'\' by WMAP and *g*-2 is indicated by the
ellipse, which is further restricted by the limit on *M~h~*. (Figure
courtesy of K. Olive).**

A second example concerns the restriction of special, highly constrained
models of new physics such as the constrained MSSM (CMSSM). The CMSSM
has only four free continuous parameters. One precise measurement such
as the future determination of *a* effectively fixes one parameter as a
function of the others and thus reduces the number of free parameters by
one. In fact, the CMSSM is very sensitive not only to *a* but also to
the dark matter (assumed to consist of neutralinos) relic density. As
shown in Figure 4.9 (Right), both observables lead to orthogonal
constraints in CMSSM parameter space, and therefore imposing both
constraints leaves only two free parameters and thus allows for very
stringent tests of the CMSSM at the LHC.

A third example is the distinction between two different, well-motivated
scenarios of supersymmetry breaking such as anomaly-mediated and
gravity-mediated supersymmetry breaking. The two scenarios lead to
different values of superpartner masses, but a major qualitative
difference is the different sign for the MSSM-parameter preferred in
both scenarios (if the current experimental constraint on *B*(*b s*) is
imposed). The LHC is not particularly sensitive to the sign of , and
thus cannot test this fundamental difference. However, the sign of
determines the sign of the supersymmetry contributions to *a*. The
current discrepancy between the standard model and experiment already
favors a positive parameter, but the magnitude of the uncertainty does
not allow a definite conclusion. An improved measurement with
uncertainty 39 x 10^-11^ has the potential to unambiguously determine
the sign of and thus one of the central supersymmetry parameters.
Depending on the future central value of *a*, either anomaly- or
gravity-mediated supersymmetry breaking could be ruled out or at least
seriously constrained.

A new more precise measurement of *a* will be highly valuable in this
respect since it will provide a benchmark and stringent selection
criterion that can be imposed on any model that is tested at the LHC.
For example, if *a* persists to be as large as it is today, many
non-supersymmetric models will be ruled out. If *a* turns out to be
rather small, supersymmetric models will be seriously constrained.

Finally, we invite the question of the usefulness of next-generation
precision measurements of the muon anomalous magnetic moment in the
advent that the LHC does not discover any new degrees of freedom other
than a standard model Higgs boson. Under these circumstances, new
physics contributions to *a* are widely expected to be smaller than the
foreseeable theoretical error on the standard model prediction of *a*,
such that the current three sigma discrepancy is expected to go away.
Nonetheless, there is no guarantee that *a* should be unobservably
small. Indeed, under these circumstances a non-zero *a* would indicate
that there is new physics at the TeV scale, but that it escaped the
scrutiny of the LHC experiments. Under these circumstances, only an
energy-frontier leptonic collider would provide valuable complementary
information to discover the new physics exposed by *a*.

*CLFV, neutrino masses, and the matter\--antimatter asymmetry of the
Universe*

As discussed in the introduction, massive neutrinos and lepton mixing
imply that CLFV *must* occur at some level. While the active neutrino
contribution to CLFV is known, as already discussed, to be tiny there
remains the likely possibility that the new physics responsible for
neutrino masses will induce CLFV at observable levels. Several examples
of this have been mentioned in passing above.

Here we will discuss in detail the MSSM case in order to underline the
potential importance of CLFV to understanding neutrino masses and other
related phenomena, including leptogenesis. In the MSSM with MSUGRA
boundary conditions large CLFV are generated if neutrino masses are a
consequence of the seesaw mechanism. In more detail, a non-zero
off-diagonal slepton mass-squared (see Figure 4.5)

${\Delta m}_{\overset{\sim}{\mu}\overset{\sim}{e}}^{2}\underline{\text{\textasciitilde}}\sum_{k}^{}\frac{M_{\text{SUSY}}^{2}}{\text{16}\pi^{2}}y_{\mu k}^{}y_{\text{ek}}\text{log}\left( \frac{M_{\text{GUT}}}{M_{k}} \right),$
(8)

is generated where y~k~, *=e,,* and *k*=1,2,3 are the neutrino Yukawa
couplings, *M~k~* are the right-handed neutrino Majorana masses,
*M~SUSY~* is a typical supersymmetric mass and *M~GUT~* is a typical
ultraviolet cut-off, often equated with the GUT scale. In this case, the
rate for muon CLFV is proportional to
$({\Delta m}_{\mu e}^{2})^{2}(\theta_{\mu e}\frac{{\Delta m}_{\mu e}^{2}}{M_{\text{SUSY}}^{2}})$,
such that it probes some combination of the neutrino Yukawa couplings
and hence provides non-trivial information regarding the neutrino mass
sector; this statement is very dependent on the physics of SUSY
breaking, which we are assuming is well known.

Knowledge of the neutrino Yukawa couplings is also fundamental when it
comes to determining whether leptogenesis is the mechanism responsible
for the matter\--antimatter asymmetry of the Universe. The amount of
baryon number generated depends on a linear combination of neutrino
Yukawa couplings and right-handed Majorana neutrino masses different
from the one above (proportional to $$Im\[(*y^†^ y*)^2^~j1~\] in the
case of thermal leptogenesis), while a third linear combination
determines the observed active neutrino masses:

> $m_{\text{αβ}} = \sum_{k}^{}y_{\alpha k}\frac{v^{2}}{M_{k}}y_{\beta k}\text{.}$
> (9)

It has been shown that, given the right circumstances, neutrino
oscillation measurements combined with positive results from CLFV,
positive results from searches for neutrinoless double-beta decay, and
information regarding the low-energy SUSY and SUSY breaking, can provide
enough information in order to test leptogenesis. Hence, if thermal
leptogenesis is ever to be tested experimentally, CLFV will certainly
play a fundamental role.

It is important to emphasize that negative results from CLFV, combined
with the discovery of SUSY at the LHC, may prove as important positive
results. The reason is as follows. In the MSSM, standard thermal
leptogenesis requires the lightest right-handed neutrino Majorana mass
to be larger than 10^-9^ GeV or so. This translates into a rough lower
bound on the neutrino Yukawa couplings, using Eq. (9): *y*^2^ $$ 10^-5^.
This, in turn, implies that *θ*~e~ \>10^-6^. Hence, if CLFV experiments
can rule out *θ*~e~ \> 10^-6^, standard thermal leptogenesis would be
severely disfavored. Such sensitivity could only be obtained, if at all,
in searches for →e conversion fed by very intense muon sources.

**4.3 Experimental Program**

**4.3.1 Muon Conversion Measurements**

Muon conversion in nuclei is unique in the sense that extremely intense
muon beams can be used to extend the experimental sensitivity orders of
magnitude beyond current limits. This is a consequence of the fact that
the detected final state consists of a single particle of fixed energy,
in contrast with other processes (e.g. →e, →eee). At the high rates
necessary to reach the desired sensitivity, processes with
multi-particle final states are limited by backgrounds from accidental
coincidences of particles from multiple decays; these increase linearly
with rate and are absent in the conversion experiment. Further, the fact
that the energy of the final state particle is significantly higher than
the majority of most particles resulting from decay or capture (again in
contrast with the case of →e, →eee) vastly simplifies the complexities
of dealing with very high instantaneous decay rates.

The only current experiment in CLFV is the MEG (→e) experiment at the
Paul Scherrer Institute in Switzerland. It uses a surface muon beam
(muons originating from the decay of pions at rest near the surface of a
production target). The antimuons are stopped in a thin target and the
monochromatic positrons and photons are detected and their momenta and
time of origin are determined. The experiment is limited in sensitivity
to a branching fraction of \~10^-13^ by a combination of reasonable
running time and maximum allowed instantaneous rates in the photon
detector, and by backgrounds. Backgrounds are dominated by accidental
coincidences of positrons from one muon decay (which peak at the
kinematic maximum) and photons from either radiative decay or
annihilation in flight of a positron from a second muon. Reducing the
background to one event at a sensitivity of 10^-13^ requires
measurements at the precision of the state-of-the-art detector
technology for the photon and positron times, the photon energy and
position, and the positron momentum. This experiment may be upgraded to
handle higher rates that could allow a measurement with a sensitivity of
10^-14^ in a few years of running, but backgrounds will then likely be
sufficiently high that the sensitivity for a discovery will increase
only with the square root of the running time. If the branching fraction
is near the current upper limit of 2 x 10^-11^, a measurement of *R~e~*
with a precision approaching 10% could be made.

Interest in improved CLFV experiments now focuses on →e conversion. All
approaches use a low energy muon beam to stop muons in a thin target,
where they are Coulomb captured. The monochromatic electron resulting
from the muon conversion is detected and its energy measured with high
precision to eliminate backgrounds. To improve significantly on the
sensitivity of previous searches, substantial improvements in all
aspects of these experiments must be made.

Two approaches have been explored. The Mu2e Collaboration, consisting of
50 scientists from 11 institutes, has recently submitted an LOI to
Fermilab to measure muon conversion with an apparatus and muon beam
based on the MECO experiment. The MECO experiment would have used a
proton beam pulsed at about 1 MHz to allow conversion electrons to be
detected between pulses when many sources of backgrounds associated with
electrons and pions in the muon beam are reduced. This proposal was
developed in great detail and was optimized to use an 8 GeV proton beam
of up to 100 kW of instantaneous power at 50% duty cycle. The proposed
sensitivity was approximately 1 detected event for a value of *R~e~* = 2
x 10^-17^~,~ with an expected background of about 1 event.

The MECO design (see Figure 4.10) was optimized for this intensity and
the performance was limited by the potential for radiation damage to the
solenoid magnet surrounding the

![](media/image18.png){width="4.023611111111111in"
height="2.8583333333333334in"}

**Figure 4.10 The muon beamline and detector apparatus proposed for the
MECO →e conversion experiment, which has been taken as the baseline
design for the Mu2e exeriment. The elements comprise a production
solenoid at the left surrounding a production target on which a proton
beam from the right impinges, a curved transport solenoid with momentum
and sign selection collimators, and a detector solenoid with muon
stopping target, proton shield (blue), tracking chambers (light green)
and calorimetric electron calorimeter.**

muon production target, by cooling for the small muon production target,
and by instantaneous intensity in the tracking chambers. With one
final-state particle, accidental backgrounds of the type that limit
→eexperiments are not present, and increased instantaneous intensity
would cause increased background only to the extent that electron
momentum resolution is degraded by effects of higher tracking chamber
rates. The dominant background is from muons that decay in a Coulomb
bound orbit (DIO electrons) and hence can have energy as large as that
of conversion electrons. This background is intrinsic to the process and
is reduced only by better electron energy resolution. In the case of
MECO, the resolution is derived in roughly equal parts from energy loss
dispersion as the electron exited the stopping target and traversed the
detectors, and from scattering within the spectrometer. The MECO design
was developed to the level of a technical proposal with a validated
cost.

The Mu2e experiment at Fermilab would run simultaneously with a neutrino
program and, depending on the development of the complex, which is
discussed below, could also run in parallel with other experiments that
would use an intense 8 GeV source.

A second approach has been proposed by the PRISM/PRIME collaboration. It
would use the much higher power (2-4 MW) that could be available in a
beam from the JPARC 30 GeV synchrotron that is currently under
construction. The proton beam would be pulsed at relatively low
frequency (perhaps 100 Hz) and a relatively pure and monochromatic muon
beam would be made using a beam channel and fixed focus, alternating
gradient (FFAG) storage ring to exchange the initial narrow time and
large momentum spread of the muon beam to produce a narrow momentum
spread. The instantaneous stopping rate would be very high (\~10^5^
times that of the MECO proposal) and a different detection technique was
proposed. It was proposed to use a large aperture, high field curved
solenoid channel to select and transport high momentum particles (e.g.
conversion electrons) to a detector region and to suppress lower
momentum particles from muon decay and capture. The beamline and
apparatus are shown in Figure 4.11. Backgrounds from DIO electrons would
be reduced by virtue of a thinner stopping target and reduced material
in the electron flight path. This approach has not yet been developed to
the level of a technical proposal and validated cost. The sensitivity
that could be achieved in this approach was estimated at \~10^-18^.

Recently, the PRISM/PRIME collaboration proposed the COMET experiment.
It would use a pion capture and muon transport similar to that of Mu2e /
MECO, and use the PRISM/PRIME approach for the electron detection. It is
proposed to run at the JPARC facility using a 56 kW 8 GeV beam, and
would reach a sensitivity of below 10^-16^. Both COMET and PRISM/PRIME
would use the full resources of the JPARC synchrotron, and could not run
simultaneously with the neutrino program at JPARC.

![](media/image19.jpeg){width="3.0770833333333334in"
height="2.453472222222222in"}![](media/image20.jpeg){width="2.832638888888889in"
height="2.43125in"}

**Figure 4.11 Left: the PRISM/PRIME proposed muon beamline and** →e
**conversion experiment. It comprises a muon production solenoid,
transport solenoid, FFAG ring, further transport solenoid, muon stopping
target solenoid, electron momentum selection solenoid, and detector
solenoid with electron detectors. Right: the COMET muon beamline and
experiment, comprising pion capture solenoid, muon transport, stopping
region, electron transport, and detector solenoid with electron
detectors.**

In principle, one or both of these approaches could be implemented at
Fermilab. The Project X implementation being discussed could provide as
much as 200 kW of 8 GeV protons (2.5 x 10^14^ Hz) with \> 90% duty
cycle, corresponding to about 2.5 instantaneous and 5 times the average
intensities for which MECO was designed. Upgrades to the MECO approach
are being studied by the Mu2e collaboration, Fermilab accelerator
physicists, and others in order to take advantage of these higher rates.

On the accelerator side, current studies at Fermilab are focused on
reusing the accumulator and debuncher rings to stack protons and
re-bunch them to provide the necessary time structure. This would be
done by coalescing the stored beam into a single bunch that would then
be resonantly extracted over a period of \~1 second. Figure 4.12 shows
the accelerator complex with modifications to use protons from either
the Booster or Project X to produce an appropriately pulsed proton beam.
Based on the potential for instabilities in these rings, from electron
cloud effects for example, it is now believed that a new ring based on
either the recycler or Tevatron tunnel may be needed to handle more than
50 kW beam power. Instantaneous intensity considerations also affect the
muon beamline. Some could be ameliorated simply, for example by
increasing the bore of the superconducting magnet surrounding the
production target and increasing the shielding around the target. Others
require more study and possibly a significant change in approach, for
example the need for a 5-fold increase in target cooling.

![](media/image21.png){width="5.947222222222222in"
height="2.6798611111111112in"}

**Figure 4.12 The Fermilab accelerator complex with provisions for a
pulsed, slow extracted 8 GeV proton beam driven from either the Booster
or Project X. Alternatives for using either the recycler or a ring in
the Tevatron tunnel to replace the debuncher/accumulator rings to
rebunch the proton beam are being studied, as are scenarios for
injecting from the Project X linac into the accumulator/debuncher
complex.**

Modifications to the MECO/Mu2e approach would also be required to deal
with increased rates, which would be above 2.5 MHz per channel. The
spectrometer design was optimized to minimize multiple scattering and
resulted in a configuration that did not have highly redundant tracking
and that would be susceptible to tracking errors at these high rates.
Most of the rate is due to products of muon capture (protons, neutrons,
and photons), and these could be reduced by increasing the length of the
solenoid surrounding the detectors, allowing the detectors themselves to
be placed farther from the stopping target and reduce their subtended
solid angle for neutral particles. Protons from muon capture typically
have momentum about 100 MeV/c and their flux at the detectors is reduced
with thin absorbers (they are very heavily ionizing) and by self
absorption in the stopping target. More complicated geometries that
exploit the opposite helicity of the trajectories of protons and
electrons could reduce the proton flux with some loss in electron
detection efficiency.

