# Presentation: 792789

## Rare Kaon Decays - 2

- Laurence Littenberg
- BNL
- E. Fermi School, Varenna - 25 July 2005

## Organization

- Introduction & general motivation
- Lepton Flavor Violation, etc.
- Brief review of Unitarity
- K++
- KL0
- K
- KLl+l-
- KL0l+l-

## Cabibbo-Kobayashi-Maskawa (CKM) Matrix

- Unitary matrix connecting weak with mass eigenstates

- Parameterization of Wolfenstein and Maiani:

|  = sin(Cabibbo) = 0.227 | from Ke3, K2,  decay |
| --- | --- |
| A  0.81 | from semi-leptonic B decay, etc |
|   0.18 | From Vub/Vcb, B – B mixing, |
|   0.33 | CP-asymm in BJ/KS, K, etc. |

- _

## Unitarity Relation

- (1-2/2)

- (1-2/2)

- (1-2/2)

## Wolfenstein parameterization to higher order

- W-M parameterization only approximate, at (4) & beyond, not unique
- Buras et al. (PR **D50** (1994) 3433) introduced a version unitary to all orders
- At the moment, don’t need to go above (5):

- Where ****** ******** ******(1- ****2/2) & ****** ******** ******(1-****2/2)
- Main effect is to move vertex of unitary triangle to (******, ******)
- In terms of ****i** ******** **VidVis*****:
- 	Im ****t** **= - Im ****c** **= ****A2** ******5
- 	Re ****c** **= - ****(1-** ******2/2)
- 	Re ****t** **= - (1-** ******2/2)A2 ****5(1**- ******)
- Note that the area of any unitarity triangle = 1⁄2*J**cp*
- Where  *J**cp *= -Im(Vts*****VtdVus*****Vud) = ****(1-****2)1⁄2Im ****t** **
- Thus, a measurement of Im ****t would determine the area of all 6 U.T.’s

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## One-loop K Decays

- Short distance contributions to K decays.  These decays include KL0,    K++, KL+-, KL0e+e-, KL0+-, etc.  The hadronic matrix elements involved are known from common K decays such as K+0e+.  These one-loop contributions can be cleanly calculated in terms of sinC, mt, mc, and the product of CKM elements Vts*Vtd  t.

- But there’s a Murphy’s Law to these processes. The same interactions that allow final  state leptons to be detected mediate long-distance contributions.  E.g.:

- To avoid this one must exploit decays containing a final state  pair.

## Rare K Decays & the Unitarity Triangle

## K++

- K++

**_**

- contains QCD corr. has been calc’d to **N**NLLA

- Vts*Vtd

- X  1.57(mt/170)1.15

- = 4.210-11A4X2(xt)[2+2⁄3(0e-)2+1⁄3(0-)2]

- calc. uncertainty only a few %

- In leading order in Wolfenstein parameters, B(K++) determines a circle in the ,  plane with center (0,0); 0 2⁄30e+1⁄30 and radius = [1010 B(K++)]1⁄2/A2
- Going beyond leading order, circle gets slightly squashed, BR formula becomes:

- The ellipse departs from a circle by only a factor : it’s 5% wider than it is tall

## Uses of CKM Unitarity

- Hard-to-calculate parts subtract away

## K Hadronic Matrix Element

## Long-distance effects

- Most long-distance contributions calculated years ago, *e.g*.:
- Come out to be a few % of the short-distance charm contribution
- New calculation of dimension-8 contribution to the charm piece by Isidori, Mescia & Smith (hep-ph/0503107) raises this contribution by 10% &  the SM branching ratio by 6%

## K++ & the U.T.

**_**

-  The usual U.T. is convenient for the *B* system, but is no more fundamental than the 5 other possible triangles.
-  One triangle can be completely determined by K measurements:
-   t + c + u = 0 (where  i  Vis*Vid)
-   This triangle is rather elongated (base to height  ~1000:1)
-  Usually see this information displayed in terms of real & imaginary part of t

## Precision of SM prediction

## Experimental considerations for K++

- 3-body decay, only 1 visible
- + common K decay product
- BR ~ few  10-11
- Backgrounds:
- K++()
- K+ + 0
- Beam
- Beam + mis-ID as K+, then fakes K decay at rest
- K+ decay in flight
- 2 beam particles
- K+nK0p; KL  + l-, lepton missed

- _

- pnn1

- pnn2

## E787/949 Detector

##  E787/949 Technique

-  Incoming 700MeV/c beam K+: identified by Č, WC, scintillator hodoscope (B4). Slowed down by BeO

-  K+ stops & decays at rest in scintillating fiber target – measure delay (2ns)

-  Outgoing +: verified by IC, VC, T counter. Momentum measured in UTC, energy & range in RS and target           (1T magnetic field parallel to beam)

-  + stops & decays in RS – detect  ++e+ chain

-  Photons vetoed hermetically in BV-BVL, RS, EC, CO, USPV, DSPV

** **E787/949 Technique

## E787/949 Analysis Strategy

-  Measure background level with real data
-  To avoid bias,
-    1/3 of data  cut development
-    2/3 of data  background measurement
-  Characterize backgrounds using back-
-   ground functions
-  Likelihood Analysis

- Signal region “the BOX”

- Background sources

- Analysis Strategy

- Identify *a priori. *at least 2 independent cuts to target each background:

**K****+**********************

- PNN1: p > p(K++0) = 205MeV/c

-  K++0
-  muon background (K++(),...)
-  Beam background
-  etc.

