1. Geographical issues and physics applications of “very long” neutrino factory baselines NuFact 05 June 23, 2005 Walter Winter Institute for Advanced Study, Princeton

2. June 23, 2005NuFact 05 - VLBL - Walter Winter2 Contents Introduction Introduction What are “very long” baselines? What are “very long” baselines? Applications of very long baselines Applications of very long baselines Detector sites for very long baselines Detector sites for very long baselines Summary Summary

3. June 23, 2005NuFact 05 - VLBL - Walter Winter3 Picture of three-flavor oscillations Magnitude of  13 is key to “subleading” effects: Mass hierarchy determination CP violation   e flavor transitions on   e flavor transitions on atmospheric oscillation scale Coupling strength:  13 Atmospheric oscillation: Amplitude:  23 Frequency:  m 31 2 Solar oscillation: Amplitude:  12 Frequency:  m 21 2 Sub- leading effect:  CP

4. June 23, 2005NuFact 05 - VLBL - Walter Winter4 Appearance channels:  e  All interesting information there:  13,  CP, mass hier.  Complicated: Problems with correlations and degs (Cervera et al. 2000; Freund, Huber, Lindner, 2000; Freund, 2001)

5. June 23, 2005NuFact 05 - VLBL - Walter Winter5 Neutrino factory Ultimative “high precision” instrument!? Ultimative “high precision” instrument!? Muon decays in straight sections of storage ring Muon decays in straight sections of storage ring Decay ring naturally spans two baselines Decay ring naturally spans two baselines Technical challenges: Target power, muon cooling, maybe steep decay tunnels Technical challenges: Target power, muon cooling, maybe steep decay tunnels Timescale: 2025? Timescale: 2025? (from: CERN Yellow Report )

6. June 23, 2005NuFact 05 - VLBL - Walter Winter6 “Very long” (VL) baselines Typical baseline: 3,000 km for 50 GeV neutrino factory (to measure CP violation) Typical baseline: 3,000 km for 50 GeV neutrino factory (to measure CP violation)  Define “very long”: L >> 3,000 km  Challenge: Decay tunnel slopes! Our benchmark neutrino factory: NuFact-II Our benchmark neutrino factory: NuFact-II E  = 50 GeV, L = 3,000 km (standard configuration) E  = 50 GeV, L = 3,000 km (standard configuration) Running time: 4 years in each polarity = 8 years Running time: 4 years in each polarity = 8 years Detector: 50 kt magnetized iron calorimeter Detector: 50 kt magnetized iron calorimeter 10 21 useful muon decays/ year (~ 4 MW target power) 10 21 useful muon decays/ year (~ 4 MW target power) 10% prec. on solar params, 5% matter density uncertainty 10% prec. on solar params, 5% matter density uncertainty Atmospheric parameters best measured by disapp. channel Atmospheric parameters best measured by disapp. channel (for details: Huber, Lindner, Winter, hep-ph/0204352)

7. June 23, 2005NuFact 05 - VLBL - Walter Winter7 Note: Pure baseline effect! A 1: Matter resonance Phenomenology of VL baselines (1) (Factor 1) 2 (Factor 2) 2 (Factor 1)(Factor 2) Prop. To L 2 ; compensated by flux prop. to 1/L 2

8. June 23, 2005NuFact 05 - VLBL - Walter Winter8 Factor 1: Depends on energy; can be matter enhanced for long L; however: the longer L, the stronger change off the resonance Factor 1: Depends on energy; can be matter enhanced for long L; however: the longer L, the stronger change off the resonance Factor 2: Always suppressed for longer L; zero at “magic baseline” (indep. of E, osc. Params) Factor 2: Always suppressed for longer L; zero at “magic baseline” (indep. of E, osc. Params) Phenomenology of VL baselines (2) (  m 31 2 = 0.0025,  =4.3 g/cm 3, normal hierarchy)  Factor 2 always suppresses CP and solar terms for very long baselines; note that these terms include 1/L 2 -dep.!

