1. Physics potential of “very long” neutrino factory baselines Seminar in Mathematical Physics At KTH Stockholm April 13, 2005 Walter Winter Institute for Advanced Study, Princeton

2. April 13, 2005KTH Stockholm - Walter Winter2 Contents Introduction: Neutrinos Introduction: Neutrinos Neutrino oscillations Neutrino oscillations Long-baseline experiments Long-baseline experiments Neutrino factories and “very long” baselines Neutrino factories and “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. April 13, 2005KTH Stockholm - Walter Winter3 Why are neutrinos so interesting? Neutrinos are everywhere: for example, 7 x 10 10 cm -1 s -1 from the Sun Neutrinos are everywhere: for example, 7 x 10 10 cm -1 s -1 from the Sun Neutrinos are important in stellar dynamics Neutrinos are important in stellar dynamics Neutrinos might be responsible for baryogenesis Neutrinos might be responsible for baryogenesis Massive neutrinos = physics beyond Standard Model Massive neutrinos = physics beyond Standard Model Smallness of neutrino mass “suspicious”: Link to very high energy scale? Smallness of neutrino mass “suspicious”: Link to very high energy scale? Observations tell us that the lepton and quark mixing patterns are very different different Observations tell us that the lepton and quark mixing patterns are very different different

4. April 13, 2005KTH Stockholm - Walter Winter4 Neutrino sources 10 -4 10 -3 10 4 10 3 10 5 10 6 10 710 10 9 10 11 10 8 10 12 keV MeVGeVTeV E [eV] Natural Artificial = ”man made”

5. April 13, 2005KTH Stockholm - Walter Winter5 Neutrino mixing Use standard parameterization - as for CKM matrix: ( ) ( ) ( ) =xx  Three mixing angles  ,        one CP phase  CP  Difference to quarks: Two mixing angles large:       (s ij = sin  ij c ij = cos  ij )

6. April 13, 2005KTH Stockholm - Walter Winter6 From oscillations: Has to be non-zero! From oscillations: Has to be non-zero! Dirac- or Majorana-type mass terms? Is the neutrino its own anti-particle? Dirac- or Majorana-type mass terms? Is the neutrino its own anti-particle? Neutrino mass (1) Note: Majorana Mass terms See-saw: Smallness of mass Leptogenesis Mechanism: Decays of M R

7. April 13, 2005KTH Stockholm - Walter Winter7 Neutrino mass (2) Mass hierarchy: Normal or inverted? Mass hierarchy: Normal or inverted? Absolute neutrino mass scale: - We know that m max > 0.05 eV (from oscillations) - Upper bounds from Tritium endpoint experiments, cosmology, 0  -decay (Majorana mass only) - Current bound about ~ 1eV - Hierarchical (m max ~ (  m 31 2 ) 1/2 ) or degenerate (m max ~ eV) spectrum? Absolute neutrino mass scale: - We know that m max > 0.05 eV (from oscillations) - Upper bounds from Tritium endpoint experiments, cosmology, 0  -decay (Majorana mass only) - Current bound about ~ 1eV - Hierarchical (m max ~ (  m 31 2 ) 1/2 ) or degenerate (m max ~ eV) spectrum? Adiabatic conversion in SN Better mass bounds from cosmology, 0  - decay

8. April 13, 2005KTH Stockholm - Walter Winter8 Neutrino oscillations in vacuum Two independent Two independent  m 2 ’s! Hamiltonian diagonal in mass space! Source of CP violation if  CP not 0 or  Oscillation “signature”:  m 2 L/E Applied quantum mechanics!

9. April 13, 2005KTH Stockholm - Walter Winter9 Neutrino oscillations with two flavors Mixing and mass squared difference:  “disappearance”:  “appearance”: Amplitude Frequency Baseline: Source - Detector Energy

10. April 13, 2005KTH Stockholm - Walter Winter10 Knowledge about mass hierarchy From atmospheric and solar neutrino oscillation experiments: From atmospheric and solar neutrino oscillation experiments: For the moment:  CP =0: For the moment:  CP =0: Atmospheric oscillations:  31 ~1 =>  21  21 <<1 Solar oscillations:  21 ~1 =>   1 >>1 Solar oscillations:  21 ~1 =>   1 >>1  ij =  m 2 ij L/(4 E) “selects” sensitive oscillation via L/E! ~ 0.5

