Steve Geer IDS Meeting CERN March 2009 1
Neutral Currents and Tests of 3-neutrino Unitarity in
Long-Baseline Exeriments
Steve Geer
Barger, Geer, Whisnant, New J. Phys. 6 (2004) 135.
Steve Geer IDS Meeting CERN March 2009 2
Introduction
• In addition to measureing oscillation parameters, it is important to test the 3-flavor mixing framework.
• The NC event rate measures the total flux of active neutrinos. Hence the anticipated far detector NC event sample will be depleted if there are transitions to sterile neutrinos
• To understand prospects observing/limiting the sterile neutrino transition probability Ps using NC measurements we must account for:– statistics– normalization uncertainties (Flux, spectrum & cross-
section)– detector efficiencies– event-type mis-identification
Steve Geer IDS Meeting CERN March 2009 3
Current Example: MINOS
arXiv:0807.24243 Oct 2008
Measured NC Spectrum in Far
Dectector
•Far detector NC prediction based on near detector measurements look for deficit
Steve Geer IDS Meeting CERN March 2009 4
Observations
Present sensitivity based on O(100) NC events is limited by statistics, and is sensitive to Ps > few 10%
NC events selected with 90% efficiency & 60% purity.
In the future expect superbeam experiments will provide very large NC event samples, and it seems likely that the systematic uncertainties will limit the ultimate sensitivity to Ps.
Steve Geer IDS Meeting CERN March 2009 5
In a Perfect World
• Pure beam with well known flux and spectrum, perfect detector, no cross-section uncertainties.
• Use NC & CC event rates integrated over spectra (NNC, N, Ne, N) oscillation probabilities
0N
/10 NCsNC PNN
PNN 0
/0eee PNN
/0PNN
DEFINE
Predicted number of CCinteractions with no oscillations
yxxy PP
NC
xNC cross-section
CC cross-sections
Steve Geer IDS Meeting CERN March 2009 6
With a Less Perfect Detector
,,
,,
0
1ex
NCxxxNCNCNCsNC PPN
N
,,
,,
0
1ex
exxxeNCNCse PPN
N
,,,,
0
1ex
xxxNCNCs PPN
N
,,,,
0
1ex
xxxNCNCs PPN
N
• Define:
• Solutions for Ps , including a statistical analysis to obtain significance Ps/(Ps), given in New J. Phys. 6 (2004) 135 for some
limiting cases.
xx ,
yx ,
Probability that event of type x correctly identified
Probability event of type x mis-identifiedas event of type y
Steve Geer IDS Meeting CERN March 2009 7
A few definitions
– Normalized mis-id factor
– Normalized NC rate
– Normalized CC rate
– Systematic uncertaintyon fluxes & NC
yyyxxyxyf /(= no. wrong / no. right)
0, NCNCNC
NCNC N
NR
0,
N
NR
No. observeddivided by No. expectedif nothinginteresting is happening
00 / NCNCNC NN
Steve Geer IDS Meeting CERN March 2009 8
Aside: Analytical expressions for Ps / Ps
Consider simplest case: Below CC threshold, & ignore e CC interactions (for other cases New J. Phys 6
(2004)135):
• If the fij are small we can ignore terms O(f2), and obtain:
• In the limiting case where normalization uncertainties dominate (over event mis-identification):
NC
NCNC
s
s
R
RfR
P
P
,1
Significance of deviation of Ps
from zero
220, )1()/()1( NCsNCNCNCs
s
s
s
PNP
P
P
P
Steve Geer IDS Meeting CERN March 2009 9
Detector Simulations
• Need efficiency and mis-id factors:
– Consider several “toy experiments” integrate over parametrized beam spectra use parametrized detector responses
– Use NEUGEN to simulate neutrino interactions
– Define NC & CC event samples using various simple selection criteria matched to candidate detector technologies (e.g. water cherenkov, iron-scintillator)
Steve Geer IDS Meeting CERN March 2009 10
Toy Results for ξxx and yyyxxyxyf /
Steve Geer IDS Meeting CERN March 2009 11
Observations
• K2K-Like experiment:– All fi,j < 0.1, hence impact of mis-id small
compared to statistical uncertainties
• T2K-Like experiment:– fNCNC ~ 0.5
– fNC ~ 0.25 suggests cannot neglect mis-id
• MINOS-Like experiment:– fNCNC ~ 1 good NC event efficiency
– fNC ~ 1 cannot neglect if stats large
– Simulated f’s consistent with present MINOS analysis (better than we have a right to expect)
Steve Geer IDS Meeting CERN March 2009 12
NC Cross-Section Uncertainty
N0 = Predicted No. CC Events (no Oscillations)
NC
PERFECT DETECTOR efficiencies ξxx = 1mis-ID factors ξxy = 0
Up
per
Bo
und
on
Ps
(90
% C
L)
0.12
0.06
0
Sensitivity of the next generation of experiments will be limited by normalization uncertainties unlessthey can be reduced below a few % Additional motivation for experiments like Minerva
Steve Geer IDS Meeting CERN March 2009 13
Efficiencies & Mis-ID: T2K-Like
N0 = Predicted No. CC Events (no Oscillations)
NC
Up
per
Bo
und
on
Ps
(90
% C
L)
NC
0.12
0.06
0
The impact of CC background in the NC sample seems also likely to limit the precision of the NC test.
Worthwhile understanding how to minimize NCf ,
Steve Geer IDS Meeting CERN March 2009 14
Efficiencies & Mis-ID: MINOS-like
MINOS-like detectordoes better at low statistics (higher efficiency) but worse at high statistics (larger mis-id).
N0 = Predicted No. CC Events (no Oscillations)
NC
PerfectMINOS-likeK2K-like
Up
per
Bo
und
on
Ps
(90
% C
L)
Steve Geer IDS Meeting CERN March 2009 15
3 Discovery Sensitivity
Steve Geer IDS Meeting CERN March 2009 16
Summary
• Sensitivity to Ps below O(0.1) will require progress on background suppression & knowledge of normal-izations (cross-sections & fluxes) motivation for experiments like Minerva.
• If the sensitivity is ultimately limited by normalization-type uncertainties NC the sensitivity to Ps can be understood analytically. For example, at 3, sensitivity 3NC/(1+3NC).
• To achieve few-percent-level 3 sensitivity on Ps is likely to require (i) percent-level knowledge of fluxes and cross-sections, (ii) minimizing NCf ,