1. Optimization of a neutrino factory for non-standard neutrino interactions IDS plenary meeting RAL, United Kingdom January 16-17, 2008 Walter Winter Universität Würzburg

2. Jan. 16-17, 2008IDS-NF @ RAL - Walter Winter2 Contents Introduction Introduction Our setup Our setup Main questions: Main questions: –What does the silver channel help? –How small can the muon energy be? –Standard versus non-standard baseline optimization Summary Summary In collaboration with Joachim Kopp and Toshihiko Ota

3. Jan. 16-17, 2008IDS-NF @ RAL - Walter Winter3 Non-standard neutrino interactions Consider effective four-point interactions Consider effective four-point interactions This leads to a Hamiltonian for propagation: matter potential: This leads to a Hamiltonian for propagation: matter potential: For antineutrinos: H  H*, a CC  -a CC For antineutrinos: H  H*, a CC  -a CC

4. Jan. 16-17, 2008IDS-NF @ RAL - Walter Winter4 NSI constraints Limits depend on chirality and fermion Limits depend on chirality and fermion Neutrino propagation in principle sensitive to 3  u +3  d +  e Neutrino propagation in principle sensitive to 3  u +3  d +  e We ignore potential production and detection effects, which can be parameterized similarly! We ignore potential production and detection effects, which can be parameterized similarly! (ISS Physics report, arXiv:0710.4947)

5. Jan. 16-17, 2008IDS-NF @ RAL - Walter Winter5 Relevant parameters for a NF Uninteresting: limited by matter density uncertainty Relatively strong constraints Weak constraints Complex numbers Real number

6. Jan. 16-17, 2008IDS-NF @ RAL - Walter Winter6 Our setup: close to IDS baseline! Two detectors at L 1 and L 2, 50 kt each Two detectors at L 1 and L 2, 50 kt each 50% E 0.5 energy resolution 50% E 0.5 energy resolution Backgrounds 0.001/E 2 Backgrounds 0.001/E 2 2.5% signal uncertainty, 20% BG uncertainty 2.5% signal uncertainty, 20% BG uncertainty 4 yr + 4 yr running time 4 yr + 4 yr running time 10 21 useful muon decays/year/detector! 10 21 useful muon decays/year/detector! E  =50 GeV, unless stated otherwise E  =50 GeV, unless stated otherwise Old analysis/det. Our detector New analysis (diff. L  ) (Cervera@Golden 07) Silver channel: 10 kt Silver* from hep-ph/0606119 (Autiero et al ECC with 5xSG, 3xBG) Silver channel: 10 kt Silver* from hep-ph/0606119 (Autiero et al ECC with 5xSG, 3xBG)

7. Jan. 16-17, 2008IDS-NF @ RAL - Walter Winter7 Performance indicators used Definition of   sensitivity similar to  13 sens.: Largest fit |    which fits a true   =0 Definition of   sensitivity similar to  13 sens.: Largest fit |    which fits a true   =0 Corresponds to a conservative case discovery potential Corresponds to a conservative case discovery potential All oscillation parameters, NSI phases marginalized over (exceptions: for  , which is real, or if   is assumed to be real) All oscillation parameters, NSI phases marginalized over (exceptions: for  , which is real, or if   is assumed to be real) Typically only one or two NSI parameters considered, such as |  e  ,  , |  e   -   -plane Typically only one or two NSI parameters considered, such as |  e  ,  , |  e   -   -plane

8. Jan. 16-17, 2008IDS-NF @ RAL - Walter Winter8 NSI with magic baseline Combing the two baselines reduces the impact of correlations drastically (only real  e  assumed!) Combing the two baselines reduces the impact of correlations drastically (only real  e  assumed!) Does one still need the silver channel in that case? Does one still need the silver channel in that case? 3000 km 7000 km Combined arXiv:0709.1980 Close to worst case for degeneracies:  CP =3  /2, sin 2 2  13 =0.001

9. Jan. 16-17, 2008IDS-NF @ RAL - Walter Winter9 Correlations at magic baseline Including NSI, the magic baseline is not exactly correlation/degeneracy-free Including NSI, the magic baseline is not exactly correlation/degeneracy-free Example: Approximation Example: Approximation a CC ~ E: Standard term drops as 1/E 4, NSI-Term as 1/E 3  High energies important for NSI! a CC ~ E: Standard term drops as 1/E 4, NSI-Term as 1/E 3  High energies important for NSI!

10. Jan. 16-17, 2008IDS-NF @ RAL - Walter Winter10 Comparison to our simulation (1) 3000 km 7000 km Combined arXiv:0709.1980 Our simulation, similar setup Our simulation, our setup Our simulation + our setup, all osc. params marginalized Only  13 and  CP marginalized!

