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 ,