9. June 23, 2005NuFact 05 - VLBL - Walter Winter9 Application 1: “Magic baseline” Idea: Factor 2=0 independent of E, osc. Params Idea: Factor 2=0 independent of E, osc. Params Purpose: “Clean” measurement of  13 and mass hierarchy Purpose: “Clean” measurement of  13 and mass hierarchy Drawback: No  CP measurement at magic baseline Drawback: No  CP measurement at magic baseline  combine with shorter baseline, such as L=3 000 km  13 -range: 10 -4 < sin 2 2  13 < 10 -2, where most problems with degeneracies are present  13 -range: 10 -4 < sin 2 2  13 < 10 -2, where most problems with degeneracies are present

10. June 23, 2005NuFact 05 - VLBL - Walter Winter10 Unstable: Disappears for different parameter values Magic baseline:  13 sensitivity Use two-baseline space (L 1,L 2 ) with (25kt, 25kt) and compute  13 sensitivity including correlations and degeneracies: No CP violation measurement there! Optimal performance for all quantities: Animation in  13 -  CP -space: (Huber, Winter, PRD 68, 2003, 037301, hep-ph/0301257)

11. June 23, 2005NuFact 05 - VLBL - Walter Winter11 CP coverage and “real synergies” 3 000 km + 7 500 km versus all detector mass at 3 000 km (2L) 3 000 km + 7 500 km versus all detector mass at 3 000 km (2L) Magic baseline allows a risk-minimized measurement (unknown  ) Magic baseline allows a risk-minimized measurement (unknown  ) “Staged neutrino factory”: Option to add magic baseline later if in “bad” quadrants? “Staged neutrino factory”: Option to add magic baseline later if in “bad” quadrants? Range of all fit values which fit a chosen simulated value of  CP Any “extra” gain beyond a simple addition of statistics One baseline enough Two baselines necessary (Huber, Lindner, Winter, JHEP, hep-ph/0412199)

12. June 23, 2005NuFact 05 - VLBL - Walter Winter12 Magic baseline: Detector sites? “Hot spots”: Interesting for many labs Pyhaesalmi mine, Finland: MB from JHF Gran Sasso, Italy: MB from Fermilab China, India: MB from CERN? (http://www.sns.ias.edu/~winter/BasePlots.htm)

13. June 23, 2005NuFact 05 - VLBL - Walter Winter13 Appl. 2: Matter effect sensitivity for  13 =0 Idea: For  13 =0 only “solar term” survives. Factor 2 is suppressed in matter vs. vacuum : Idea: For  13 =0 only “solar term” survives. Factor 2 is suppressed in matter vs. vacuum : Purpose: Verify MSW effect at high CL even for  13 =0 Purpose: Verify MSW effect at high CL even for  13 =0 Drawback: No mass hierarchy measurement (this term) Drawback: No mass hierarchy measurement (this term)  13 -range: Interesting for sin 2 2  13 < 10 -3  13 -range: Interesting for sin 2 2  13 < 10 -3 Note: No 1/L 2 suppression of solar term in vacuum! Note: No 1/L 2 suppression of solar term in vacuum!

14. June 23, 2005NuFact 05 - VLBL - Walter Winter14 MSW sensitivity:  13 -L-dependence For sin 2 2  13 >>  2 ~ 10 -3 : Depending on sin 2 2  13, L=3 000 km might be sufficient For sin 2 2  13 >>  2 ~ 10 -3 : Depending on sin 2 2  13, L=3 000 km might be sufficient For sin 2 2  13 6 000 km required! For sin 2 2  13 6 000 km required! (Winter, PLB 613, 2005, 73, hep-ph/0411309) No sensitivity here (  CP =0)

15. June 23, 2005NuFact 05 - VLBL - Walter Winter15 MSW effect vs. mass hierarchy Both qualitatively similar for large  13, but: matter effect sens. harder (Difference vacuum-matter < difference normal-inverted) Both qualitatively similar for large  13, but: matter effect sens. harder (Difference vacuum-matter < difference normal-inverted) Small  13: No mass hierarchy sensitivity whatsoever Small  13: No mass hierarchy sensitivity whatsoever Some dependence on  CP, but L > 6 000 km safe Some dependence on  CP, but L > 6 000 km safe (5  dashed curve: no correlations  ) (Winter, PLB 613, 2005, 73, hep-ph/0411309)