11. April 13, 2005KTH Stockholm - Walter Winter11 Knowledge about mixing angles From reactor experiments:  13 small From reactor experiments:  13 small From solar experiments:  12 large, but not max. (  /4) From solar experiments:  12 large, but not max. (  /4) From atmospheric experiments:  23 close to max. (  /4) From atmospheric experiments:  23 close to max. (  /4) To zeroth order in  13 : Solar and atmospheric oscillations decouple: Effective two-flavor oscillation formulas for - P ee (solar) and - P , P  (atmospheric) - P e  ~ 0 (Reactor, Long-baseline appearance) To zeroth order in  13 : Solar and atmospheric oscillations decouple: Effective two-flavor oscillation formulas for - P ee (solar) and - P , P  (atmospheric) - P e  ~ 0 (Reactor, Long-baseline appearance)

12. April 13, 2005KTH Stockholm - Walter Winter12 Picture of three-flavor oscillations Magnitude of  13 is key to “subleading” effects: Mass hierarchy determination CP violation   e flavor transitions   e flavor transitions in atmospheric oscillations (“Oscillation maximum”) Coupling strength:  13 Atmospheric oscillation: Amplitude:  23 Frequency:  m 31 2 Solar oscillation: Amplitude:  12 Frequency:  m 21 2 Sub- leading effect:  CP

13. April 13, 2005KTH Stockholm - Walter Winter13 What we (don’t) know about neutrinos Come in three active (=weakly interacting) flavors Come in three active (=weakly interacting) flavors Neutrino oscillation parameters (1  ):  m 21 2 ~ 8.2 10 -5 eV 2 +- 5% sin 2 2  12 ~ 0.83 +- 5% |  m 31 2 | ~ (2 – 2.5) 10 -3 eV 2 sin 2 2  23 ~ 1+- 7% sin 2 2     CP  Neutrino oscillation parameters (1  ):  m 21 2 ~ 8.2 10 -5 eV 2 +- 5% sin 2 2  12 ~ 0.83 +- 5% |  m 31 2 | ~ (2 – 2.5) 10 -3 eV 2 sin 2 2  23 ~ 1+- 7% sin 2 2     CP  Other parameters:      (Majorana phases) Mass hierarchy: Normal or inverted? Absolute mass scale: < eV; hierarchical or degenerate? Mass terms: Dirac or Majorana? Other parameters:      (Majorana phases) Mass hierarchy: Normal or inverted? Absolute mass scale: < eV; hierarchical or degenerate? Mass terms: Dirac or Majorana? Small “non-standard” ad-mixtures, such as light steriles, decoherence, decay etc? Small “non-standard” ad-mixtures, such as light steriles, decoherence, decay etc? Maximal mixing excluded at 5  ! Quite flat in fit minimum! Only upper bound! (see e.g. Bahcall et al, hep-ph/0406294; Super-K, hep-ex/0501064; CHOOZ+solar papers)

14. April 13, 2005KTH Stockholm - Walter Winter14 Future measurements: Implications for theory Good “Model discriminators”:  13, Mass hierarchy, Deviations from max. mixing Good “Model discriminators”:  13, Mass hierarchy, Deviations from max. mixing Example: Zero  13 or exactly maximal mixing would point towards a symmetry Example: Zero  13 or exactly maximal mixing would point towards a symmetry Experiment driven field! Example:  sin     (from: FNAL Proton Driver Study, to appear in 2005)

15. April 13, 2005KTH Stockholm - Walter Winter15 What are long-baseline experiments? Artificial source: Accelerator, Reactor Often: Near detector to measure X-sections, control systematics, … Far detector Baseline: L ~ E/  m 2 (osc. length)   ?

16. April 13, 2005KTH Stockholm - Walter Winter16 “Artificial” neutrino sources Source Production … and Detection LimitationL<E> ReactorSystematics 1-2 km ~4 MeV Super- beam Intrinsic beam background 100- 2,500 km 0.5 – 5 GeV Neutrino factory Charge identification 700- 7,500 km 15-30 GeV  -beam Radioactivity 100- 2,000 km 0.3 – 10 GeV For leading atm. params Signal prop. sin 2 2  13 Contamination

17. April 13, 2005KTH Stockholm - Walter Winter17 Matter effects in -oscillations (MSW) Ordinary matter contains electrons, but no ,  Ordinary matter contains electrons, but no ,  Coherent forward scattering in matter has net effect on electron flavor (relative phase shift) Coherent forward scattering in matter has net effect on electron flavor (relative phase shift) Matter effects proportional to electron density and baseline Matter effects proportional to electron density and baseline Hamiltonian in matter: Hamiltonian in matter: Y: electron fraction ~ 0.5 (electrons per nucleon) (Wolfenstein, 1978; Mikheyev, Smirnov, 1985)

18. April 13, 2005KTH Stockholm - Walter Winter18 Disappearance measurements Use expansions in small parameters: Use expansions in small parameters: Short baseline reactor experiments: Second term small for sin 2 2  13 >> 0.001 ! Short baseline reactor experiments: Second term small for sin 2 2  13 >> 0.001 ! Long baseline accelerator experiments: Long baseline accelerator experiments: (see e.g. Akhmedov et al., hep-ph/0402175)