An upgraded Mu2e experiment could reach a sensitivity of 1 event for
*R~e~* = 10^-18^ in a few years (5 x 10^7^ seconds) data collection. If
*R~e~* is near the current limit of 6 x 10^-13^ (or the limit of
\~10^-13^ implied by limits on *B~e~*in photon mediated mechanisms) it
would be measured with a statistical precision below 1%. With a large
data sample, background from muon decay in orbit and other sources would
not significantly increase the uncertainty in this measurement.
Different nuclei (at least aluminum and titanium) could be studied, and
the value of *R~e~* compared with *B~e~* If *R~e~* is small (\<10^-17^),
this approach would likely not be background free without additional
improvements that will require significant study to implement. The
stopping target thickness could be re-optimized to reduce energy loss of
the outgoing electron, with some loss in muon stop rate. Re-optimized
selection criteria and analysis strategies could also be directed to
increase background rejection at the cost of reduced sensitivity.

This approach could be phased, with the first phase using the booster as
the proton source and the second phase using the Project X linac. The
first phase could reach a sensitivity of a few times 10^-17^ in 2-3
years of running simultaneous with a neutrino program. Depending on
results of the first phase, the second phase, also run in parallel with
a neutrino program and possibly other experiments, would either measure
*R~e~* with precision and for different nuclei or extend the search
sensitivity by 1-2 orders of magnitude. Provisions for running at the
highest Project X intensity would be incorporated. For example
sufficient production solenoid bore to accommodate increased shielding
and a detector solenoid long enough to reduce detector rates would be
incorporated in the experiment.

**4.3.2 Muon g-2 Measurements**

All currently discussed experiments to improve the measurement of g-2
would use the existing precision superconducting muon storage ring that
was built for E821 at BNL. The experimental concept would also be
essentially unchanged. It is based on injecting highly polarized muons
at the magic momentum of 3.094 GeV/c; at this momentum, the electric
field used for weak focusing does not affect the muon spin precession.
The muons circle the storage ring and their spins advance with a
"precession frequency" proportional to g-2. The decay positrons times
and energies are measured by calorimeters placed on the inside of edge
of the storage ring (see Figure 4.13). Decay positrons from the stored
muons are collected over an interval of 700 s, \~11 time-dilated muon
lifetimes.

Muons were produced using twelve 50 ns wide pulses of 24 GeV protons per
2.7 s AGS acceleration cycle delivered to a pion production target.
Pions were momentum selected (0.5% *p/p*) and near-forward muons from
the approximately 40% of the pions that decayed were collected. A final
beamline bend, tuned to pass particles at the magic momentum, was used
to separate muons from the pions entering the storage ring. Once in the
ring, three fast kickers were fired to deflect the muons (\~15,000 per
spill) onto stable orbits. E821 was limited by the high instantaneous
rate of stored muons and by the background *flash* that originated from
pions that entered the ring during the injection.

E821 achieved an overall uncertainty of 0.54 ppm on the muon anomaly, a
precision deduced from three high-statistics runs with approximately
equal contributions of \~0.7 ppm from positive and negative muon
samples. The final error included a 0.46 ppm statistical contribution,
0.21 ppm precession frequency systematic, and 0.17 ppm event-averaged
magnetic field systematic.

A next-generation experiment would use at least 20 times more stored
muons with a goal of improving the precision by a factor of 5 or more.
More highly segmented detectors and faster electronics aimed at reducing
systematic uncertainties for the same instantaneous muon intensity are
envisaged. Significant improvement in the g-2 measurement also requires
increasing the frequency of muon stores and reducing pion-induced
background. Ways to increase the number of stored muons have been well
documented in Proposal E969 to BNL. They include improvements to the
muon decay beam lattice design, the inflector magnet, and the kicker.
Required additional improvements would use a much longer decay beamline
and significantly greater pulse frequency. The longer decay line would
allow nearly all pions to decay, eliminating the pion flash and
increasing the muon/pion yield. Also, the ratio of the central pion to
final muon momentum could be set to the optimal value of 1.005,
increasing the figure-of-merit, *NA^2^.* To achieve the long decay beam,
a muon accumulator ring to store the pion / muon burst for up to 10
turns is being studied at BNL. At FNAL, a very long (0.5 -- 1.0 km)
decay beamline is envisioned. At BNL, the pulse frequency might be
increased to 36 per 2.7 s cycle time. At Fermilab, schemes to extract as
many as 84 pulses per 1.33 s cycle are being studied. The latter would
be an increase of about 14 and 5 with respect to E821 and an upgraded
experiment at BNL.

![](media/image22.jpeg){width="2.0645669291338584in"
height="1.7708661417322835in"}![](media/image23.png){width="0.9125984251968504in"
height="0.2137795275590551in"}

**Figure 4.13 Left: Muon spin and momentum vectors with exaggerated spin
motion as the muon circles the ring. The difference between the spin and
momentum directions is the precession frequency, which is directly
proportional to the muon anomaly, a~m~. Right: Photo of the same arc of
the storage ring with partial installation of detectors.**

The cross section for 3.1 GeV/c positive pion production is 3 times
smaller using the 8.9 GeV/c protons compared with 24 GeV/c protons. This
reduction is contrasted by the combined effect of many storage
improvements from upgrades and the forward decay long beamline to yield
an overall *increase* in muons per proton of at least tenfold. In such a
plan, more muons are delivered per second but at a lower instantaneous
rate compared to BNL, a distinct advantage both for statistics and for
systematic error control.

Reductions in the systematic uncertainties will also be required.
Upgrades to the measurement design will reduce the uncertainty on the
precession measurement and improvements in the shimming and monitoring
of the magnetic field will reduce the uncertainty on the magnetic field
systematic. The aim is to keep all systematic uncertainties below the
statistical errors. Of the total running time, roughly 25% would be
devoted to the study of systematic errors.

At Fermilab, it is estimated that \~4(6) x 10^20^ protons will give a
0.1 ppm measurement using positive (negative) muons. This corresponds to
8x10^7^ s, a number of operational years, running at 16kW beam power or
proportionately less if greater beam power (up to 50 kW?) with a Project
X beam.

Both theory and experiment have now reached similar sub-ppm precision
and a plan is seen to get to 0.1 ppm. The g-2 experimental team has also
considered plans for efforts beyond 0.1 ppm in precision. One idea,
which would require an extremely powerful accelerator, such as the
Project X linac, is an "all-integrating" experiment where very intense
muon fills in a storage ring are measured by calorimeters in current
mode. The g-2 asymmetry is carried by the flow of energy vs. time. Monte
Carlo studies show that even with a reduced asymmetry due to integrating
over the full decay spectrum, the statistical precision suffers by only
about 10% compared with the conventional method. There is no pileup
effect in this method; it is quite similar to high-rate,
parity-violating electron scattering asymmetry measurements. Perhaps in
the Project X era, this type of measurement can be realized. This
concept could be tested parallel with conventional event analysis in the
early phases of a Fermilab experiment.

**4.4 Muon Summary**

Both an experiment to search for muon to electron conversion at a
sensitivity starting below 10^-16^ and extending to \~10^-18^ and an
experiment to improve the measurement of the muon's anomalous magnetic
moment (g-2) are highly motivated and should be part of a strong program
in flavor physics at Fermilab. For both experiments, a phased approach
is proposed.

The design for a conversion experiment (MECO) is rather mature and could
be implemented relatively quickly (the Mu2e proposal), probably limited
by the time for funding approval. It could be running within 5 years of
initial funding. Even with 16-20 kW of beam power, it would be a
powerful probe of new physics. The strategy would be to incorporate the
possibility of modifying the beam and detectors to take advantage of the
significant flux increase that could be provided by Project X. Again,
the MECO design has the advantage that it could run at 100 kW of
instantaneous power, within a factor of two of the 200 kW from a 100%
duty cycle storage ring. The advantages of the extra power are clear,
particularly in the case that a signal is seen and studies of target
dependence and precise comparison with the decay rates for muon to
positron and photon are possible. Better understanding of how the
experiment could handle the full 200 kW from a Project X beam should be
a priority.

In the context of experiments outside the U.S., the situation is not
clear. A proposal for a rather different concept (PRISM/PRIME), to reach
sensitivity about what might be done at Project X, is proposed for
JPARC, also with an earlier phase at lesser sensitivity. It is likely to
be a number of years before the PRISM/PRIME proposal is definitively
acted on. The earlier phase (COMET) could be done on a timescale
comparable to the first phase of mu2e.

A g-2 experiment with precision a factor of 5 better than the current
precision could also be implemented relatively quickly, assuming that a
way of ejecting \>50 pulses per second from a storage ring can be found.
Achieving this improvement with only the 16 kW booster source would
require extended running and a somewhat increased flux from the Project
X linac would reduce this. The advantages of Fermilab vs. another site
(e.g. BNL or JPARC) are not so clear. Decreased pion production at 8 GeV
vs 24 or 30 GeV could be offset by more efficient pion production or
muon capture. The choice of an optimal site would likely depend more on
facility availability and total cost than on technical considerations.
An even more ambitious plan that would utilize a large fraction of the
available Project X intensity requires extensive study and testing; the
latter could be done during the first phase of running.

### 5 Kaons

# 5.1 Introduction

The rare decays ![](media/image25.wmf) and ![](media/image26.wmf) play
an important role in the search for the underlying mechanism of flavor
mixing and *CP* violation. As such they are among the most incisive
probes of physics beyond the Standard Model (SM). Of the many rare *K*-
and *B*-decays, the ![](media/image25.wmf) and ![](media/image26.wmf)
modes are unique since their SM branching ratios can be computed to an
exceptionally high degree of precision, not matched by any other
flavor-changing neutral current (FCNC) process involving quarks, and
they have exquisite sensitivity to new physics contributions.

The exceptional theoretical cleanness of ![](media/image27.wmf) decays
is a consequence of the severe suppression of non-perturbative effects
in these processes: a powerful suppression which is not present in meson
decays receiving contributions gluon-penguin and/or photon-penguin
amplitudes. A related important virtue, following from their peculiar
electroweak structure, is the fact that ![](media/image27.wmf)amplitudes
can be described in terms of a single effective operator, namely

![](media/image28.wmf){width="3.990972222222222in"
height="0.42777777777777776in"}

The hadronic matrix elements of *Q~sd~* relevant for
![](media/image27.wmf) amplitudes can be extracted directly from the
well-measured *K* *e* decay rates, taking into account small Isospin
Breaking (IB) corrections. The latter have recently been estimated
beyond the leading order and turn out to be a negligible source of
uncertainty.

In the case of ![](media/image26.wmf), which is *CP*-violating and
dominated by the top-quark contribution, the SM Short-Distance (SD)
dynamics is encoded in a perturbatively calculable real function *X*
that multiplies the CKM factor *~t~=V~ts~\* V~td~*. In the
![](media/image25.wmf)case a charm quark contribution proportional to
*~c~=V~cs~\* V~cd~* also has to be taken into account, but the recent
NNLO QCD calculation of the dimension-six charm quark corrections (A.J.
Buras et al., Phys. Rev. Lett. 95, 261805) and the progress in the
evaluation of the residual Long-Distance (LD) effects (G. Isidori et
al., Nucl. Phys. B 718, 319 (2005)) elevated the theoretical cleanness
of ![](media/image25.wmf) almost to the level of ![](media/image26.wmf).
More details will be given in the following.

An striking feature of ![](media/image27.wmf) decays is that their clean
theoretical character remains valid in essentially all extensions of the
SM and that *Q~sd~*, due to the special properties of the neutrinos,
remains the only relevant operator. Consequently, in most SM extensions
the New Physics (NP) contributions to ![](media/image25.wmf)and
![](media/image26.wmf) can be parametrized in a model-independent manner
by just two parameters, the magnitude and the phase of the function

*X = \|X\| exp(i~X~)*, (2)

that multiplies *~t~* in the relevant effective Hamiltonian. In the SM,
\|*X*\| = *X~SM~* and *~X~* = 0. The parameters \|*X*\| and*~X~* can be
extracted from *B(*![](media/image26.wmf)*)* and
*B(*![](media/image25.wmf)*)* with small, controllable uncertainties,
while the function *X* can be calculated in any extension of the SM
within perturbation theory. Of particular interest is the ratio

*B(*![](media/image26.wmf)*) / B(*![](media/image26.wmf)*)~SM~* = \|*X /
X~SM~*\|^2^ \[sin(*~X~*) / sin\]^2^ (3)

Bearing in mind that \~ 21.4^o^, this equation shows that
![](media/image26.wmf) is a very sensitive function of the new phase
*~X~*, or of new sources of *CP* violation. The pattern of the two
![](media/image27.wmf)branching ratios as a function of *~X~* is
illustrated in Figure 5.1 (left). We note that the ratio of the two
modes shown in Figure 5.1 (right) depends very mildly on \|*X*\| and
therefore provides an excellent tool to extract the non-standard
*CP*-violating phase *~X~*.

![](media/image29.wmf){width="5.991666666666666in"
height="1.9215277777777777in"}

**Figure 5.1 Left: *B(K^+^* *^+^)* vs. *B(K~L~* *^0^)* for various
values of *~X~ =* *-* *~X~* (including E949 data) characterizing new
physics as discussed in the text. The dotted horizontal lines indicate
the lower part of the experimental range and the grey area the SM
prediction. We also show the Grossman-Nir (GN) bound. Right: The ratio
of the *K* branching ratios as a function of ~X~ for \|*X*\|=1.25, 1.5,
2.0. The horizontal line is again the GN bound (from A. J. Buras,et al.,
Nucl. Phys. B 697, 133 (2004) ).**

The exceptional cleanness of the two decays, and their strong
suppression within the SM, implies a sensitivity to new particles well
above the TeV scale in several realistic scenarios such as supersymmetry
or little-Higgs models (see below). As stressed in a series of recent
works, sizable non-standard effects could show up in these rare decays
without significant signals in B physics and, in specific scenarios,
even without new particles within the LHC reach. On the other hand, if
LHC finds new physics in the TeV range, then the energy scale of the new
degrees of freedom will be known and the measurements of the two
![](media/image27.wmf)rates will be essential in determining the flavor
structure of the new theory. An updated discussion about the impact of
rare K decays in the LHC era can be found in the recent review by G.
Buchalla *et al.* (arXiv:0801.1833) on which the present discussion on
![](media/image30.wmf)is largely based.

**5.1.1** ![](media/image25.wmf) **and** ![](media/image26.wmf)**in the
SM**

After summation over the three lepton families, the SM branching ratios
for the ![](media/image27.wmf)decays can be written as

![](media/image31.wmf){width="5.313194444444444in"
height="0.9881944444444445in"}

where = \|*V~us~*\|, while *~+~* = (5.165 ± 0.025) x 10^-11^ *(*
/0.225)^8^ and *~L~* = (2.231 ± 0.013) x 10^-10^ ( /0.225)^8^ include
the IB corrections in relating ![](media/image27.wmf) to the *K e* rates
(Mescia and Smith, Phys. Rev. D 76 (2007) 034017). The dimension-six top
quark contribution, *X~SM~* = 1.464 ± 0.041, accounts for 63% and almost
100% of the total rates in the charged and neutral decay, respectively.
The top-quark contribution is known at the NLO accuracy, with a scale
uncertainty of slightly below 1%. In the charged decay, dimension-six
charm-quark corrections and sub-leading dimension-eight charm and
up-quark effects, characterized by *P~c~* = 0.38 ± 0.04 and *P~cu~* =
0.04 ± 0.02, amount to moderate 33% and a mere 4%. Light quark
contributions are negligible in the case of the ![](media/image26.wmf)
decay.

