BNL Very Long Baseline Experiment With a Super Neutrino Beam

Stephen Kahn

Brookhaven National Laboratory, Upton, NY, 11973

**Abstract.** An upgrade to the BNL AGS could produce a very intense
proton source at a relatively low cost. This proton source could produce
a conventional neutrino beam with a very significant flux at large
distances from the laboratory. In this paper we examine the possibility
of using this neutrino beam for a very long baseline oscillation
experiment where a 500 kiloton water Cherenkov detector is situated at
the Homestake mine in South Dakota. We study the physics potential of a
high intensity neutrino oscillation experiment with a 2540 km baseline
and a peak neutrino energy of \~1 GeV.

# INTRODUCTION

Recent results have shown that neutrinos can oscillate between flavor
states. This has created interest in understanding the fundamental
aspects of neutrino oscillations. To explore the physics of the neutrino
masses and mixing angles will require new facilities with intense proton
beam sources. A working group at Brookhaven National Laboratory is
studying the feasibility of upgrading the AGS to a 1.0 MW proton sources
and using it to create an intense neutrino super-beam capable of
producing a significant flux at a large distance from BNL. The AGS
upgrade would increase the repetition rate of the accelerator from 0.5
to 2.5 Hz with 8.9×10^13^ protons per pulse. The expected integrated
intensity for a typical year of operation (10^7^ sec.) is expected to be
2.2×10^21^ 28 GeV protons on target. A description of the accelerator,
target and horn system, and ν beamline of this super-beam facility is
given in a report by the working group \[1\]. The physics potential of
this proposed long baseline experiment is described in another report
\[2, 3\]. The goal of this facility is to have the ability to measure
all of the parameters of the SMN matrix in a single experiment. This
includes:

-   A precise determination of the oscillation disappearance parameters
    ∆m~32~^2^ and sin^2^2θ~23~.

-   The detection of the appearance oscillation ν~μ~→ν~e~ and the
    measurement of sin^2^2θ~13~.

-   The measurement of ∆m^2^~21~ sin^2^2θ~12~ in a ν~μ~→ν~e~ appearance
    mode.

-   The verification of the matter enhancement and the sign of
    ∆m~32~^2^.

-   The determination of the CP-violation parameter δ~CP~ in the
    neutrino sector.

The useful neutrino energy range is restricted at \~1 GeV on the low end
by Fermi motion in the nucleus and by \~6 GeV on the high end by
background from inelastic ν interactions. Placing the detector at the
Homestake Mine, which is 2540 kilometers from BNL, allows the
oscillation phase to vary from below π/2 to above 5π/2 for
∆m~32~^2^=0.0025 eV^2^, which would clearly demonstrate oscillations in
the energy distribution and provide a precise measurement of ∆m~32~^2^.
For the purposes of calculating expected event rates and backgrounds a
0.5 megaton water Cherenkov detector is used. A neutrino beam directed
at the Homestake Mine must be inclined into the ground by 11.3° with
respect to the surface. This incline restricts the location of the
close-in detector to be just outside the beam dump at 275 m from the
target.

# Flux Calculations and event estimates

Neutrino flux spectra have been calculated for the upgraded AGS with a
horn design proposed for this beam \[4\]. Fig 1a shows the expected ν~μ~
and ν~e~ flux distributions for this beam in units of
ν/GeV/m^2^/Proton-on-target at 1 km from the target. The expected ν~e~
event contamination is \~1% in this wide-band beam. At distances greater
than 1 km the spectrum is not strongly dependent on the on the ν source
position and the consequently the flux at the detector scales with
*r^-2^*. The table in Fig 1b shows the number of events expected at 2540
km in a 0.5 megaton water Cherenkov detector for a 5×10^7^ sec running
period. We expect to see 52000 charged current and 17000 neutral current
events during that run. The event analysis in a water Cherenkov detector
will concentrate on the quasi-elastic samples since the neutrino energy
is better known and the backgrounds in the ν~e~ appearance are better
understood. A liquid argon detector would be a better detector to
analyze the multiple particle channels.

![](media/image1.png){width="5.79375in" height="2.901388888888889in"}

**Figure 1a:** The ν~μ~ and ν~e~ flux spectra from 28 GeV protons on a
graphite target seen at 1 km. **b:** Table of events seen in neutrino
induced channels at 2540 km during a 5×10^7^ sec run in a 0.5 megaton
water Cherenkov Detector.