## Calculation of backgrounds 

- Calculation of backgrounds

- Tag with 

- Tag kinematics
- outside 
- box – in K2 peak

- kinematics

- Photon veto

## Background Characterization

- Background can be characterized using specially constructed functions

- For muon backgrounds

- Neural net function for  & 

-   K2(tail):     K2 but range is small due to interactions in RS.
-  K2(band):  multibody K++ decay (K+ +, etc.)

- Momentum (P) for  and 

- +  +  e+ in the + stopping counter

## Verify background prediction 

- Loosen cuts and look in M x N times larger box
- Two independent cuts for one background
- For ex., Photon Veto or TD(NN function), and KINematics
- Compare prediction and observed # of events

| K2 | PV x KIN | 10 x 10 | 20 x 20 | 20 x 50 | 50 x 50 | 50 x 100 |
| --- | --- | --- | --- | --- | --- | --- |
|  | Observed | 3 | 4 | 9 | 22 | 53 |
|  | Predicted | 1.1  0.18 | 4.9  0.6 | 12.4  1.3 | 31.1  3.1 | 62.4  5.6 |
| K2 | TD x KIN | 10 x 10 | 20 x 20 | 50 x 50 | 80 x 50 | 120 x 50 |
|  | Observed | 0 | 1 | 12 | 16 | 25 |
|  | Predicted | 0.35  0.03 | 1.4  0.1 | 9.1  0.6 | 14.5  1.0 | 21.8  1.5 |
| K | TD x KIN | 10 x 10 | 20 x 20 | 50 x 20 | 80 x 20 | 80 x 40 |
|  | Observed | 1 | 1 | 4 | 5 | 11 |
|  | Predicted | 0.31  0.09 | 1.3  0.4 | 3.2  1.0 | 5.2  2.2 | 10.4  2.8 |

## E787  E949

-  Much higher proton flux (65 TP)
-  Improved tracking and energy resolution
-  Higher rate capability due to DAQ, electronics and trigger improvements
-  Lower beam duty factor (Siemens  Westinghouse)
-  Lower proton energy    (by 10%, cost 10% in flux)
-  Problematic separators, worse K/π ratio (4 3), fewer K/proton (factor ~1.5)
-  **Total cost, factor 2**

- E787  E949

## E787/949 Events

- B(K+******+******) =
-  (1.47+1.30-0.89)10-10

**_**

## Combined E787/949 Result

- (68% CL interval)
- E787 result:

## K++ contour on the unitarity plane

- K++ contour on the unitarity plane

**Green arcs indicate****  this ****K****+************+******** result**
- (including theoretical uncertainties)

- Contour in - plane		     courtesy of G. Isidori

**Central value**

- 90% interval

- 68% interval

- Central value        off the “SM”
-  **Need more data!!**

## Acceptance larger than for pnn1 (in principle)
E787 bkgnd-limited at  ~10-9, another factor 10 needed to get to S:B ~ 1

Main background from 
   K2 w/nasty correlation                   	
Improved photon vetoing in E949 very encouraging.
Answer expected in a few months.

- E787

- Acceptance larger than for pnn1 (in principle)
- E787 bkgnd-limited at  ~10-9, another factor 10 needed to get to S:B ~ 1
- Main background from
-    K2 w/nasty correlation
- Improved photon vetoing in E949 very encouraging.
- Answer expected in a few months.

- pnn2

- E949

## Status & prospects for E949

* *E949 detector worked well
-  Obtained ~2/3 sensitivity of E787 in 12 weeks (1/3 pnn1+1/3 pnn2)
-  Found one new pnn1 candidate
-  pnn2 analysis currently in progress – looks promising
-   AGS & beamline problems cost a factor ~2 in sensitivity/hour
-   DOE cut off experiment after 12 of 60 promised weeks
-   Currently seeking NSF support

## J-PARC K++ LOI

-  Stopped K+ experiment
-  Builds on E787/949 experience
-  Lower energy separated beam
-  Higher B spectrometer
-  More compact apparatus
-  Better resolution
-  Finer segmentation
-  Improved  veto (crystal barrel)
-  Aims for 50 events
-  Not an early experiment for J-PARC
-  Needs beamline
-  place on the floor
-  $ for detector

## Pros & cons of stopped-K technique

- PROs
- Long history
- The enemies are known
- Well-honed methods
- S/B good enough!
- Effective particle ID
- Easy to be hermetic
- Very pure beam
- In CM right away
- Clean separation of kinematics/part-ID

- CONs
- Decay in matter
- Nuclear effects
- Require ’s to stop
- ID sensitive to rates
- 3 timescales (up to 10s)
- Need low veto thresholds
- Limited K flux
- Most K’s interact (typ 4/5)
- Correlation of detector geometry w/CM system