Taking into account all the indirect constraints from the latest global
Unitarity Triangle (UT) fit, the SM predictions of the two
![](media/image27.wmf) rates are

*B(*![](media/image25.wmf)*)~SM~* = (8.22 ± 0.84) x10^-11^

*B(*![](media/image26.wmf)*)~SM~* = (2.76 ± 0.40) x10^-11^ (6)

with an uncertainty which is mainly of parametric nature (top- and
charm-quark masses, and CKM factors as discussed below).

While the determination of *\|V~td~\|*, sin2, and from the
![](media/image27.wmf) system is without doubt still of interest, with
the slow progress in measuring the relevant branching ratios and much
faster progress in the extraction of the angle from the *B~s~ DK* system
to be expected at the LHC, the role of the ![](media/image27.wmf) system
will shift towards the search for NP rather than the determination of
the CKM parameters.

In fact, determining the UT from tree-level dominated *K*- and
*B*-decays and thus independently of NP will allow determination of the
true values of the CKM parameters. Inserting these values in Eqs. (4)
and (5) yields very precise SM predictions for the rates of both rare
*K*-decays. A comparison with future data on ![](media/image27.wmf) may
then give a clear signal of potential NP contributions in a
theoretically clean environment. In the ![](media/image26.wmf) case,
even deviations by 15% from the SM expectations could be considered as
signals of NP, while such a conclusion cannot be drawn in most other
decays in which the theoretical errors are typically of order 10%.

**5.1.2** ![](media/image25.wmf) **and** ![](media/image26.wmf) **beyond
the SM**

[Minimal Flavor Violation]{.underline}

In models with Minimal Flavor Violation (MFV) both decays are, as in the
SM, governed by a single real function *X* that can take a different
value than in the SM due to new particle exchange in the relevant
*Z*-penguin and box diagrams. First restricting our discussion to the
so-called constrained MFV (CMFV), in which strong correlations between
*K*- and *B*-decays exist, one finds that the branching ratios for
![](media/image25.wmf) and ![](media/image26.wmf) cannot be much larger
than their SM values given in Eq. (6). The 95% probability bounds are
(Bobeth et al. Nucl. Phys. B726, 252 (2005)):

*B(*![](media/image25.wmf)*)~CMFV~* \< 11.9 x10^-11^,
*B(*![](media/image26.wmf)*)~CMFV~* \< 4.6 x10^-11^ (7)

Explicit calculations in a model with one Universal Extra Dimension
(UED) and in the littlest Higgs model without *T*-parity give explicit
examples of this scenario with the branching ratios within 20% of the SM
expectations. Effects of similar size are also found in the MFV version
of the Minimal Supersymmetric of the SM (MSSM).

Probably the most interesting property of this class of models is a
theoretically clean determination of the angle of the standard UT, which
utilizes both branching ratios and is independent of the value of *X*.
Consequently, this determination is universal within the class of MFV
models and any departure of the resulting value of from the
corresponding one measured in *B*-decays would signal non-MFV
interactions.

[Littlest Higgs Model with *T*-parity]{.underline}

The structure of ![](media/image27.wmf) decays in the Littlest Higgs
model with *T*-parity (LHT) differs notably from the one found in MFV
models due to the presence of mirror quarks and leptons that interact
with the light fermions through the exchange of heavy charged (*W~H~*)
and neutral (*Z~H~*, *A~H~*) gauge bosons. The mixing matrix *V~Hd~*
that governs these interactions can differ from *V~CKM~*, which implies
the presence of non-MFV interactions. Instead of a single real function
*X* that is universal within the *K*-, *B~d~*- and B~s~-systems in MFV
models, one now has three functions

*X~K~ = \|X~K~\| exp(i~K~), X~d~ = \|X~d~\| exp(i~d~), X~s~ = \|X~s~\|
exp(i~s~)* (8)

that, due to the presence of mirror fermions, can have different phases
and magnitudes. This possibility can have a major impact on the
![](media/image27.wmf) system, since the correlations between *K*- and
*B*-decays are partly lost and the presence of a large phase ~*K*~ can
change the pattern of these decays from the one observed in MFV. A
detailed analysis shows that both branching ratios can depart
significantly from their SM values, and can be as high as 5.0 x 10^-10^.
As shown in Figure 5.2 (left), there are two branches of allowed values
with strong correlations between both branching ratios within a given
branch. In the lower branch only *B(*![](media/image25.wmf)*)* can
differ substantially from the SM expectations reaching values well above
the present central experimental value. In the second branch
*B(*![](media/image26.wmf)*)* and *B(*![](media/image25.wmf)*)* can be
as high as 5.0 x 10^-10^ and 2.3 x 10^-10^, respectively. Moreover,
*B(*![](media/image26.wmf)*)* can be larger than
*B(*![](media/image25.wmf)*)* which is excluded within MFV models. Other
features distinguishing this model from MFV are thoroughly discussed in
arXiv:hep-ph/0610298 (M. Blanke et al).

![](media/image32.wmf){width="5.997916666666667in"
height="1.8611111111111112in"}

**Figure 5.2 Left: *B(K~L~* *^0^)* vs. *B(K^+^* *^+^)* in the LHT model.
The shaded area represents the experimental 1-range for *B(K^+^* *^+^)*.
The GN bound is displayed by the dotted line, while the solid line
separates the two areas where *B(K~L~* *^0^)* is larger or smaller than
*B(K^+^* *^+^)*. Right: *B(K~L~* *^0^e+e-)* (upper curve) and *B(K~L~*
*^0^)* (lower curve) as functions of *B(K~L~* *^0^)* in the LHT model.**

[Supersymmetry]{.underline}

Within the MSSM with *R*-parity conservation, sizable non-standard
contributions to ![](media/image27.wmf)decays can be generated if the
soft-breaking terms have a non-MFV structure. The leading amplitudes
giving rise to large effects are induced by: (i) chargino/up-squark
loops (ii) charged Higgs/top quark loops. In the first case, large
effects are generated if the left-right mixing (*A* term) of the
up-squarks has a non-MFV structure. In the second case, deviations from
the SM are induced by non-MFV terms in the right-right down sector,
provided the ratio of the two Higgs vacuum expectation values (*tan =
v~u~/v~d~*) is large (*tan* \~ 30-50).

The effective Hamiltonian encoding SD contributions in the general MSSM
has the following structure:

![](media/image33.wmf){width="5.48125in" height="0.5736111111111111in"}

where the SM case is recovered for *X~R~* = 0 and *X~L~ = X~SM~*. In
general, both *X~R~* and *X~L~* are non-vanishing, and the misalignment
between quark and squark flavor structures implies that they are both
complex quantities. Since the *K* matrix elements of (*s~L~ d~L~*) and
(*s~R~ d~R~*) are equal, the combination *X~L~ + X~R~* allows us to
describe all the SD contributions to ![](media/image27.wmf) decays. More
precisely, we can simply use the SM expressions for the branching ratios
in Eqs. (4) to (5) with the following replacement

*X~SM~ X~SM~ + X^SUSY^~L~ + X^SUSY^~R~ .* (10)

In the limit of almost degenerate superpartners, the leading
chargino/up-squarks contribution is:

![](media/image34.wmf){width="5.042361111111111in"
height="0.6756944444444445in"}

As pointed out by Colangelo and Isidori (JHEP 9809, 009 (1998)) a
remarkable feature of the above result is that no extra
*O(M~W~/M~SUSY~)* suppression and no explicit CKM suppression is present
(as it happens in the chargino/up-squarks contributions to other
processes). Furthermore, the (*^u^~LR~*)-type mass insertions are not
strongly constrained by other *B*- and *K*-observables. This implies
that large departures from the SM expectations in ![](media/image27.wmf)
decays are allowed. As illustrated in Figure 5.3 (left),
![](media/image27.wmf)are the best observables to determine/constrain
from experimental data the size of the off-diagonal (^u^~LR~) mass
insertions or, equivalently, the up-type trilinear terms
![](media/image35.wmf){width="1.5284722222222222in"
height="0.19236111111111112in"} Their measurement is therefore extremely
interesting in the LHC era.

![](media/image36.wmf){width="5.986805555555556in"
height="2.573611111111111in"}

**Figure 5.3 Supersymmetric contributions to** *K* **(from Isidori et
al. JHEP 0608, 064 (2006), Phys. Rev. D73 (2006), 055017). Left:
Dependence of various FCNC observables (normalized to their SM value) on
the up-type trilinear terms A~13~ and A~23~, for *A~ij~ \<* *A~0~* and
tan =2-4 (other key parameters in GeV: = 500 ± 10, *M~2~* = 300 ± 10,
*M~uR\ tilde~* = 600 ± 20, *M~qL\ tilde~* = 800 ± 20, *A*~0~=1000).
Right: Sensitivity to *(^d^~RR~)~23~(^d^~RR~)~31~* of various rare *K*-
and *B*-decays as a function of *M~H+~*, setting tan = 50, \< 0 and
assuming almost degenerate superparteners (the bounds from the two *K*
modes are obtained assuming a 10 % measurements of their branching
ratios while the *B~s,d~* *^+^* *^-^* bounds refer to the present
experimental limits).**

In the large tanlimit, the charged Higgs/top-quark exchange leads to:

![](media/image37.wmf){width="4.877083333333333in"
height="0.6166666666666667in"}

where *y~tH~* = *m~t~^2^/M~H~^2^*, *f~H~(x)* = *x* / 4(1-*x*) + *x* log
*x* / 4(*x*-1)^2^ and *~i,RR~ t = O*(1) for *t =* tan\~ 50. The first
term of Eq. (12) arises from MFV effects and its potential tan
enhancement is more than compensated by the smallness of *m~d,s~*. The
second term on the r.h.s. of Eq. (12), which would appear only at the
three-loop level in a standard loop expansion can be largely enhanced by
the tan^4^ factor and does not contain any suppression due to light
quark masses. Similarly to the double mass-insertion mechanism of Eq.
(11), in this case the potentially leading effect is the one generated
when two off-diagonal squark mixing terms replace the two CKM factors
*V~ts~* and *V~td~*.

The coupling of the *(s~R~ d~R~) (~L~ ~L~)* effective FCNC operator
generated by charged-Higgs/top-quark loops is phenomenologically
relevant only at large tan and with non-MFV right-right soft-breaking
terms: a specific but well-motivated scenario within grand-unified
theories. These non-standard effects do not vanish in the limit of heavy
squarks and gauginos, and have a slow decoupling with respect to the
charged-Higgs boson mass. Moreover, the *B*-physics constraints still
allow large room for non-standard effects in *K* even for flavor-mixing
terms of CKM size (see Figure 5.3 right).

**5.1.3 Theoretical Uncertainties**

In the following sections on experimental prospects at Fermilab for
![](media/image25.wmf)and ![](media/image26.wmf), we outline a series of
measurements culminating with O(1000) events, in each channel, at the
rates predicted by the Standard Model. Here we outline the main sources
of theoretical uncertainty in the SM predictions and discuss prospects
for reducing them over the coming decade.

We expect that the measurements will remain statistics limited, so the
target for the theoretical uncertainty on the rate is 3%. The present
status, Eqs. (6), of the SM calculations yield total "theoretical"
uncertainties of 14% (*K~L~*) and 10% (*K^+^*). In both cases, the
dominant error comes from the determination of the CKM matrix, which in
Eqs. (6) is taken from the global UT fit. Other important uncertainties
stem from the experimental error in *m~t~*, experimental and theoretical
errors in *~s~*, theoretical errors in *m~c~* (for *K^+^* only),
higher-order electroweak and QCD corrections, higher-dimension
contribution with a charmed quark (for *K^+^* only), and long-distance
effects (for *K^+\ ^*only).

Let us start with the neutral mode. It is convenient to summarize the
theoretical calculation in a way that shows the origin of the
uncertainties:

![](media/image38.wmf){width="5.481944444444444in" height="0.6875in"}

where *r~KL~* = 0.944 summarizes corrections to isospin symmetry,
necessary to extract the semileptonic form factor from *K^+^ ^0^e^+^*.
Higher-order corrections would improve the short-distance factor *X*,
which is where the *m~t~* and *~s~* dependence enter. In the region of
interest *X*(*m~t~*) \~ *m~t~*^1.15^; if, as seems likely, the Tevatron
and LHC experiments bring the error in the top mass down to 0.5%, then
the error from this source in Eq. (13) from *m~t~* fits within the error
desired budget. A more subtle concern, when *m~t~* is so precise, is how
to connect the experimental definition of *m~t~* with a clear
field-theoretical concept necessary for compatibility with perturbative
QCD corrections to *X*. Similarly, it seems likely that the precision of
, sin*~W~*, and *~s~* are good enough, but care is needed to make sure
that all factors in Eq. (13) are in the same scheme.

The most challenging uncertainties are in the CKM factors. At the
amplitude level one has

![](media/image39.wmf){width="5.23125in" height="0.6270833333333333in"}

where the first relation exploits three-generation unitarity, and the
last form uses the Wolfenstein parametrization. If one is confident that
new physics does not alter the rate, then the rate prescribes a precise
constraint on the CKM combination (*A*^24^)^2^. At the percent level of
precision, however, it is more likely that (and more interesting if) new
TeV-scale physics interferes with the SM. Then, to obtain a precise test
of the SM, the CKM parameters must be improved by other means.

Two general strategies may be envisioned, either determining individual
CKM elements directly, or constraining the four free parameters of the
CKM matrix through a global fit. In the context of searches for
percent-level deviations from the SM, these strategies may be not so
different: processes that occur at the tree level of the electroweak
interactions will be used to determine CKM, with SM loop processes used
for searches. A global fit based on SM-dominated processes could, then,
leverage several quantities to improve the overall precision.

For this document we will focus on the direct approach. The current
error on \|*V~us~*\| is close to 1%, with *K~13~* and *K~12~* decays
giving similar accuracy and good agreement. Within the next decade
improvements in lattice QCD will reduce the error further, and better
computing resources will enable lattice calculations with several
formulations of the computationally demanding sea quarks. As long as one
does not propagate errors in *B(*![](media/image26.wmf)*)* as *^8^*, the
error from \|*V~us~*\| = is not an obstacle.

The current error on \|*V~cb~*\| is also close to 1% from inclusive
semileptonic decays of B mesons. With a recent unquenched lattice
calculation for the exclusive decay *B D\*l*, however, the inclusive and
exclusive determinations disagree. (The error on the exclusive method is
2-3% and the discrepancy is 8%.) Nevertheless, this discrepancy will
very likely be resolved before a 1000-event experiment taken place
because it has repercussions throughout flavor physics.

The real challenges come from *V~ub~*. The magnitude comes from
semileptonic decays, inclusive or exclusive, and the phase from *CP*
asymmetries. At present the theoretical uncertainties on \| *V~ub~* \|
are 5-10%, for both inclusive and exclusive approaches. One will
probably have to tame higher-dimension corrections to the inclusive
rate, to attain percent-level accuracy. This may not be feasible. For
the exclusive decays, one must focus on *B l*, and compute the decay
form factor with lattice QCD. The current error budget contains several
few-percent contributors, so it will be challenging, albeit feasible, to
control all of them at the sub-percent level. The LHCb experiment
forecasts an uncertainty in the UT angle *= ~KM~* of 5^o^ (2.5^o^) in 2
fb^-1^ (10 fb^-1^). For\~ 80^o^, this corresponds to a 1% (0.6%) error
in sin*~KM~*.

