1. 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.

2. 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 P  s using NC measurements we must account for: –statistics –normalization uncertainties (Flux, spectrum & cross- section) –detector efficiencies –event-type mis-identification

3. Steve Geer IDS Meeting CERN March 2009 3 Current Example: MINOS arXiv:0807.2424 3 Oct 2008 Measured NC Spectrum in Far Dectector Far detector NC prediction based on near detector measurements  look for deficit

4. 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 P  s > 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 P  s.

5. 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 (N NC, N , N e, N  )  oscillation probabilities DEFINE Predicted number of  CC interactions with no oscillations NC cross-section CC cross-sections

6. Steve Geer IDS Meeting CERN March 2009 6 With a Less Perfect Detector Define: Solutions for P  s, including a statistical analysis to obtain significance P  s /  (P  s ), given in New J. Phys. 6 (2004) 135 for some limiting cases. Probability that event of type x correctly identified Probability event of type x mis-identified as event of type y

7. Steve Geer IDS Meeting CERN March 2009 7 A few definitions –Normalized mis-id factor –Normalized NC rate –Normalized CC rate –Systematic uncertainty on fluxes &  NC (= no. wrong / no. right) No. observed divided by No. expected if nothing interesting is happening

8. Steve Geer IDS Meeting CERN March 2009 8 Aside: Analytical expressions for P  s /  P  s Consider simplest case: Below  CC threshold, & ignore e CC interactions ( for other cases  New J. Phys 6 (2004)135 ): If the f ij are small we can ignore terms O(f 2 ), and obtain: In the limiting case where normalization uncertainties dominate (over event mis-identification): Significance of deviation of P  s from zero

9. 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)

10. Steve Geer IDS Meeting CERN March 2009 10 Toy Results for ξ xx and

11. Steve Geer IDS Meeting CERN March 2009 11 Observations K2K-Like experiment: –All f i,j < 0.1, hence impact of mis-id small compared to statistical uncertainties T2K-Like experiment: –f NC  NC ~ 0.5 –f  NC ~ 0.25  suggests cannot neglect mis-id MINOS-Like experiment: –f NC  NC ~ 1  good NC event efficiency –f  NC ~ 1  cannot neglect if stats large –Simulated f’s consistent with present MINOS analysis (better than we have a right to expect)

12. Steve Geer IDS Meeting CERN March 2009 12 NC Cross-Section Uncertainty N  0 = Predicted No.  CC Events (no Oscillations)  NC PERFECT DETECTOR efficiencies ξ xx = 1 mis-ID factors ξ xy = 0 Upper Bound on P  s (90% CL) 0.12 0.06 0 Sensitivity of the next generation of experiments will be limited by normalization uncertainties unless they can be reduced below a few %  Additional motivation for experiments like Minerva

13. Steve Geer IDS Meeting CERN March 2009 13 Efficiencies & Mis-ID: T2K-Like N  0 = Predicted No.  CC Events (no Oscillations)  NC Upper Bound on P  s (90% CL)  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

14. Steve Geer IDS Meeting CERN March 2009 14 Efficiencies & Mis-ID: MINOS-like MINOS-like detector does better at low statistics (higher efficiency) but worse at high statistics (larger mis-id). N  0 = Predicted No.  CC Events (no Oscillations)  NC Perfect MINOS-like K2K-like Upper Bound on P  s (90% CL)

15. Steve Geer IDS Meeting CERN March 2009 15 3  Discovery Sensitivity

16. Steve Geer IDS Meeting CERN March 2009 16 Summary Sensitivity to P  s 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 P  s can be understood analytically. For example, at 3 , sensitivity  3  NC /(1+3  NC ). To achieve few-percent-level 3  sensitivity on P  s is likely to require (i) percent-level knowledge of fluxes and cross-sections, (ii) minimizing