# ν~μ~ Disappearnce

Figure 2a shows the energy spectrum of ν~μ~ quasi-elastic channel for a
running period of 5×10^7^ seconds with a 1 MW beam and a 0.5 megaton
water Cherenkov detector at 2540 km. The top curve shows the event
spectrum without oscillations. The middle curve with error bars shows
the event spectrum with oscillations when ∆m~32~^2^=0.0025 eV^2^ and
sin^2^2θ~23~=1. In this figure we have assumed that the resolution in
the reconstructed ν energy (E~ν~) is 10%, which should be achievable
with 10% photo multiplier tube coverage. This does not include a
systematic error from the calibration of the overall detector energy
scale. A great advantage of the very long baseline and the multiple
oscillation pattern is that the systematic errors for flux
normalization, background subtraction, and nuclear effects are small.
The background shown in the lower curve of the figure comes from non
quasi-elastic charged current events that also oscillate and will tend
to smear the nodal pattern.

![](media/image2.png){width="5.7972222222222225in"
height="3.0729166666666665in"}

**Figure 2a:** ν~μ~ Quasi-elastic event spectrum. Curves show events
without oscillations, with oscillations, and the background to
oscillated QE events. The oscillated events assume that ∆m~32~^2^=0.0025
eV^2^. **b:** A comparison of the precision of the measurement of
∆m~32~^2^ and sin^2^2θ~23~ for this experiment and that expected by the
MINOS experiment and seen by the Super-Kamiokande experiment.

Figure 2b shows a comparison of the experimental precision of ∆m~32~^2^
and sin^2^2θ~23~ expected in this experiment with those seen in the
Super-Kamiokande experiment and expected in the MINOS experiment.

## ν~μ~→ν~e~ APPEARANCE

The measurement of θ~13~, δ~CP~ and ∆m~21~^2^ and the sign of ∆m~32~^2^
can be extracted from the wideband ν~e~ appearance spectrum. The
probability for the appearance of ν~μ~→ν~e~ oscillations from
3-generation mixing including matter effects can be expressed
analytically \[3\]. Figure 3a shows the expected ν~e~ event distribution
for sin^2^2θ~13~=0.04 and ∆m~32~^2^=0.0025 eV^2^ and the same running
conditions previously mentioned. The matter enhancement (suppression)
for the normal (reversed) ∆m~32~^2^ sign ordering dominates the spectrum
for E~v~\>3 GeV. Sensitivity to the CP phase is greatest for E~ν~ range
from 1 to 3 GeV. The effect of the solar oscillation from ∆m~21~^2^ is
largest at low E~ν~. Figure 3b shows the event spectrum with
sin^2^2θ~13~=0. The appearance mode is more sensitive to the presence of
backgrounds. The main sources of background come from ν~e~ contamination
in the beam and neutral current reactions that have a single π° that are
misidentified as electrons. An estimate of these backgrounds is shown in
figure 3. There is concern at this point that the detection efficiency
of π° is overestimate in the current simulation. This is being
investigated.

![](media/image3.png){width="5.79375in" height="2.973611111111111in"}

**Figure 3a:** The expected ν~e~ event spectrum for sin^2^2θ~13~=0.04
and for 3 values of δ~CP~. The figure also shows the total background
for ν~e.~ **b:** The expected spectrum for sin^2^2θ~13~=0. The resultant
spectrum shows ∆m~21~^2^ oscillations.

# Acknowledgments

This work was performed with the support of the US DOE under Contract
No. DE-AC02-98CH10886.

# References

1\. *The AGS-Based Super Neutrino Beam Facility, The BNL Neutrino
Working Group Report II,\
*BNL-71228-2003-IR.

2\. *Report of the BNL Neutrino Working Group: Very Long Baseline
Neutrino Oscillation Experiment for Precise Determination of Oscillation
Parameters and Search for ν~μ~→ν~e~ Appearance and CP Violation,* BNL
Report 69395 (2002).

2.  M.V. Diwan et al., Physical Review D **68**, 012002 (2002)

4\. S.A. Kahn et al., *Focusing Horn System for the BNL...,*Proc of the
2003 Particle Accelerator Conference, BNL-71411-2003-CP.