In summary, reducing the parametric and theoretical uncertainties in
*B*(![](media/image26.wmf))~SM~ to the 3-5% level seems feasible, but
challenging both for theory (particularly lattice QCD) and experimental
(for sin*~KM~*).

For the charged mode, the analog of Eq. (13) reads

![](media/image40.wmf){width="5.311111111111111in"
height="1.0791666666666666in"}

where *r~K+~* = 0.901 summarizes corrections to isospin asymmetry,
similarly to *r~KL~*. The short-distance contribution of the charmed
quark, *X~NL~(m~c~, m~t~, ~s~)*, sums large logarithms ln(*m~c~/M~W~*)
and depends on the lepton mass *m~l~*. The contribution *X~NL~(m~c~,
m~t~, ~s~)* is GIM-suppressed relative to *X(m~t~, ~s~)* by
(*m~c~/m~t~*)^2^, so only the O(l) real part of *V~cs~\*V~cd~* plays a
significant role, even at the percent level. In addition to CKM
uncertainties, an important uncertainty comes from the charmed-quark
mass, taken in Eqs. (6) to be *m~c~* = 1.30 ± 0.05, leading to a 5%
uncertainty in *B(*![](media/image25.wmf)*)*. Unquenched lattice QCD
calculations with a non-perturbative mass renormalization could cut this
in half, bringing us close to the target. An additional complication for
the charged mode, when the target is 3% precision, is the contribution
from the up quark in the loop. Here one can have long-distance effects
of the form *K^+^ ^0^l^+^ ^+^***.** A combination of ChPT and lattice
QCD should be able to control this contribution at the needed level.

In the charged mode, the combined error from CKM uncertainties and the
charmed-quark mass may make it difficult to reduce the theoretical error
to 3%. Much of the CKM error cancels, however, in the ratio
*B(*![](media/image25.wmf)*) / B(*![](media/image26.wmf)*)*. If we can
observe 1000 events of each, it may be most incisive to confront the
ratio and *B(*![](media/image26.wmf)*)* with the SM. In both cases the
theoretical and experimental errors would be comparable.

**5.1.4 Conclusions**

The rare ![](media/image27.wmf) decays are excellent probes of new
physics. Firstly, their exceptional cleanness allows access to very high
energy scales. As stressed in a series of recent works, new physics
could be seen in rare *K* decays without significant signals in
*B~d,s~*-decays and, in specific scenarios, even without new particles
within the LHC reach. Secondly, if LHC finds new physics, its energy
scale will be fixed. Then, the measurements of the two
![](media/image27.wmf)rates would be very helpful in discriminating
among models.

The sensitivity to the scale of new physics from precise measurements of
these modes grows like 1/, where is the relative experimental error.
This growth is valid up to the level where the theory errors start to
dominate (i.e. up to \~3% measurements). The normalization of this law
depends on the flavor structure of the model. In pessimistic scenarios
(such as MFV models), new particle masses in the (few) x (100 GeV) range
can be accessed with \~3%, while with the same precision new particles
well above the TeV (even up to 10 TeV) are probed in new physics models
with a non-minimal flavor structure.

It is worth stressing that if a deviation from the SM is seen in one of
the two ![](media/image27.wmf) channels, key independent information
about the nature of new physics can be obtained also from the two *K~L~
^0^l^+^l^-^ (l=e,)* modes. The latter are not as clean as the neutrino
modes, but are still dominated by SD dynamics and very sensitive to new
physics. Different correlations among these four channels are expected
in different models (see e.g. Figure 5.2). These correlations can be
used as powerful tests to shed light on the nature of new effects. In
all cases where visible effects are found, the information extracted
from the four modes is essential to establish the new flavor structure
in the *s d* sector. Rare *K* decays are thus an integral part, along
with B-physics and collider observables, of the grand project of
reconstructing the best model from data.

# 5.2 Prospects for Measuring ![](media/image41.wmf) at Fermilab

**5.2.1 General Considerations and the KOPIO Experiment at BNL**

Definitively measuring ![](media/image41.wmf) decay at the few 10^-11^
branching ratio level represents a significant experimental challenge.
The poorly defined signal consists of a neutral kaon followed by a
neutral pion, *K~L~^0^*, with the pion immediately decaying into two 's
with no other observed particles. Potential backgrounds, from other *K*
decays, at branching ratios many orders of magnitude higher, have
similar signatures. In addition, neutrons, which are inevitably present
in a neutral beam, can create *^0^*s from material in or near the beam.
Therefore, the experimental strategy involves proving that candidate
events have low probabilities of being due to background. The principal
intrinsic source of background is *K~L~^00^* with branching ratio 8.64
10^-4^. This can fake signal either when one of the two *^0^*s is missed
entirely by the detector, or when one from each of the *^0^*s is missed
and the two odd 's happen to reconstruct to a *^0^* to within the
resolution of the detector. Another kaon-induced background comes from
*K~L~3^0^* which is much less likely to be mistaken for the signal but
which has a much higher branching ratio. Other backgrounds can be
induced by *K~L~^+-0^* to the extent that charged particle vetoing is
imperfect, and *K~L~ ^-^e^+^* if charged particle vetoing fails and the
two charged particles manage to make or appear to be 's. There are many
other possible background processes.

Any attempt to detect ![](media/image41.wmf) must rely on extremely
efficient charged and neutral particle vetoing and very good resolution
for 's. There have been two approaches suggested, basically a high and a
low energy approach. The former relies on a small, intense forward beam
of kaons, high resolution detection and the highly efficient neutral and
charged vetoing possible at high energies. The dedicated
![](media/image41.wmf) experiment, KEK-391a, has taken this approach
(although the KEK-PS was limited to medium energies), and recently
released a new 90% CL upper limit, *B(*![](media/image41.wmf)*)* \< 6.7
10^-8^. This experiment will be upgraded and moved to JPARC where a
future second phase (presently not defined) will seek a clear
measurement. The low energy approach was epitomized by the KOPIO
experiment proposed for the Brookhaven AGS which aimed at accumulating
several hundred events. [^2]

The low energy technique is illustrated in Figure 5.4. It focuses upon
obtaining the maximum possible information about each event, i.e. the
direction, energy, production time and decay position of the K~L~, and
the directions, energies and times of the 's. In addition, it requires
highly efficient hermetic rejection of events (vetoing) with extra
particles. A low energy neutral beam is created by protons tightly
bunched in time, so that the production time of the kaons is known,
modulo the 25 MHz period of the proton μ-bunches. Combined with
direction and timing measurements on the final state 's, this gives the
time-of-flight (TOF) and therefore the energy of the incident kaon. The
directional measurement of the 's also gives the kaon decay position,
assuring that the photons originated in a ![](media/image42.wmf) decay.
Finally, energy measurement of the 's allows powerful kinematic
constraints to be imposed on candidate events in the
![](media/image43.wmf) center-of-mass system.

![](media/image44.png){width="2.875in" height="1.3395833333333333in"}

**Figure 5.4 Left: The principles of the low energy approach to
measuring** ![](media/image41.wmf)**. Right: Kinematic measurements.**

In order to optimize the low energy beam to enable the TOF technique
(with usable *K~L~*'s between 0.4 and 1.4 GeV/c), it is necessary to go
to a very large production angle. To obtain the high flux necessary for
a measurement at the 10^-12^/event level, KOPIO was forced to use a
rather large beam solid angle; to maintain at least one beam kinematic
constraint the beam profile was made very asymmetric, (narrow in the
vertical and extremely wide in the horizontal). Figure 5.5 shows the
result of a simulation of a 6000-hr KOPIO run. Figure 5.6 shows the
results of a maximum likelihood analysis developed to use events of
varying signal to background resulting in the precision of a measurement
at the Standard Model level \~11%.

![](media/image46.png){width="3.064583333333333in"
height="3.064583333333333in"}

> **Figure 5.5 Signal/background vs number of signal events for 6000-hr
> run of KOPIO at the BNL AGS. Beyond S:B of \~1:2, the gain in
> precision is very slow, and the requirements on knowledge of the
> background become more and more difficult to meet.**

![](media/image47.png){width="4.622916666666667in"
height="3.557638888888889in"}

**Figure 5.6 Reach of KOPIO experiment (as of 2005) as a function of
running time. Solid lines show the 5 limits in terms of branching ratio
relative to that of the Standard Model (SM). Dashed lines show the
corresponding 3 limits. "Equivalent Standard Model Events" means the
number of SM events with no background that would have equivalent
reach.**

**5.2.2.**![](media/image41.wmf)**at Fermilab**

Given the possible progression of 8 GeV intensity at Fermilab from the
existing Booster complex to Project X beams, a low-energy
![](media/image41.wmf) experiment is a very appealing possibility. As
will be discussed below, an experiment at the SM-level precision \~3%
(7-10%) appears feasible for Project X (Booster intensity) beams.
Perhaps the most attractive approach is a version of the low energy
experiment in which the beam aperture is substantially reduced compared
to KOPIO. This would allow the experiment to benefit greatly from any
increase in the available proton flux. Moreover it would be much easier
to mount, and more robust than KOPIO. The large beam aperture was a
factor that made KOPIO as technically challenging as it was due to the
very large, very thin vacuum chamber required.

To make estimates of the sensitivity achievable at Fermilab, we assume
based on simulations that the effective cross section at 8 GeV is half
of that at 21 GeV and compare with projections for the experiment
proposed at BNL. In terms of available protons, we also assume Booster
performance of 22.5 x 10^12^ every 1.4 second where the average proton
flux per second is 16.1 x 10^12^ which is 60% that assumed at BNL; when
factors relating to accidental losses are taken into account the ratio
of effective kaons per second is 0.93. When Project X beams are
available at 10 times the intensity of the Booster, significant further
progress in precision can be made although the technique is eventually
limited by instantaneous rates of various types (accidental spoiling of
events by other kaon decays in the same microbunch, accidentals due to
stopped muons, accidentals due to neutron interactions in the beam veto,
etc.). Figure 5.7 shows the effective yield relative to that for the
Booster, as a function of the relative proton intensity available for
the KOPIO beam geometry. Using three times Booster intensity provides
the maximum gain. Based on parameter variations studies, one could
benefit significantly by improving on the resolutions.

![](media/image48.wmf){width="3.3229166666666665in"
height="4.069444444444445in"}

**Figure 5.7 Relative effective yield of a KOPIO-type experiment at
Project X, as a function of the ratio of the proton intensity relative
to that available at the Booster.**

A possible approach for a Fermilab ![](media/image41.wmf) is to put the
entire experiment in vacuum and to use a small symmetric beam aperture.
Placing all detectors in vacuum would remove the difficult thin vacuum
vessel but would require vacuum operation of the preradiator photon
tracking chambers. Reducing the size of the beam would make the
experiment much less difficult. Many mechanical issues would be made
easier and the experiment could be reconfigured to have a considerably
higher acceptance. Moreover, many types of background would be
diminished or eliminated. As mentioned above, the spoiling of event
candidates by additional decays in the same *μ*-bunch would be much
reduced. The loss in effective statistics due to the small beam
acceptance would be somewhat mitigated because of the reduction in
accidentals, and in spoilage by additional events in a *μ*-bunch.
However, the reconfiguration of the experiment that this geometry allows
could result in an increase in geometric acceptance of a factor 2 or
even more. Assuming improvements up to a factor 4.3 for the best events
(S/B \~ 8) and 1.7 for medium quality events (S/B \~ 2) a statistical
precision of 10% may be reached at the Booster intensity level in a 5
year run. At initial Project X intensity (10 x Booster intensity), 300
equivalent events would be observed per year which allows a 3%
measurement to be made for ![](media/image49.wmf). The sensitivity of
the experiment would continue to increase if more proton intensity were
available. At 60 times the Booster intensity there would be \~900
equivalent events per year. As shown in Figure 5.8, this is the peak
sensitivity that could be reached given the above assumptions although
optimization promises to provide further gains.[^3]

![](media/image50.wmf){width="3.490972222222222in"
height="4.522916666666666in"}

**Figure 5.8 Equivalent events per year for a small aperture, low energy
experiment as a function of the proton intensity.**

# 

# 5.3 Prospects for Measuring ![](media/image51.wmf) at Fermilab

Definitively measuring ![](media/image51.wmf) decay at the
![](media/image52.wmf) branching ratio level represents a significant
experimental challenge. The poorly defined signal consists of a charged
kaon followed by a charged pion,![](media/image53.wmf), with no other
observed particles. Potential backgrounds, primarily from other K decays
at branching ratios 10 orders of magnitude higher, have similar
signatures. Therefore, the experimental strategy involves proving that
candidate events have low probabilities of being due to background. The
principal sources of background are shown in Figure 5.9. To be
successful at detecting ![](media/image51.wmf) and separating it from
background, the detector must have powerful π^+^ identification so that
![](media/image54.wmf)and ![](media/image55.wmf) decays can be rejected,
highly efficient 4π solid angle photon detection coverage for vetoing
![](media/image56.wmf) events and other decays, and an efficient K^+^
identification system for eliminating beam-related backgrounds.

![](media/image57.wmf){width="3.6256944444444446in"
height="2.8465277777777778in"}

**Figure 5.9 Momentum spectra (in MeV/c) of charged particles from
*K^+^* decays in the rest frame. The values in the parentheses represent
the branching ratios of the decay modes. The hatched spectrum shows the
*π^+^* momentum from** ![](media/image51.wmf)**decay assuming the V − A
interaction.**

BNL E949 (which was upgraded from E787) was the culmination of long
series of stopped kaon experiments searching for ![](media/image51.wmf)
spanning 50 years. Like its predecessors, it employed a low momentum
beam of stopping kaons. E949 used a 710 MeV/c ![](media/image58.wmf)
beam which was slowed in a degrader and stopped in a scintillating fiber
detector. Measurement of the ![](media/image51.wmf) decay involved
observation of the daughter π^+^ in the absence of other coincident
activity. The π^+^ was identified by its kinematic features obtained
from energy in scintillator calorimeter, momentum, and range
measurements. In addition, E949 used high-speed digitizers on all fast
detectors to make precise observations of the complete
![](media/image59.wmf)decay sequence. The entire E949 spectrometer was
surrounded by a 1 T solenoidal magnetic field along the beam direction.
In addition to the use of scintillating fibers and the large systems of
500 MHz digitizers, the challenges of E949 spurred the development of
the world's most efficient detector of radiation and the invention and
development of a version of blind analysis methodology to avoid bias in
background predictions and analysis of data. The numerous sources of
potential background were extensively studied in E787 and E949 resulting
in reliable and testable background predictions and a likelihood
analysis method for evaluating potential candidate events for
probability of being due to ![](media/image51.wmf) or background. For
the entire data sets from the E787/E949 experiments the number of
background events expected was considerably less than 1 event.

![](media/image60.wmf){width="5.996527777777778in" height="2.06875in"}

> **Figure 5.10 Schematic side (a) and end (b) views of the upper half
> of the E949 detector. Illustrated in this figure, an incoming K+ that
> traverses all the beam instruments, stops in the target and undergoes
> the decay** ![](media/image61.wmf)**. The outgoing π+ and one photon
> from** ![](media/image42.wmf) **are also shown.**

Three events consistent with ![](media/image62.wmf) decay were observed
by E787 and E949 in the momentum region 211 ≤ *P* ≤ 229 MeV/c as shown
below in Figure 5.11. The branching ratio observed was
![](media/image63.wmf). The estimated probability that all the
![](media/image51.wmf) candidates observed by E787 and E949 were due to
background was 0.001. The measured branching ratio was twice as large as
the SM prediction of ![](media/image64.wmf) but was consistent within
the uncertainty. Limits were obtained from E787 data for the phase space
region below the *K~π2~* peak, and E949 data are still under analysis.
E787 and E949 also studied many other rare K decay processes and
provided the most sensitive searches for several non-Standard Model
processes such as ![](media/image65.wmf) where a is an axion.