16. June 23, 2005NuFact 05 - VLBL - Walter Winter16 Application 3: Measurement of the Earth’s core density Idea: Factor 1 does not drop prop. 1/L 2 close to resonance Idea: Factor 1 does not drop prop. 1/L 2 close to resonance But: The longer L, the sharper the change off the resonance Very sensitive to matter density especially for large L But: The longer L, the sharper the change off the resonance Very sensitive to matter density especially for large L Purpose: Measure the absolute density of the Earth’s core Purpose: Measure the absolute density of the Earth’s core Drawbacks: Not possible to measure  CP ; “vertical” decay tunnel sophisticated Drawbacks: Not possible to measure  CP ; “vertical” decay tunnel sophisticated  13 -range: sin 2 2  13 >> 10 -3  13 -range: sin 2 2  13 >> 10 -3  13 large, A~1 (resonance)

17. June 23, 2005NuFact 05 - VLBL - Walter Winter17 Core density measurement: Principles  Most direct information on the matter density from Earth’s mass and rotational inertia, but:  Least sensitive to the innermost parts  Seismic waves: s-waves mainly reflected on core boundaries  Least information on inner core  No “direct” matter density measurement; depends on EOS  No “absolute” densities: mainly sensitive to density jumps  Neutrinos: Measure Baseline- averaged density:  Equal contribution of innermost parts. Measure least known innermost density!

18. June 23, 2005NuFact 05 - VLBL - Walter Winter18 Core density measurement: Results First: consider “ideal” geographical setup: Measure  IC (inner core) with L=2 R E First: consider “ideal” geographical setup: Measure  IC (inner core) with L=2 R E Combine with L=3000 km to measure oscillation parameters Combine with L=3000 km to measure oscillation parameters Key question: Does this measurement survive the correlations with the unknown oscillation parameters? Key question: Does this measurement survive the correlations with the unknown oscillation parameters?  For sin 2 2  13 > 0.01 a precision at the per cent level is realistic  For 0.001 < sin 2 2  13 < 0.01: Correlations much worse without 3000 km baseline (Winter, hep-ph/0502097) (1 , 2 , 3 ,  CP =0, Dashed: no correlations)

19. June 23, 2005NuFact 05 - VLBL - Walter Winter19 Density measurement: Geography Something else than water in “core shadow”? Inner core shadow Outer core shadow

20. June 23, 2005NuFact 05 - VLBL - Walter Winter20 “Realistic geography” … and sin 2 2  13 =0.01. Examples for  IC : There are potential detector locations! There are potential detector locations! Per cent level precision not unrealistic Per cent level precision not unrealistic (Winter, hep-ph/0502097) BNL CERN JHF Inner core shadow

21. June 23, 2005NuFact 05 - VLBL - Walter Winter21 Summary: VL baseline applications Excluded 10 -1 10 -2 10 -3 10 -4 10 -5 10 -6 sin 2 2  13 Pur- pose Measure density of the Earth’s core Magic baseline: Resolve correlations/ degeneracies Verify Earth matter effects at high CL L L>10 665 km (outer core) L ~ 7 500 km L > 6 000 km Major challenge: Decay ring/decay tunnel slope Major challenge: Decay ring/decay tunnel slope Open question: Simultaneous or subsequent operation of VL baseline? Feasiblity study for storage ring configurations needed! Open question: Simultaneous or subsequent operation of VL baseline? Feasiblity study for storage ring configurations needed!

22. June 23, 2005NuFact 05 - VLBL - Walter Winter22 Outlook: Further applications? de Gouvea, Jenkins, Kayser, hep-ph/0503079: Mass hierarchy sensitivity for  13 = 0 (disappearance channels) requires very long baseline!? de Gouvea, Jenkins, Kayser, hep-ph/0503079: Mass hierarchy sensitivity for  13 = 0 (disappearance channels) requires very long baseline!? How much does it take to determine the hierarchy for  13 = 0 at a high CL? How much does it take to determine the hierarchy for  13 = 0 at a high CL? 4  signal 4 MW OA beam, 1Mt Water Cherenkov NuFact w/o CID! (de Gouvea, Winter, in preparation) Synergy: Both superbeam + NuFact required?  13 = 0