## P326 (NA48/3) K++ 

- Proposal submitted to CERN for ~100 events

## P326 Technique

- Detection in-flight
- High energy (75 GeV/c) unseparated beam (800 MHz!)
- Careful design to keep halo to ~7MHz
- Measure all beam tracks (“Gigatracker”)
- Differential Cerenkov (“CEDAR”) for K ID
- Redundant measurement of pion momentum
- Two-stage magnetic spectrometer (straws in vacuum)
- Require large missing momentum
- Redundant pion I.D.
- Magnetized hadron calorimeter (“MAMUD” + RICH)
- (Almost) hermetic photon veto system
- NA48 liquid Krypton calorimeter
- Small angle charged & neutral vetoes (beam bent out of the way)
- Wide-angle frame anti’s

## Kinematics

- + momentum cut requires a huge momentum mismeasurement to mistake a beam + for a final state particle (7535 GeV/c).  Also guarantees large missing momentum, *e.g.* so that there’s plenty of  energy from *K**+* +0

- Assumption of pion mass spreads out *K**+*+ peak
- 0.3% resolution on pK and
- 1% resolution on p allows ~10% acceptance

## Plan for P326

- 2005
- Gigatracker R&D
- Vacuum tests
- Technical design & cost estimate
- 2006
- Detector tests in present beam
- Construction & installation 2007-8
- Construct new beamline
- Construct & install detectors
- 2009-10
- Running
- Expect ~80 events with S:B ~ 10:1

## How to pursue K++?

- In-flight has the “appeal of the new”
- The only way to get >100 events
- But requires 11 O.M. leap!
- Watch out for tails, acceptance losses, the unexpected
- Stopping experiment very well understood
- Technique shown to have sufficient S/B
- Any further improvements can increase acceptance
- Note acceptance of 787/949 is ~0.002
- Plenty of room for improvement!
- Could ***really know*** if 50-100 events possible
- But so far very little support for such an experiment

## Why is KL0 CP-violating?

- To lowest electroweak order in the SM
- 0 is CP-even (can be thought of as 0Z*)
- Spin of K is 0, so must have l = 1
-  KL is CP-odd (to corrections of order K)
-  since
-  & |q/p| = 1-2Re K (from CP asymmetry in Kl3)
- Define
-          &  the phase between K mixing & sd
- Note         ~ 1,   = e2i
- Ratio between decay rates is
- Then

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## KL0 & CP-violation – 2

- Use
- to replace unmeasurable
- yields
- where ris  0.954 is isospin breaking (mass diff., etc.)
- In SM,  =  (*e.g.* from BJ/KS)
- this comparison one of many clean tests of CP
- In this case parameters like CKM *A* and *m**t** *divide out

**_**

## KL0 in the Standard Model

**_**

- Suppressed to the 1-loop level by GIM.
- No competing long-distance contributions
- KL0  is t-quark dominated in the loops
- Direct CP-violating to ~1%
- No significant QCD correction
- Hadronic m.e. from Ke3
- BR = (1.5580.025)10-3  (11.3m/mt)  (Im t)2
-      < 2% intrinsic            uncertainty due to
- theoretical uncertainty        that on mt

**_**

## A Model-independent limit on B(KL0)

- B(KL0) < 4.4  B(K++)
- Proposed by Y. Grossman & Y. Nir
- Phys. Lett. **B398** (1997) 163
- A consequence of the I = 1⁄2  Rule
- trivial in the SM (imaginary part of amplitude < modulus)
- True for almost any short-distance interaction, even if that interaction conserves CP
- Expressed as a limit, E787/949 result is
- B(K++)<3.22  10-10 @ 90% C.L.
- Yields B(KL0) < 1.4  10-9
- Far better than any other limit
-  c.f. 2.86  10-7 from E391a
- But still 50 times larger than SM expectation

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**_**

## BSM

- Beyond the SM, K’s don’t have to agree with B’s!

## KL0 Beyond the SM

- Unique because
-  retains its clean connection to short distance parameters BSM
- NOT the case for e.g. BJ/KS where new physics can be observed but not interpreted.
-  probes the flavor structure of any new physics
- A 10% deviation in B-physics can translate into an O(1) deviation in this decay.
- See e.g. Buras *et al.*, PRL **92** (2004) 101804
- Even if result agrees with B-physics prediction, gives unique constraint on new physics operators
- A 10% measurement can probe new physics scales > 1000 TeV!
- See Buras *et al.,* hep-ph/0505171

**_**

**Notes:**
Either the processes are tree-diagram-dominated (& thus naturally insensitive to new physics) or it is very difficult to determine their direct-CP violating phases with good theoretical control
The left side is 1/sqrt of the coefficient of the non-SM contribution to the Qsd operator (unlikely tree-level & all couplings O(1)

## Comparison of reach in MFV models

## K in the MSSM

- SM

- Soft breaking trilinear couplings
- squark & chargino masses fixed

- Sign ambiguity of
- overall MSSM
- coupling

- From E949

**_**