![](media/image66.wmf){width="2.78125in" height="2.9270833333333335in"}

**Figure 5.11 Range vs kinetic energy of the events satisfying all of
the cuts, except for the phase space cuts on both the range and energy.
The plot shown combines E787 and E949 data. The inner rectangle
represents the signal region defined in E787 (dashed lines) and E949
(solid lines). Events near *E* = 108 MeV were due to *K~π2~* decays
which were not removed by the photon veto cuts. The light points
represent the expected distribution of** ![](media/image51.wmf) **events
from simulation.**

The CERN NA62 experiment proposes to take the next step in sensitivity
of up to 80 SM events with a promising high energy in-flight decay
experiment. Other ultra-rare in-flight decay experiments such as the
search for *K~L~ e* have obtained very high sensitivities, but the new
techniques proposed for the high
sensitivity![](media/image67.wmf)in-flight experiment have yet to be
demonstrated.

In order to evaluate the potential of a new stopping kaon experiment
driven by 8 GeV beams potentially available at the Fermilab Booster (16
kW) and upgraded to Project X (205 kW), we will extrapolate from the
experience of E949 taking advantage of the potential for incremental
improvements in a well-established technique. All estimates are made
relative to the expectations for E949 at the BNL AGS.[^4] For the
Fermilab experiments, it is assumed that kaon beams of lower momentum,
e.g. 450-400 MeV/c will be used instead of the 710 MeV/c used by E949,
in order to improve the kaon stopping efficiency to approximately 70%
from 20% in E949. In addition, the following assumptions were made:

-   **Project X primary beam properties.** It is assumed there will be
    ![](media/image68.wmf) (10 x higher than for the existing Booster
    complex) available at 8 GeV for 5000 hrs./yr. with a 100% duty
    factor.

-   **K Production Cross Sections at 8 GeV.** *K* production cross
    sections at 0 degrees for 8 GeV protons relative to 21.5 GeV protons
    were estimated using several codes. The values for 8 GeV yields at
    450 and 400 MeV/c relative to those for 21.5 GeV at 710 MeV/c were
    estimated to be 0.16 and 0.11.

-   **Kaon beam line:** A separated beam of 13 m length with acceptance
    of 25 msr was assumed for operation at ![](media/image69.wmf). This
    would be a gain of a factor of about 2 in solid angle acceptance and
    1.2 in momentum acceptance relative to LESB3 at the AGS used by
    E949.

-   **Detector Improvements.** For the Fermilab experiments, a momentum
    spectrometer with a 2-3 T magnetic field will be assumed allowing
    the detector to be considerably smaller in diameter than the E949
    detector; the detector can also be made longer to increase the
    momentum acceptance. A detector of reduced radius will facilitate
    many improvements in performance: 1) The small overall acceptance
    attained by E949, approximately 0.002, was due in part to the
    necessity for tight cuts suppressing muon backgrounds; isolated
    accidentals in the range stack (RS) counter where the pion stopped
    could fake the second pulse in the ![](media/image70.wmf) decay
    sequence. Using much finer segmentation of the RS (e.g. 5 mm x 5 mm
    elements instead of the 20 mm x 200 mm counters of E949) this
    background source would be suppressed by a factor of 100 allowing a
    significant improvement in acceptance. Fine segmentation of the RS
    will also facilitate improvements in
    ![](media/image71.wmf)tracking; 2) It will be assumed that 2x better
    momentum resolution can be obtained due to the higher field. This
    will make 2-body background rejection easier and result in
    acceptance gains; 3) The smaller detector will allow use of a higher
    quality non-sampling photon veto detector such liquid xenon with
    more radiation lengths than in E949. This will also result in better
    background rejection and higher acceptance. Overall, an acceptance
    gain of 2.5 will be assumed.

-   A**ccidental losses.** Accidental losses (killing of valid events)
    due to extraneous hits in the photon veto system were substantial in
    E949. These accidental losses appeared to scale with the incident
    flux, or kaon energy E~k~ lost by beam kaons which did not stop in
    the E949 target; although there was some accidental spoiling from
    old ![](media/image72.wmf) decays it appears that most of the losses
    were due to kaons which interacted in the E949 absorber producing
    neutral particles interacting in the RS. Applying this model to the
    Fermilab experiments which would be run at much lower momenta with
    consequently much higher stopping efficiency, accidental spoiling
    would be much less of a problem resulting in only small acceptance
    losses.

Based on the assumptions above and five years of operation, the number
of events to be expected for Fermilab experiments using the 8 GeV
Booster intensity and the projected Project X (206 kW) beams would be
approximately 200 and 1300, corresponding to an anticipated precision,
including projected background subtraction, of approximately 10% and 3%
respectively. Further improvements in precision could be anticipated if
the beam power were to increase.

# 5.4 Kaon Strategy

The kaon experimental strategy consists of developing a set of
world-class experiments that evolve into world-leading experiments in a
phased approach with ever increasing beam intensities and relatively
modest detector upgrades. The physics reach of this program compared to
other world-wide programs is tabulated below. The world-class
experiments can be driven with an 8 GeV Booster beam, followed by
world-leading experiments driven by Project X beam. This evolution is
illustrated in the road-map. The road-map and table below includes the
possibility of 120 GeV Main Injector beam driving higher energy kaon
experiments that are not discussed here, but could play an important
role if the schedule for Project X is substantially delayed.

+-----------------------------------+-----+-----+-----+---------------+
| Facility                          | D   | Cl  | B   | Projected     |
|                                   | uty | ock | eam |               |
|                                   | Fac |     | ho  | \# of K       |
|                                   | tor | ho  | urs |               |
|                                   |     | urs |     | per year      |
+-----------------------------------+-----+-----+-----+---------------+
| CERN-SPS (450 GeV)                | 30% | 1   | 405 | 40 (charged)  |
|                                   |     | 420 |     |               |
+-----------------------------------+-----+-----+-----+---------------+
| FNAL: Booster Stretcher (8GeV,    | 90% | 5   | 5   | 40 (charged)  |
| 17kW)                             |     | 550 | 000 |               |
+-----------------------------------+-----+-----+-----+---------------+
| FNAL: Main Injector-Tev-Stretcher | 90% | 5   | 5   | 200 (charged) |
| (120 GeV)                         |     | 550 | 000 |               |
+-----------------------------------+-----+-----+-----+---------------+
| FNAL: Project X Stretcher (8GeV,  | 90% | 5   | 5   | 250 (charged) |
| 200kW)                            |     | 550 | 000 |               |
+-----------------------------------+-----+-----+-----+---------------+
| JPARC-I (30 GeV)                  | 21% | 2   | 580 | \*\~1         |
|                                   |     | 780 |     | (neutral)     |
+-----------------------------------+-----+-----+-----+---------------+
| BNL AGS (24 GeV)                  | 50% | 1   | 600 | 20 (neutral)  |
|                                   |     | 200 |     |               |
+-----------------------------------+-----+-----+-----+---------------+
| JPARC-II (30 GeV)                 | 21% | 2   | 580 | \*30          |
|                                   |     | 780 |     | (neutral)     |
+-----------------------------------+-----+-----+-----+---------------+
| FNAL: Booster Stretcher (8GeV,    | 90% | 5   | 5   | 30 (neutral)  |
| 17kW)                             |     | 550 | 000 |               |
+-----------------------------------+-----+-----+-----+---------------+
| FNAL: Project X Stretcher (8GeV,  | 90% | 5   | 5   | 300 (neutral) |
| 200kW)                            |     | 550 | 000 |               |
+-----------------------------------+-----+-----+-----+---------------+

\*For JPARC, we assume that neutrino and kaon programs share the beam
(50% - 50%).

[Developing a Common Platform]{.underline}

The charged and neutral kaon experiments driven by an 8 GeV beam could
likely share a common target station, possibly without compromising flux
for either experiment, thereby easing proton economics. These
experiments share experimental and theory proponents, beam and detector
technology issues, design and analysis techniques. The proponents could
naturally self-organize into a common collaboration that would be best
suited to develop the details of the Fermilab kaon roadmap matched to
various resource profiles. (This collaboration would be robust against
variations in the relative schedule between the charged and neutral
programs that could arise through limited-resource staging pressures or
the state of world-wide competition.) A plausible scenario is the
relatively early start of the![](media/image51.wmf) experiment that
benefits from the BNL E787/E949 recent experience, followed by a start
for the ![](media/image49.wmf) experiment which ultimately may be more
incisive but may benefit from additional R&D. The resources required for
construction and early start of the charged program are likely less than
the neutral program, and the![](media/image51.wmf) experiment does not
require the micro-bunching RF beam structure necessary for the neutral
experiment.

A cohesive approach also leverages the usefulness of these modes to
understanding new short-distance physics. Although each mode is
interesting in its own right, the combination of both measurements
provides an incisive test of flavor violation mediated by new particles,
such as those that may be observed at the LHC.

[The R&D Phase Today through 2010:]{.underline}

The next generation ![](media/image51.wmf) experiment will benefit from
the past decade of HEP detector R&D that has made major strides in very
low-mass tracking, calorimetry and data acquisition. One year of design
effort will be necessary to transfer these R&D dividends to the next
generation experiment based on the stopped kaon technique. For the
![](media/image49.wmf)experiment new detector technologies have emerged
recently, in particular, charged particle tracking in vacuum, which may
substantially improve the performance of the experiment. R&D will be
necessary to exploit these recent developments and to design the
![](media/image49.wmf) experiment so that it can take full advantage of
the Project X intensity. In parallel with development of the detector
projects, the 8 GeV slow-spill source, RF structure, target station and
beamlines must be developed.

[The Phase-I Construction and Operation Phase, 2011-2018:]{.underline}

Both the ![](media/image51.wmf) and![](media/image49.wmf) experiments
will be multi-year construction efforts. As previously noted,
construction of the ![](media/image51.wmf) experiment could plausibly
start earlier and be shorter in duration. Early results from either the
JPARC neutral experiment or the CERN charged experiments, if they take
place, could inform staging, particularly if an anomalous signal is
seen. New physics seen at the LHC in this time-frame may also influence
the sequence of events leading to these experiments.

[Transitioning to Project X intensity 2018-2020:]{.underline}

Both experiments will be designed at the outset to exploit the intensity
upgrade of Project X. It is likely however that some upgrades to the
detectors and beamlines will be necessary for this step. After this
transition the![](media/image51.wmf) and ![](media/image49.wmf)
experiments will lead the field and will be in a position to deliver
very high sensitivity. During this phase, both experiments will detect
O(1000) events (at the Standard Model rate). The resulting 3% precision
is well matched to the theoretical and parametric uncertainties expected
at this time. These measurements, with their well-understood theoretical
description, will be needed to help distinguish between competing models
that accommodate the TeV-scale discoveries of the LHC.

# 5.5 Kaon Summary

Precise measurements of the rare decays ![](media/image51.wmf) and
![](media/image41.wmf) are essential for a deeper understanding of the
mechanism of flavor mixing and *CP* violation. Among the many rare *K*-
and *B*-decays, the ![](media/image27.wmf) modes are unique: they are
highly sensitive to new physics at mass scales up to *O*(1000) TeV, and
their Standard Model rates can be computed to exceptionally high degrees
of precision, not matched by any other flavor-changing neutral current
process involving quarks. Fortunately, precise measurements of
![](media/image51.wmf) and ![](media/image41.wmf) at the few per cent
precision (at the SM levels) appear to be feasible at Fermilab beginning
with the 8 GeV Booster level intensity and progressing to the use of the
intense beams of Project X. The charged mode ![](media/image51.wmf) has
already been observed at BNL and an evolution of the well established
technique would confidently yield a high statistics result. Observation
of the more challenging neutral mode would be pursued using a carefully
studied proposed method involving neutral *K* time-of-flight for
suppression of backgrounds; beginning at the Booster intensity level and
progressing to Project X would also yield a clean high sensitivity
result. The combination of these high precision measurements on
![](media/image27.wmf) and decays, in conjunction with complementary
proposed efforts at CERN and JPARC, would result in a powerful
contribution to the interpretation of possible new physics appearing at
the LHC or at much higher mass scales.

**6 Charm Mixing and *CP* Violation Program at the Tevatron**

Over the past year the Belle and Babar experiments have published
evidence for mixing in the *D*^0^ system (Belle Collaboration, Phys.
Rev. Lett. 98, 211803, 2007, and Babar Collaboration, Phys. Rev. Lett.
98, 211802, 2007). The CDF experiment has also presented evidence for
this effect (CDF Collaboration, arXiv:0712.1567; submitted to Phys. Rev.
Lett.). These measurements indicate a relatively large value for the
mixing parameter *y* of \~1%; for *x =* *M*/, a statistically
significant nonzero value is obtained from a fit combining all
measurements of *D*^0^ mixing parameters (http://www.slac.stanford.
edu/xorg/hfag/charm/Beijing07/results_mix+cpv.html). If the values of
*x* and *y* turned out to be larger than SM predictions, or if *x* \>\>
*y*, new physics would be indicated. To search for *CP*-violating
effects, *x* and *y* can be measured separately for *D*^0^ and
anti*D*^0^ decays. *CP* violation is parameterized by the ratio of the
complex coefficients relating flavor eigenstates to mass eigenstates,
\|*q/p*\|, and by a possible weak phaseArg*q/p*). Differences in
\|*q/p*\| and from 1 and 0, respectively, would indicate new physics.
Figure 3.4.1 (left) shows the current Heavy Flavors Averaging Group
(HFAG) confidence contours for \|*q/p*\| and
(http://www.slac.stanford.edu/xorg/hfag/charm/Beijing07/results_mix+cpv.
html). The central value is one standard deviation away from the
no-*CP*-violation point.

There has been a series of fixed-target charm experiments performed at
Fermilab using both photon and hadron beams. Technological advances that
have occurred since those experiments ran (*e.g.*, in radiation-hard
tracking, triggering, and computing) could greatly increase the
sensitivity of such experiments. It is now feasible to trigger on decay
vertices at the first or second level. The latter was realized by the
HERA-B experiment at DESY, and the former was planned for the BTeV
experiment at the Tevatron. Such a trigger would allow an experiment to
run at much higher interaction rates than previously, and thus greatly
increase the number of recorded charm decays. Recently, some work has
begun to study the feasibility of a fixed-target-geometry experiment
running at the Tevatron. The goal would be to measure the mixing
parameters *x* and *y* and *CP*-violating parameters \|*q/p*\| and with
very high statistics. Below we estimate the expected sensitivity and
compare it to that expected for *ee* experiments Belle and Babar. We
also briefly discuss prospects for LHCb.