11. Jan. 16-17, 2008IDS-NF @ RAL - Walter Winter11 Comparison to our simulation (2) 3000 km + 7000 km 3000 km + 7000 km + Silver*@3000km 3000 km + 7000 km + Disappearance 3000 km + 7000 km Silver*@3000km + Disappearance Disappearance important for  ,   !

12. Jan. 16-17, 2008IDS-NF @ RAL - Walter Winter12 When does the silver channel help … in a two baseline setup? Assume one NSI parameter at first, such as  e  Assume one NSI parameter at first, such as  e  Fix golden detectors Fix golden detectors Where is the optimal silver baseline? Where is the optimal silver baseline? Place Silver* at golden baseline 1! E  >= 50 GeV! Place Silver* at golden baseline 1! E  >= 50 GeV! 0.01 0.004 Golden detector 1 = Silver baseline

13. Jan. 16-17, 2008IDS-NF @ RAL - Walter Winter13 Minimum muon energy? Higher muon energy helps; low-E NF not an option Higher muon energy helps; low-E NF not an option Silver channel: Not relevant for IDS baseline; helps for E  ~ 50 GeV Silver channel: Not relevant for IDS baseline; helps for E  ~ 50 GeV IDS baseline?High-E NFIDS baseline?High-E NF

14. Jan. 16-17, 2008IDS-NF @ RAL - Walter Winter14 What if more parameters? Marginalize over phase of  e  as well: Marginalize over phase of  e  as well: Absolute limits: |   | < 0.03, |  e  | < 0.006 (3  ) Two orders of magnitude improvement of current bounds! Absolute limits: |   | < 0.03, |  e  | < 0.006 (3  ) Two orders of magnitude improvement of current bounds! 3000km+7000km3000km+7000km+ Silver*@3000km

15. Jan. 16-17, 2008IDS-NF @ RAL - Walter Winter15 Standard versus non-standard optimization Obviously, the main NSI sensitivity comes from the golden and disappearance channels Obviously, the main NSI sensitivity comes from the golden and disappearance channels Changing the golden baselines will affect the NSI sensitivities Changing the golden baselines will affect the NSI sensitivities What if there is no silver channel, do the standard and non-standard optimizations coincide? What if there is no silver channel, do the standard and non-standard optimizations coincide? Perform optimizations in L 1 -L 2 -space Perform optimizations in L 1 -L 2 -space

16. Jan. 16-17, 2008IDS-NF @ RAL - Walter Winter16 Standard optimization revisited All regions: Sensitivity for sin 2 2  13 >10 -4.2 (5  ) for the shown performance indicator All regions: Sensitivity for sin 2 2  13 >10 -4.2 (5  ) for the shown performance indicator True  CP chosen close to worst case True  CP chosen close to worst case Robust optimum for ~ 4000 + 7500 km (not <= 3000 km!) Robust optimum for ~ 4000 + 7500 km (not <= 3000 km!)

17. Jan. 16-17, 2008IDS-NF @ RAL - Walter Winter17 NSI optimization: one parameter Similar to matter effects (which increase with baseline!), NSI sensitivities want one very long baseline Similar to matter effects (which increase with baseline!), NSI sensitivities want one very long baseline

18. Jan. 16-17, 2008IDS-NF @ RAL - Walter Winter18 Combined optimization: Example 4000 + 7500 km consistent with NSI optimization 4000 + 7500 km consistent with NSI optimization But: In general, choose both baselines rather longer than shorter! But: In general, choose both baselines rather longer than shorter! Standard opt: combined NSI example (  CP =  /2, sin 2 2  13 =0.01)

19. Jan. 16-17, 2008IDS-NF @ RAL - Walter Winter19 Summary and conclusions The leading NSI sensitivity comes from the golden + disappearance channels The leading NSI sensitivity comes from the golden + disappearance channels The silver channel might help if E  > 40 GeV  Return to high-E NF for IDS baseline? The silver channel might help if E  > 40 GeV  Return to high-E NF for IDS baseline? A low-E NF (E  << 20 GeV) probably has very little NSI sensitivity beyond the current limits A low-E NF (E  << 20 GeV) probably has very little NSI sensitivity beyond the current limits The currently used IDS baseline setup 4000 km + 7500 km is consistent for both standard and non-standard effects; the baselines be rather longer than shorter! The currently used IDS baseline setup 4000 km + 7500 km is consistent for both standard and non-standard effects; the baselines be rather longer than shorter! NSI are important to establish the physics case for a very long baseline NSI are important to establish the physics case for a very long baseline