**6.1 Expected Sensitivity**

We scale our sensitivity estimate from that of HERA-B. This experiment
reconstructed 61.3 13 "*D*^\*^-tagged" Cabibbo-favored *D*^0^ *K* decays
in 182 x 10 hadronic interactions (HERA-B Collaboration, Eur. Phys.
Jour. C 52, 531, 2007). Multiplying this yield by the ratio of partial
widths (*D*^0^ *K* ) */* ( *D*^0^ *K* ) = 0.377% gives a *D*^0^ *K*
fractional yield (including trigger and reconstruction efficiencies) of
1.3 x10^9^. If we assume a future fixed-target experiment runs at a 5
MHz interaction rate (as achieved by HERA-B), then in one year of
running the experiment could potentially reconstruct (5 MHz)(2 x 10^7^
s)(1.3 x 10^9^)(0.5) = 64,000 tagged *D*^0^ *K* decays, where we have
assumed a trigger efficiency of 50% relative to that of HERA-B. We can
also scale from the E791 experiment, which reconstructed \~35
*D*^\*^-tagged *D*^0^ *K*decays in \~5 x 10^10^ hadronic interactions
(E791 Collaboration, Phys. Rev. D 57, 13, 1998). These values imply a
fractional yield of 7 x 10^10^, and thus an absolute yield of 35,000
events per year. Here we have assumed a trigger and selection cut
efficiency of 50% relative to that of E791. This assumption is
conservative, as E791 had a deadened region in the center of the drift
chambers where the 500 GeV beam passed through. If we assume a
reconstruction efficiency similar to that of the FOCUS photoproduction
experiment, we obtain a yield of \~70,000 events per year.

To compare with the *B* factories, we note that Belle has reconstructed
4024 *D*^\*^-tagged *D*^0^ *K* candidates in 400 fb^1^ of data (Belle
Collaboration, Phys. Rev. Lett. 96, 151801, 2006). If the *B* factories
were to run until an aggregate sample of 1500 fb^1^ were collected, they
would have a total of 15,000 *D*^0^ *K* decays, only 1/4 to 1/2 of our
estimate for a fixed-target experiment after one year of running. Three
years of fixed-target running could provide more than an
order-of-magnitude more decays, substantially increasing the sensitivity
to *x* and *y*. This is just one example of the mixing and *CP*
measurements possible. It should also be noted that a fixed-target
experiment would have much better lifetime resolution than that of the
*B*-factory experiments. This would reduce backgrounds and also
systematic errors in time-dependent measurements.

To compare to LHCb, we use numbers from a Monte Carlo study of the
sensitivity of LHCb to *D^\*+^* *D*^0^*~tag~* *K* *~tag~* decays (LHCb
public note LHCb-2007-049, July 10, 2007). Assuming *~bb~* = 500 b, and
estimating various trigger and reconstruction efficiencies, this study
concludes that 58,000 "wrong-sign" signal decays would be reconstructed
in one year of running (2 fb^1^). This yield is similar to our estimate
above for a Tevatron experiment. However, there are important
differences between LHCb and a Tevatron experiment:

-   LHCb would use *D*^\*^'s produced in *B* decays rather than prompt
    *D*^\*^'s, as the trigger is efficient only for the former. However,
    there will be a substantial number of prompt *D*^\*^'s selected that
    will affect the decay time distribution and thus must be accounted
    for; this may not be straightforward. A Tevatron fixed-target
    experiment would produce (essentially) only prompt *D*^\*^'s.

-   To reconstruct the *D*^\*^ decay vertex position (which is the
    *D*^0^ birth position), LHCb must partially reconstruct a *B*
    *D^\*^X* decay. The efficiency for this is estimated from MC
    simulation to be 51% (Table 15 of LHCb public note LHCb-2007-049,
    July 10, 2007), but this factor is not known and may be smaller. At
    a fixed-target experiment, the *D*^\*^ vertex position is at the
    target (and known with high precision).

-   The trigger electronics for a future Tevatron experiment would be at
    least one generation more advanced than that of LHCb.

To estimate the sensitivity of a Tevatron experiment, we use the fact
that the expected signal yield, background level, and decay time
resolution are similar to those assumed for LHCb. The LHCb study found
that the statistical errors on mixing parameters *x*\'^2^ and *y*\' for
232,500 reconstructed signal decays would be 8.1 x 10^5^ and 1.1 x
10^3^, respectively (assuming a signal-to-background ratio of 0.20).
This yield corresponds to 3.6 years of running of a Tevatron experiment.
Using these statistical errors in a global fit to present measured
values of observables (and also correspondingly reducing the statistical
error on *y~CP~*, which a Tevatron experiment would also measure), we
obtain the contour plot shown in Figure 3.4.1(right). This plot has much
smaller allowed regions for \|*q/p*\| and than does the current world
average plot (Figure 3.4.1, left).

**6.2 Experimental Strategy**

A Tevatron charm mixing + *CP* violation experiment could play an
important and unique role in future flavor physics measurements. If a
Super-*B* factory were not built, then the only other experiment able to
make these measurements would be LHCb, and, as discussed above, it is
uncertain what their sensitivity to mixing will be. The BES-III
experiment at IHEP has sensitivity to *R~M~* = *x*^2^+*y*^2^ and *y* via
correlated *D* branching fractions measured in 3770) *DD* decays (D. M.
Asner and W. M. Sun, Phys. Rev. D 73, 034024, 2006; hep-ph/0507238,v4),
but the *D*'s are essentially at rest, so time-dependent measurements
are not possible. A Tevatron fixed-target experiment could provide an
order-of-magnitude more sensitivity than will result from the current
generation of *B*-factory experiments. This region is of particular
interest for physics beyond the SM that could be discovered at the
Tevatron Collider or at the LHC.

Following the shutdown of the Tevatron collider program, it would be
opportune to proceed with a diverse Tevatron fixed-target program of
neutrino experiments and slow-spill experiments. In such a scenario, a
major component of the slow-spill program could be a very high
statistics charm mixing + *CP* violation experiment. We believe it would
be timely to begin studying and designing such an experiment now, such
that an experimental program could follow the shutdown of the collider
program in an efficient manner.

![](media/image73.wmf){width="5.999305555555556in"
height="3.098611111111111in"}

**Figure 3.4.1 Contour plots for *CP*-violating parameters \|*q/p*\| and
. Left: using current measured values and errors. Right: reducing the
error bars for *y~CP\ ~*and the Belle** *D*^0^ *K* **result for *x'^2^*
and *y'* according to the LHCb MC study.**

**7 Physics with Antiprotons**

### With its intense cooled antiproton beam, Fermilab can explore issues in QCD, search for new physics using hyperons and charmed mesons, and pursue unique investigations of the properties of antihydrogen. Project X will improve Fermilab's "proton economics," enhancing the ability for this physics to be pursued in parallel with the initiatives described elsewhere in this report.

![](media/image74.jpeg){width="3.875in"
height="3.6069444444444443in"}The theory of the strong interaction plays
an important role in allowing us to infer the flavor physics of quarks
and extract the quark mixing matrix from observations made on hadrons.
Heavy-quark--antiquark bound states ("quarkonia") offer a unique testing
ground for QCD. Both potential-model and lattice-gauge Monte Carlo
tech­niques have had success in predicting aspects of heavy-quark
systems. Quenched-approxi­mation lat­tice-QCD predic­tions of the masses of
low-lying char­monium states are already in qualitative agree­ment with
the expe­rimental values, and agreement at the few-percent level is now
becom­ing possible using dyna­mical quarks on the lattice. The char­monium
system (depicted in the figure) is an important proving ground for QCD
calculations in that the bound *c* and ![](media/image75.wmf) quarks are
moving slowly enough that relativistic effects are sig­nificant but not
dominant, and are suf­ficiently massive that non-perturbative effects are
well understood. After certification by com­parison with experiment,
these techniques can then be confidently applied in inter­preting such
physics re­sults as *CP* asymmetries in the beauty system.

Physics topics that can be addressed with an antiproton facility include

> • precision ![](media/image76.wmf){width="0.2361111111111111in"
> height="0.20833333333333334in"} → charmonium studies;
>
> • elucidation of several "mystery states" in the charmonium region;
>
> • studies of open charm, including measurements of
> ![](media/image77.wmf) mixing and searches for *CP* violation;
>
> • hyperons, including searches for hyperon *CP* violation and studies
> of rare decays;
>
> • the search for glueballs and gluonic hybrid states predicted by QCD;
> and
>
> • trapped-![](media/image78.wmf) and antihydrogen studies.

![](media/image79.jpeg){width="2.829861111111111in"
height="2.509027777777778in"}The anticipated shutdown of the Tevatron in
2009 presents the opportunity for a world-leading antiproton physics
program. To maximize the Tevatron Collider luminosity, Fermilab has
developed the world's most intense (as well as highest-energy)
antiproton source. At CERN, the LEAR antiproton storage ring was
decommissioned in 1996 to make way for the LHC. Its successor facility,
the Antiproton Decelerator (AD), provides antiproton beams at momenta of
100 and 300 MeV/c, at intensities up to ≈ 2 × 10^7^ per minute. Of the
topics listed above, the CERN AD is pursuing the last one. Germany's
≈billion-Euro upgrade plan for the GSI-Darmstadt nuclear-physics
laboratory includes construction of 30 and 90 GeV rapid-cycling
synchrotrons for protons and radioactive beams as well as low- and
medium-energy antiproton storage rings, which are planned to start
operating in 2016. Even after this Facility for Antiproton and Ion
Research (FAIR) comes on line, the antiproton production capability of
the Fermilab Antiproton Source will remain unequalled. All of the listed
topics have been discussed as components of the physics program of the
GSI-FAIR project with many covered by its general-purpose PANDA
detector. Many of them are within the energy range of the Accumulator
(see table) and can be pursued more rapidly at Fermilab.

In the charmonium region, the list includes a number of intriguing
recent discoveries: the states provisionally named *X*^ ^(3872),
*X*^ ^(3940), *Y*^ ^(3940), *Y*^ ^(4260), and *Z*^ ^(3930). In addition,
the *h~c~*, ![](media/image80.wmf) and ![](media/image81.wmf) masses and
widths, *~c~* radiative-decay angular distributions, and
![](media/image82.wmf)(2*S*) radiative widths, important parameters of
the charmonium system that remain to be precisely determined, are well
suited to the ![](media/image76.wmf){width="0.2361111111111111in"
height="0.20833333333333334in"} technique. As discussed later, the
recent observation of apparent flavor-changing neutral currents in
hyperon decay can also be investigated; indeed, high sensitivity can be
achieved to rare and symmetry-violating hyperon decays generally.

Fermilab experiments E760 and E835 made the world's most precise
(\~\< 100 keV) measurements of charmonium masses and widths. This was
possible thanks to the extra­ordinarily narrow energy spread of the
stochastically cooled antiproton beam and the absence of Fermi motion
and negligible energy loss in the hydrogen cluster-jet target. The other
key advantage of the antiproton-proton annihilation technique is its
ability to produce charmonium states of all quantum numbers, in contrast
to *e*^+^*e*^−^ machines, which produce primarily 1^−^ states and the
few states that couple directly to them, and (with relatively low
statistics) states accessible in *B* decay or in 2 production.

We propose an experimental program aimed at those measurements for which
the Fermilab Antiproton Source is best suited: (1) precision studies of
states in the charmonium region, (2) the search for new physics in
hyperon decay, (3) the search for new physics in charm mixing and *CP*
violation, and (4) precision studies of antihydrogen. Many of these
measurements can be performed with a common apparatus using existing,
well-developed experimental technologies. Depending on the resources
that will be available, existing detector components might be recycled
for these purposes; alternatively, modest expenditures for new equipment
could yield improved performance.

**7.1 Capabilities of the Fermilab Antiproton Source**

The Antiproton Source now cools and accumulates antiprotons at a
stacking rate of ≈ 2 × 10^11^ antiprotons/hr. Given the 60 mb
annihilation cross section, it could thus support in principle a
luminosity up to about 5 × 10^32^ cm^−2^ s^−1^, with antiproton stacking
≈ 50% of the time and collisions during the remaining ≈ 50%. However, we
anticipate operating at \~\< 2 × 10^32^ cm^−2^ s^−1^, which allows \~\>
80% duty cycle, poses less of a challenge to detectors and triggers, and
requires a smaller fraction of the protons from the Main Injector. An
order of magnitude above the typical E835 luminosity of 2 × 10^31^
cm^−2^ s^−1^, this assumes increased target density, possible via
various approaches: an improved cluster jet, a wire or pellet of plastic
or metal in the beam halo, a solid-hydrogen target on the tip of a cold
finger, or a stream of solid-hydrogen pellets.

Comparison of run­ning conditions and antiproton yields for FNAL after
the Tevatron program and poss­ible new facilities at FNAL and GSI are
pre­sented in the table below.

  --------------------------- ------------- ---------- ------- ----------------
  Facility                    Stacking Rate Stacking   Clock   Yearly
                              (10^10^/hr)   duty       hours   antiprotons
                                            factor             produced
                                                               (10^13^)

  FNAL Accumulator Experiment 20            15%        5550    17

  FNAL New Ring Experiment    20            90%        5550    100

  GSI FAIR                    3.5           90%        2780    9
  --------------------------- ------------- ---------- ------- ----------------

**7.2 Physics Goals**

![](media/image83.jpeg){width="3.573611111111111in"
height="1.7402777777777778in"}To clarify the issues for a future
low-energy antiproton facility, we next consider a few representative
physics examples: studying the mysterious *X*^ ^(3872) state, improved
measurement of the parameters of the *h~c~*, searching for hyperon *CP*
violation, and studying a recently discovered rare hyperon-decay mode.
(This is of course far from an exhaustive list of the topics to be
studied.)

**7.2.1 X (3872)**

The *X* (3872) was discovered in 2003 by the Belle Collaboration via the
decay sequence *B*^±^ → *K*^±^ *X*^ ^(3872), *X*^ ^(3872) → *^+--^ J/*.
Its existence was quickly confirmed by CDF, DØ, and BaBar. It has now
been seen in a variety of modes as shown in the table above; taken
together, these results imply *J^PC^* = 1^++^. A state at this mass with
these quantum numbers does not appear to fit within the charmonium
spectrum.

Inspired by the coincidence of the *X* (3872) mass and the
![](media/image84.wmf) threshold, a number of ingenious solutions to
this puzzle have been proposed, including an *S*-wave cusp or a
tetraquark state. Perhaps the most intriguing possibility is that the
*X*^ ^(3872) represents the first clear-cut observation of a
meson-antimeson molecule: specifically, a bound state of
![](media/image85.wmf). A key measurement is then the precise mass
difference between the *X* and that threshold; if the molecule
interpretation is correct, it should be very slightly negative, in
accord with the small molecular binding energy:

![](media/image86.wmf).

With the latest CLEO measurement ![](media/image87.wmf)= 1864.847 ±
0.150 ± 0.095 MeV/c^2^, we have *E~X~* = 0.6 ± 0.6 MeV/c^2^, with the
uncertainty dominated by our knowledge of *m~X~*. A measurement of the
width is also highly desirable. According to the Particle Data Group
(2007), the width is expected to be less than 2.3 MeV. The systematic
uncertainties in the width measurements of *~c1~* and (2S) of the FNAL
experiment E835 can serve as guidance here, allowing us to project to a
width measurement better than 30 keV. Additional important measurements
include *B*\[*X*^ ^(3872) → *^00^ J/ψ*\] and *B*\[*X* (3872) → *J/ψ*\],
to confirm the quantum-number assignment and further exclude
identification as a charmonium state. The recent report from the Belle
Collaboration of a near-threshold enhancement in ![](media/image88.wmf)
decays tends to support the ![](media/image89.wmf)-molecule
interpretation. Interestingly, the enhancement is observed at a mass of
![](media/image90.wmf) MeV/c^2^, 2.0σ higher than the world-average
value of *m~X~*. With the fine resolution available in
![](media/image76.wmf){width="0.2361111111111111in"
height="0.20833333333333334in"} formation the line shape of the X(3872)
can be measured and the "single" or "double" peak issue can be resolved.
It is clear that the additional avenue that
![](media/image76.wmf){width="0.2361111111111111in"
height="0.20833333333333334in"} formation provides to the study of this
state could be extremely valuable in deciphering the nature of the *X*
(3872).

The production cross section for *X* (3872) in
![](media/image76.wmf){width="0.2361111111111111in"
height="0.20833333333333334in"} annihilation has not been measured, but
it has been estimated by Braaten to be similar in magnitude to that of
the *~c~* states. Additionally, the observed rate and kinematic
distributions of ![](media/image76.wmf){width="0.2361111111111111in"
height="0.20833333333333334in"} → *X *(3872) + anything at the Tevatron
and of *B*^±^ → *K*^±^ *X* (3872) suggest that the production rate of
*X* (3872) in ![](media/image76.wmf){width="0.2361111111111111in"
height="0.20833333333333334in"} formation (at √*s* = 3871.2 ± 0.5
MeV/c^2^) should not differ greatly from that for charmonium states. By
scaling from E760, at 10^32^ cm^−2^ s^−1^ we could then expect to
produce \~ 0.1 *X*^ ^(3872) event per second. The lower limit *B*
\[*X*(3872) → *π^+^π^−^ J/ψ*\] \> 0.042 at 90% C.L. then implies a
signal of \~\> 4 × 10^−3^ detected events per second in the experiment
we propose, or \~\> 4 × 10^3^ events in that mode per nominal month (1.0
× 10^6^ s) of running. By way of comparison, the table above shows
current sample sizes, which are likely to increase by not much more than
an order of magnitude as the experiments complete during the current
decade. (Although CDF and D0 could amass samples of order 10^4^
*X*^ ^(3872) decays, the large backgrounds in the CDF and D0
observations, reflected in the uncertainties on the numbers of events
observed, limit their incisiveness.)

Given the uncertainties in the cross section and branching ratios, the
above may well be an under- or overestimate of the
![](media/image76.wmf){width="0.2361111111111111in"
height="0.20833333333333334in"} formation and observation rates, perhaps
by as much as an order of magnitude. Nevertheless, it appears that a new
experiment at the Antiproton Accumulator could obtain the world's
largest clean samples of *X* (3872), in perhaps as little as a month of
running. The high statistics, event cleanliness, and unique precision
available via ![](media/image76.wmf){width="0.2361111111111111in"
height="0.20833333333333334in"} formation could enable the world's
smallest systematics. Such an experiment could thus provide a definitive
test of the nature of the *X*^ ^(3872).

**7.2.2 h~c~**

Observing the *h~c~* (1 ^1^*P*~1~) charmonium state and measuring its
parameters were high-priority goals of both E760 and E835, as well as of
their predecessor experiment, CERN R704. Being very narrow and having
suppressed couplings both to *e*^+^*e^−^* and to the states that are
easily produced in *e*^+^*e^−^* annihilation, the *h~c~* is difficult to
study experimentally.

![](media/image91.jpeg){width="3.686111111111111in"
height="3.3097222222222222in"}

A key prediction of QCD and perturbation theory is that the charmonium
spin-zero hyperfine splitting, as measured by the mass difference
∆*m~hf~* between the *h~c~* and the spin-weighted average of the *~c~*
states, should be close to zero. Using the current PDG-aver­age values,
*m*(^3^*P~J~*) = 3525.36 ± 0.06 MeV and *m*(*h~c~*) = 3525.93 ± 0.27
MeV, we find ∆*m~hf~* = −0.57 ± 0.28 MeV, non-zero at the 2σ level but
within the range expected from QCD. The PDG error on *m*(*h~c~*)
includes a scale factor of 1.5 due to the tension among the four most
precise measurements. More­over, the most precise measurements (from E760
and E835) are based on signals that are statistically marginal, and
whether the E760 observation was in fact a signal has been called into
question by E835. The R704 result is on even weaker ground: a
![](media/image76.wmf){width="0.2361111111111111in"
height="0.20833333333333334in"} → *h~c~* → *J^ ^/ψ X* decay at the level
im­plied by Baglin et al. is most likely ruled out by both E760 and E835.
Thus of the four results used by the PDG, only one is clearly reliable,
and the claimed precision on *m*(*h~c~*) is far from established. This
motivates an improved measurement. Also of interest are the width and
branching ratios of the *h~c~*, for which QCD makes clear predictions;
the decay modes also bear on the question of isospin conservation in
such decays.

E835 sensitivity in the *h~c~ → η~c~ γ → (γγ)γ* mode was limited by the
*η~c~ → γγ* branching ratio of only (2.8 ± 0.9) × 10^−\ 4^. Moreover,
the acceptance times efficiency was reduced to only ≈ 3% by cuts needed
to eliminate the substantial background from *π^0^* decays. Given a
magnetic spectrometer, favorable modes in which to observe *η~c~*
include (among others) *φφ*, *φK^+^K^−^, KK*, and *ηπ^+^π^−^*. These
have branching ratios up to two orders of magnitude larger, as well as
more-distinctive decay kinematics, than *η~c~* → γγ, probably allowing
looser cuts to be used and higher efficiency to be achieved. For
example, the *K^+^K^−^K^+^K^−^* final state which would be a signature
of *η~c~* → *φφ* has no quarks in common with the initial
![](media/image76.wmf){width="0.2361111111111111in"
height="0.20833333333333334in"} state and so should contain very little
background. The *η~c~* → *φφ* mode was searched for in E835 but without
a magnet its detection was barely feasible. Reliably assessing the
improvement in performance for these modes with a magnetic spectrometer
will require detailed simulation work, but at least an order of
magnitude in statistics seems likely. Additional improvement in
sensitivity will come from increased luminosity.

Provided detailed simulation studies bear out these ideas, we will soon
have the opportunity to resolve this 20-year-old experimental
controversy.

**7.2.3 Hyperon CP violation**

In addition to the well-known *CP* violation in kaon and *B*-meson
mixing and decay, the standard model predicts slight *CP* asymmetries in
decays of hyperons. In the kaon and beauty systems, such effects appear
to be dominated by standard model processes. It thus behooves us to
study other systems as well (such as hyperons), in which the signatures
of new physics might stand out more sharply.

Hyperon *CP* violation would be of the direct type, since
hyperon/antihyperon mixing would violate conservation of baryon number.
The hyperon *CP* asymmetries heretofore considered most accessible
involve comparison of the angular distributions of the decay products of
polarized hyperons with those of the corresponding antihyperons;
however, partial-rate asymmetries are also expected and may be
detectable. More than one hyperon *CP* asymmetry may be measurable in
medium-energy ![](media/image76.wmf){width="0.2361111111111111in"
height="0.20833333333333334in"} annihilation to hyperon-antihyperon
pairs. To be competitive with previous and angular-distribution
asymmetry measurements would require higher luminosity (≈ 10^33^) than
is likely to be available, as well as a very substantial upgrade
relative to the E835 apparatus. While summarizing the state of hyperon
*CP* asymmetries generally, we here emphasize in particular
![](media/image92.wmf)partial-rate asymmetries, for which there is no
previous measurement.

By angular-momentum conservation, in the decay of a spin-1/2 hyperon to
a spin-1/2 baryon plus a pion, the final state must be either *S*-wave
or *P*-wave (or in the case of the *^--^*, *P-* or *D*-wave). The
interference term between the two amplitudes gives rise to parity
violation, described by Lee and Yang in terms of two independent
parameters and : is proportional to the real and to the imaginary part
of this interference term. *CP* violation can be sought as a difference
in \|\| or \|\| between a hyperon decay and its *CP*-conjugate
antihyperon decay or as a particle--antiparticle difference in the
partial widths for such decays. For a precision angular-distribution
asymmetry measurement, it is necessary to know the relative
polarizations of the initial hyperons and antihyperons to high accuracy.

The table below summarizes the experimental situation. The first three
experiments cited studied Λ decay only, setting limits on the
*CP*-asymmetry parameter

![](media/image93.wmf),

where *~Λ~* (![](media/image94.wmf)) characterizes the *Λ*
(![](media/image95.wmf)) decay to (anti)proton plus charged pion. If
*CP* is a good symmetry in hyperon decay, *~Λ~* =
−![](media/image96.wmf).

Fermilab E756, E871 ("Hyper*CP*"), and CLEO used the cascade decay of
charged Ξ hyperons to produce polarized *Λ*'s, in whose subsequent decay
the slope of the (anti)proton angular distribution (in the "helicity"
frame) measures the product of α~Ξ~ and α~Λ~. If *CP* symmetry is obeyed
in hyperon decay this product should be identical for *Ξ^−^* and
![](media/image97.wmf)^+^ events. The asymmetry parameter is thus
![](media/image98.jpeg){width="2.1180555555555554in"
height="2.5652777777777778in"}![](media/image98.jpeg){width="3.8854166666666665in"
height="2.5652777777777778in"}

![](media/image99.wmf)

The power of this technique derives from the relatively large \|α\|
value for the *Ξ^−^ → Λπ^−^* decay, α~Ξ~ = −0.458 ± 0.012. Hyper*CP*
recorded the world's largest samples of hyperon and antihyperon decays,
including 2.0 × 10^9^ and 0.46 × 10^9^ *Ξ^−^* and
![](media/image100.wmf)^+^ events. When the full analysis is complete,
it should determine *A~ΞΛ~* with a statistical uncertainty *δA ≈* 2 ×
10^−4^. The standard model predicts this asymmetry to be of order
10^−5^. Thus if the Hyper*CP* full analysis reveals a significant
effect, it will be evidence for a new source of *CP* violation in the
baryon sector. (Various standard model extensions predict effects as
large as *O*(10^−3^)). Such an observation could be of relevance to the
mysterious mechanism that gave rise to the cosmic baryon asymmetry.
Hyper*CP* has also set the world's first limit on *CP* violation in *Ω*
decay, using a sample of 5.5 × 10^6^ *Ω^−^ → ΛK^−^* and 1.9 × 10^6^
![](media/image101.wmf)^+^ → *ΛK^+^* events: *A* = \[−0.4 ± 9.1 (stat) ±
8.5 (syst)\] × 10^−2^. This asymmetry is predicted to be ≤ 4 × 10^−5^ in
the standard model but can be as large as 8 × 10^−3^ if new physics
contributes.

While *CPT* symmetry requires the lifetimes of a particle and its
antiparticle to be identical, partial-rate asymmetries violate only
*CP*. For most hyperon decays, partial-rate asymmetries are expected to
be undetectably small. However, this need not be the case for the decays
*Ω^−^ → ΛK^−^* and *Ω^−^ → Ξ^0^π^−^*, for which the
particle/antiparticle partial-rate asymmetries could be as large as 2 ×
10^−5^ in the standard model and one to two orders of magnitude larger
if non-SM contributions are appreciable. The quantities to be measured
are

![](media/image102.wmf)

where in the last step we have assumed nearly equal numbers (*N*) of *Ω*
and (![](media/image103.wmf)) of ![](media/image104.wmf) events, as
would be the case here. Sensitivity at the 10^−4^ level then requires
*O*(10^7^) reconstructed events. Measuring such a small branching-ratio
difference reliably will require the clean exclusive
![](media/image105.wmf) event sample produced less than a *π^0^* mass
above threshold, or 4.94 \< ![](media/image106.wmf)\< 5.44 GeV/c.

Hyperon-production cross sections in low- and medium-energy
![](media/image107.wmf){width="0.2361111111111111in"
height="0.20833333333333334in"} annihilation are known for *,* , and .
The inclusive hyperon-production cross section at
![](media/image108.wmf)= 5.4 GeV/c (√*s* = 3.5 GeV) is about 1 mb. At 2
× 10^32^ cm^−2^ s^−1^ this amounts to some 2 × 10^5^ hyperon events
produced per second, or 2 × 10^12^ per year.[^5] The exclusive
![](media/image109.wmf) cross section can be estimated by extrapolation,
giving \~ 60 nb at 5.4 GeV/c. At luminosity of 2.0 × 10^32^ cm^−2^
s^−1^, some 1.2 × 10^8^ ![](media/image110.wmf) events are then produced
in a nominal 1-year run (1.0 × 10^7^ s). Assuming the typical detector
acceptance times efficiency of 50% and given the various branching
ratios, an estimated 1.4 × 10^7^ events each in ![](media/image111.wmf)
and ![](media/image112.wmf)are observed, and 4.1 × 10^7^ events each in
![](media/image113.wmf)and ![](media/image114.wmf), giving the following
statistical sensitivities for partial-rate asymmetries:

*δ∆~Ξπ~* ≈ 0.5 /√*N*~Ξπ~ ≈ 1.3 × 10^−4^ ,

*δ∆~ΛK~* ≈ 0.5 /√*N*~Λ*K*~ ≈ 7.8 × 10^−5^ .

![](media/image115.jpeg){width="4.0in"
height="1.2555555555555555in"}Tandean and Valencia have estimated ∆~Ξπ~
≈ 2 × 10^−5^ in the standard model but possibly an order of magnitude
larger with new-physics contributions. Tandean has estimated *∆~ΛK~* to
be ≤ 1×10^−5^ in the standard model but possibly as large as 1 × 10^−3^
if new physics contributes.[^6] It is worth noting that these
potentially large asymmetries arise from parity-conserving interactions
and hence are limited by constraints from *~K~*; they are independent of
*A*~Λ~ and *A*~Ξ~, which arise from the interference of parity-viola­ting
and parity-con­serv­ing processes. The table sum­marizes predicted hyperon
*CP* asymmetries.

Of course, experimental sensitivities will include systematic components
whose estimation will require careful and detailed simulation studies,
beyond the scope of this report. Nevertheless, the potential power of
the technique is apparent: the experiment discussed here may be capable
of observing the effects of new physics in Omega *CP* violation via
partial-rate asymmetries, and it will represent a substantial
improvement over current sensitivity to Omega angular-distribution
asymmetries.

**7.2.4 FCNC hyperon decays**

Among recent Hyper*CP* results is the observation of the rarest hyperon
decay ever, *Σ^+^* → *pμ*^+^*μ*^−^. Surprisingly, based on the 3
observed events, the decay is consistent with being two-body: *Σ^+^ → p
X~0~, X~0~ → μ^+^μ^−^*, with *m*(*X~0~*) = 214.3 ± 0.5 MeV/c^2^. With
current statistics this interpretation is of course not definitive: the
estimated probability that the 3 events are consistent with the SM
form-factor decay spectrum is 0.8%. The measured branching ratio is
\[3.1 ± 2.4 (stat) ± 1.5 (syst)\] × 10^−8^ assuming intermediate
two-body decay, or \[![](media/image116.wmf) (stat) ± 5.5 (syst)\] ×
10^−8^ assuming three-body *Σ^+^* decay.
![](media/image117.wmf){width="3.8291666666666666in"
height="1.7666666666666666in"}

If real, the *X~0~* cannot be an ordinary hadron: at that mass it would
certainly have been observed in previous experiments. The Hyper*CP*
result has notably been interpreted in the context of non-minimal
supersymmetry by D. S. Gorbunov and co-workers and by He, Tandean, and
Valencia: the *X~0~* might be an "sgoldstino" (the supersymmetric
partner of a Goldstone fermion) or a light pseudoscalar Higgs boson.

Confirming or refuting the existence of the *X~0~* should be a high
priority for a new hyperon experiment. While it might be desirable to
use clean, exclusive ![](media/image118.wmf) events just above
threshold, this would require a ![](media/image119.wmf) momentum well
below what has been accomplished in the past by deceleration in the
Antiproton Accumulator, as well as very high luminosity to access the
*O*(10^−8^) branching ratio. An experimentally less challenging but
equally interesting objective is the corresponding FCNC decay of the
*Ω^−^*, with predicted branching ratio of *O*(10^−6^) if the *X~0~* is
real. (This large increase over that for *Σ^+^* → *pμ*^+^*μ*^−^ reflects
the additional phase space available; the standard model prediction is
*B*(Ω^−^ → Ξ^−^*μ*^+^*μ*^−^) = 6.6 × 10^−8^.) Again assuming a 60 nb
cross section, 2 × 10^32^ luminosity, and 50% acceptance times
efficiency, 120 or 40 observed events are predicted in the two cases
(pseudoscalar or axial-vector *X~0~*) that appear to be viable.

In addition, given the large inclusive hyperon rates at √*s* ≈ 3.5 GeV,
sufficient sensitivity might be available at that setting to test the
Hyper*CP Σ^+^ → pμ^+^μ^−\ ^*result directly. Alternatively, it is
possible that a dedicated run just above ![](media/image120.wmf)
threshold may have competitive sensitivity; evaluating this will require
a detailed simulation study.

**7.2.5 Charm**

A recent calculation by Braaten implies competitive sensitivity for open
charm, with *D*-pair production rate about 100/s at √*s* ≈ 4 GeV ( ≈ 1
µb). This could lead to a sample of *O*(10^9^) events/year produced and
more than 10^8^/year reconstructed, an order of magnitude beyond the
statistics accumulated by the *B* Factories. Whether this sensitivity
can be realized in practice will depend on details of trigger and
analysis efficiency whose estimation will require detailed simulation
studies. Nevertheless, there appears to be the potential for competitive
measurements, e.g., of *D*^0^ mixing and possible *CP* violation in
charm decay.

**7.2.6 Antihydrogen CPT tests**

There is also interest in the possibility of decelerating antiprotons
sufficiently to carry out trapped-antiproton and antihydrogen
experiments. This capability could make Fermilab the world's premiere
facility for this kind of research, and could attract a new community of
physicists, including some now working at CERN's AD. Such experiments
are already possible at low (\~1%) efficiency using existing equipment
at Fermilab, via antiproton deceleration in the Main Injector followed
by energy degradation in a block of suitable material (e.g., steel). The
efficiency could be somewhat improved by the addition of a small
decelerating linac and concomitant reduction in degrader thickness.
Ultimately, with the addition of a new, wider-energy-range antiproton
ring (which might be built for a variety of applications as mentioned
below), the rate of antiprotons deliverable to traps could substantially
exceed that available at the AD.

A complementary approach is the study of antihydrogen atoms in flight,
which may overcome some of the difficulties encountered in the trapping
experiments at CERN. The first steps in this direction were taken by
Fermilab E862, in which the formation of antihydrogen in flight was
observed during 1996--7. Methods to measure in flight the antihydrogen
Lamb shift and ﬁne structure (the 2s~1/2 ~-- 2p~1/2~ and
2p~1/2 ~--~ ~2p~3/2~ energy differences) were subsequently worked out.
Additional progress on this program of measurements may be compatible
with normal Tevatron Collider operations ---- a possibility that is
currently under investigation. In any case, if the feasibility of the
approach is borne out by future work, the program is likely to continue
into the post-Tevatron era.

**7.2.7 Antimatter gravitation measurement**

The intensity of the Fermilab antiproton beam appears sufficient to
allow the gravitational force on antimatter to be measured for the first
time. Such a measurement will allow us to test our understanding of
gravity in new ways. General Relativity (GR) makes a strong prediction
that gravity does not distinguish between matter and antimatter. A
direct measurement will thus allow some fundamental assumptions of GR to
be tested experimentally (for example, the equivalence principle has
never been tested with antimatter). While we have some very good
experimental evidence that supports GR, we also know that there are
serious fundamental inconsistencies between GR and quantum mechanics.
This is illustrated by the cosmological-constant problem, where the
prediction from quantum mechanics is 120 orders of magnitude larger than
the observed value ---- possibly the largest discrepancy in physics. It
is clear that some theory adjustments are needed. Some experimental
guidance would be extremely helpful in resolving these issues.

The antimatter gravity experiment is particularly promising in this
regard because if we discover "antigravity" (i.e., that antimatter
"falls" upward), this may answer several questions at once. Antigravity
could explain the apparent absence of naturally occurring antimatter,
since the repulsive force would cause matter and antimatter to segregate
in the early universe, leading to domains in which one or the other
dominates. Furthermore, the net gravitational force from such a system
of domains would be repulsive, and this would cause the expansion of the
universe to accelerate. Thus a single, perhaps counterintuitive,
result -- the observation of a repulsive force between matter and
antimatter -- would simultaneously furnish possible explanations both of
the baryon asymmetry of the universe and of dark energy.

Should the initial measurement show that antimatter falls down, there
are still some interesting possibilities. For example, antimatter could
fall faster than matter if there are gravivector and graviscalar forces
that cancel for matter but add for antimatter. A sufficiently precise
difference measurement between matter and antimatter would be sensitive
to a fifth force that is too weak to have been detected in
equivalence-principle experiments. Interferometric techniques have been
used to measure the local gravitational force to better than one part in
10^10^, and similar techniques could be used to measure the difference
between the gravitational forces on hydrogen and antihydrogen.

We have the opportunity to measure the gravitational force on antimatter
for a very modest cost by taking advantage of Fermilab's ability to
accumulate large numbers of antiprotons. Once the apparatus is
commissioned, the initial measurement could most likely be made with the
antiprotons from a single store. Yet this experiment has the potential
to create a revolution in the way we think about the universe.
Regardless of the outcome, the antimatter gravity experiment is one that
the general public can understand and appreciate ---- while not the
reason we do experiments, the potential public-relations value should
not be underestimated.

**7.2.8 Additional Physics**

Besides the *X* (3872), the experiment should have competitive
capabilities for studying the additional charmonium-related states
mentioned above. The very large inclusive hyperon samples should enable
new and precise measurements of hyperon semileptonic and other rare
decays. The APEX experiment vacuum tank and pumping system could be
reinstalled, enabling a substantial increase in sensitivity for the
antiproton lifetime and decay modes.

The bottomonium system has not benefited from
![](media/image76.wmf){width="0.2361111111111111in"
height="0.20833333333333334in"} formation studies but is potentially
accessible if the Antiproton Accumulator (or perhaps a new storage ring)
can be configured for colliding beams. The
![](media/image76.wmf){width="0.2361111111111111in"
height="0.20833333333333334in"} widths of bottomonium states are
unknown. If they can be shown to be sufficiently large,
![](media/image76.wmf){width="0.2361111111111111in"
height="0.20833333333333334in"} formation could lead to the discovery of
bottomonium singlet states, which have so far eluded observation, as
well as precise measurements of the many states already observed. The
current data sets of the B-factories could provide the first measurement
or a stringent upper limit on the coupling between bottomonium and the
![](media/image76.wmf){width="0.2361111111111111in"
height="0.20833333333333334in"} system.

Antiprotons have a range of potential applications outside of particle
physics, to e.g. medicine, homeland security, and nuclear physics. In
future these might motivate the construction at Fermilab of an optimized
facility for antiproton trapping, including a new storage ring and
decelerating linac as touched upon above. (We mention this for
completeness; the detailed discussion of such a facility is outside the
scope of this report.)

**7.3 Experimental Strategy**

The variety of measurements discussed here cannot all be carried out
with any one apparatus, nor in any one operating mode. We anticipate
operating a "medium-scale" spectrometer at a variety of beam momenta in
order to carry out the program of charmonium, charm, and hyperon
measurements; this program will require a large duty factor and long
running times. In parallel, smaller experiments using trapped
antiprotons, or antihydrogen trapped or in flight, will be able to take
data occasionally for R&D, with more extended data-acquisition periods
as needed.

**7.3.1 Charmonium, Charm, and Hyperon Measurements**

Many of the measurements discussed here can be made with an improved
version of the E835 detector. The key improvement is the addition of an
analyzing magnet, e.g., a solenoid surrounding or inserted into the
barrel calorimeter. The use of an existing magnet from a previous
experiment seems feasible, although a custom magnet may prove superior.
Charged-particle tracking can be provided using scintillating fibers
(for which a very capable readout system will become available once the
DØ experiment finishes), with vertex reconstruction by means of silicon
pixel detectors as developed for BTeV. The MICE experiment has
demon­strated the efficient tracking of minimum-ionizing particles using
fibers only 350m in diameter; this approach minimizes both the
scattering and energy loss of the charged particles of interest, as well
as the premature showering of pho­tons to be measured in the
electro­magnetic calorimeter.

![](media/image121.jpeg){width="3.673611111111111in"
height="1.7930555555555556in"}

For operation at the proposed 2 × 10^32^ luminosity, some upgrading of
the E835 calorimeter may be required. The shower light pulse develops
promptly via Cherenkov radiation in the highly segmented E835 lead-glass
calorimeter, but the response of the E835 photomultiplier tubes is
slower than is desirable. The PMTs could possibly be replaced with
faster photodetectors that have recently become practical. This could
also overcome the degradation in performance that would result if the
PMTs were required to operate in a significant magnetic field.
Alternatively, use of a new calorimeter could be considered.

Triggering on events of interest should be based on a combination of
charged-track multiplicity, particle transverse momentum and energy, and
separated decay vertices. The anticipated interaction rate is about 10
MHz. A factor 10--100 bandwidth reduction by the first-level trigger
would allow the remaining events to be read out into buffer memory and
processed at trigger-level 2 in an on-line computer farm, with the
*O*(10%) that pass level-2 requirements sent to archival media for
off-line analysis. Due to the low energies and multiplicities, the
needed data-acquisition bandwidth and sizes of the computing farm and
resulting data set are expected to be small in comparison with those of
CDF, DØ, and the LHC experiments.

**7.3.2 Antihydrogen Measurements**

The gravitational force on antimatter will be measured by directing a
low-velocity beam of antihydrogen through an atomic interferometer and
measuring the gravitational phase shift. The antihydrogen can be made by
accelerating cold, trapped antiprotons to a velocity of a few kilometers
per second and directing them through a positron plasma. A similar
technique has been demonstrated to make a beam of antihydrogen at CERN's
AD.

A transmission-grating atomic interferometer could have a net
transmission exceeding 10%, and could measure sub-micron phase shifts
with a reasonable number of antihydrogen atoms. Such an interferometer
has been in use with a sodium beam at MIT for over a decade. (Sodium has
a much smaller wavelength than hydrogen at the same velocity, so the
gratings for the MIT interferometer are much finer than would be needed
in this experiment.)

The atomic interferometer would permit a 1% measurement of the
gravitational force on antimatter very soon after the apparatus is shown
to be working. A precision difference measurement between matter and
antimatter would require a longer-term program, and the highest
precision would require a laser-based interferometer such as has been
used to measure local *g* to better than one part in 10^10^. Such a
measurement with antihydrogen would be sensitive to possible new forces
much weaker than gravity that might couple differently to matter and
antimatter.

**7.4 Antiproton Summary**

There is clearly the opportunity at Fermilab upon completion of the
Tevatron program to mount a vital, varied physics program using the
Antiproton Source. Such a program can answer a number of interesting
physics questions while providing continuity for researchers during the
construction of Project X and the larger experiments that it will
support.

### 8. Conclusions

In order to maintain the discovery potential, scientific productivity,
and vitality of the field during the next two to three decades it is
necessary that the Fermilab research program pursues these same
objectives.

This book has presented a set of flexible options for the
accelerator-based Fermilab program and its scientific goals. The options
rely on a new high-intensity proton source (Project X) as a national
project with international collaboration and relevant experiments to it.
The physics program exploiting the opportunities provided by Project X
is compelling, rich, and robust.  It has exciting opportunities in
neutrino, muon, kaon, charm, and antiproton physics. The strength and
uniqueness of Project X includes

-   Delivering over 2 MW beam power in the wide range of proton energy
    between 60 and 120 GeV for neutrino oscillation programs.

-   delivering 100 -- 200 kW 8 GeV beam for rare decay and precision
    programs in parallel with 2 MW neutrino oscillation experiments.

-   providing excellent beam structures by reconfiguring the existing
    rings. This would enhance significantly sensitivities of rare decay
    and precision experiments.

-   providing potential upgrade paths to multi-MW at 8 GeV.

Some of the physics program at the intensity frontier can already be
started with the existing source at Fermilab, and would benefit from
physics results in the near term and a much higher intense proton source
in the future. The program is continuous with current world leading
programs in neutrinos.

A high-intensity proton source based on a superconducting linear
accelerator would further develop the US and broader community
capability to build the ILC and other accelerator projects in the
future.  Furthermore, such an accelerator provides a capable and
upgradable platform for the field. It may also serve as the front end to
the devices that might be indicated by the development of our physics
understanding during the coming decades, whether for a neutrino factory,
muon collider, or other machines at the frontier.\
\
The community of users of an intense proton source has responded
enthusiastically to the possibilities enabled by increased capabilities
at the intensity frontier. Their active participation in working groups
and workshops bodes well for the field if we can find the resources to
follow through with the important opportunities presented in this book.

Working with the community and its Physics Advisory Committee, Fermilab
will propose programs selected from among the high intensity source
based opportunities.

[^1]: The ILC\'s opportunities for discovery have motivated the global
    particle physics community to come together in an effort to design
    the accelerator and its experimental program. Fermilab has
    contributed strongly to this effort: the design of the accelerator;
    the development of SCRF technology in the U.S.; the design of the
    physics and experimental program; the site studies necessary for
    hosting the ILC at or near Fermilab; and the establishment of a
    test-beam facility for the development of ILC detectors. The ILC and
    related SCRF efforts at Fermilab make up by far the laboratory\'s
    largest future program.

[^2]: KOPIO passed all technical reviews and had progressed to a
    baseline review commissioned by the NSF in May of 2005. The RSVP
    program (KOPIO and MECO) was canceled for financial reasons relating
    to NSF and DOE funding issues.

[^3]: Note that the potential of such a detector has not been fully
    explored. The reduction of beam aperture has profound effects on
    many aspects of the experiment. To give an example, KOPIO's
    acceptance was reduced by randoms in the beam "catcher" veto, and by
    the fact that the initial "flash" of photons from the μ-bunch tended
    to blind the veto for a few ns. To achieve this recovery speed, it
    was necessary to insert a 7 cm Pb absorber in the upstream beam.
    Simulation indicated that the beam veto could be made redundant at
    the cost of tightening the kinematic cuts to the point where 20% of
    the acceptance was lost. This cost would clearly be very much
    smaller for a twenty-fold smaller beam. If the beam veto were
    removed, there would be no need for the photon absorber, increasing
    the kaon flux by nearly a factor 2, and eliminating a major source
    of scattering of beam neutrons. This in turn reduces random veto
    effects and allows the detection elements to be moved closer to the
    beam, thus increasing the geometric acceptance. This is only one
    example among many of the advantages of this configuration.

[^4]: See E949 proposal. Actual operation of E949 was prematurely
    stopped by DOE after one short run.

[^5]: Experience suggests that a data-acquisition system that can cope
    with such a high event rate is both feasible and reasonable in cost.

[^6]: The large sensitivity of *∆~ΛK~* to new physics in this analysis
    arises from chromomagnetic penguin operators and final-state
    interactions via *Ω → Ξπ → ΛK*. (Large final-state interactions of
    this sort should also affect *∆~Ξπ~* but were not included in that
    prediction.)