19. April 13, 2005KTH Stockholm - Walter Winter19 Appearance channels:  e  Complicated, but all interesting information there:  13,  CP, mass hierarchy (via A) (Cervera et al. 2000; Freund, Huber, Lindner, 2000; Freund, 2001)

20. April 13, 2005KTH Stockholm - Walter Winter20 (Animation) Correlations and degeneracies Connected or disconnected degenerate solutions (at a chosen CL) in parameter space Connected or disconnected degenerate solutions (at a chosen CL) in parameter space Affect performance of appearance measurements. For example,  13 sensitivity Affect performance of appearance measurements. For example,  13 sensitivity (Huber, Lindner, Winter, hep-ph/0204352) Example: Intrinsic ( ,  13 )-deg. at a neutrino factory Example: Intrinsic ( ,  13 )-deg. at a neutrino factory (Burguet-Castell et al, 2001) Depends on simulated values of  13 and , which change the topology! (see e.g. Huber, Lindner, Winter, hep-ph/0412199)

21. April 13, 2005KTH Stockholm - Walter Winter21 Oscillation physics landscapes:  13 Toy scenario with specific assumptions; bands reflect unknown  CP Toy scenario with specific assumptions; bands reflect unknown  CP Obviously different generations of experiments Obviously different generations of experiments New generation will quickly determine potential New generation will quickly determine potential (from: FNAL Proton Driver Study, to appear in 2005)

22. April 13, 2005KTH Stockholm - Walter Winter22 Mass hierarchy and CP violation (from: FNAL Proton Driver Study, to appear in 2005) PD: FNAL Proton driver NUE: NuMI Upgraded Experiment 2 nd NUE: 2 nd NUE off-axis detector T2K*: T2K with PD upgrade T2HK: T2K* with Hyper-K detector Measure for probability to find quantity

23. April 13, 2005KTH Stockholm - Walter Winter23 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 )

24. April 13, 2005KTH Stockholm - Walter Winter24 “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 5.3 10 20 useful muon decays/ year (4 MW target power) 5.3 10 20 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)

25. April 13, 2005KTH Stockholm - Walter Winter25 Note: Pure baseline effect! A 1: Matter resonance Phenomenology of VL baselines (1) (Term 1) 2 (Term 2) 2 (Term 1)(Term 2) Prop. To L 2 ; compensated by flux prop. to 1/L 2

26. April 13, 2005KTH Stockholm - Walter Winter26 Term 1: Depends on energy; can be matter enhanced for long L; however: the longer L, the stronger change off the resonance Term 1: Depends on energy; can be matter enhanced for long L; however: the longer L, the stronger change off the resonance Term 2: Always suppressed for longer L; zero at “magic baseline” (indep. of E, osc. Params) Term 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)  Term 2 always suppresses CP and solar terms for very long baselines; note that these terms include 1/L 2 -dep.!

27. April 13, 2005KTH Stockholm - Walter Winter27 Application 1: “Magic baseline” Idea: Term 2=0 independent of E, osc. Params Idea: Term 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

28. April 13, 2005KTH Stockholm - Walter Winter28 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)

29. April 13, 2005KTH Stockholm - Walter Winter29 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, hep-ph/0412199)

30. April 13, 2005KTH Stockholm - Walter Winter30 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)

31. April 13, 2005KTH Stockholm - Walter Winter31 Appl. 2: Matter effect sensitivity for  13 =0 Idea: For  13 =0 only “solar term” survives. Term 2 is suppressed in matter vs. vacuum : Idea: For  13 =0 only “solar term” survives. Term 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!

32. April 13, 2005KTH Stockholm - Walter Winter32 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, hep-ph/0411309, to appear in PLB) No sensitivity here (  CP =0)

33. April 13, 2005KTH Stockholm - Walter Winter33 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 (includes disappearance channel!) Small  13: No mass hierarchy sensitivity whatsoever (includes disappearance channel!) 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, hep-ph/0411309, to appear in PLB)

34. April 13, 2005KTH Stockholm - Walter Winter34 MSW sensitivity: Geography MSW effect sensitivity given below thick curves!

35. April 13, 2005KTH Stockholm - Walter Winter35 Application 3: Measurement of the Earth’s core density Idea: Term 1 does not drop prop. 1/L 2 close to resonance Idea: Term 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)

36. April 13, 2005KTH Stockholm - Walter Winter36 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!

37. April 13, 2005KTH Stockholm - Walter Winter37 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)

38. April 13, 2005KTH Stockholm - Walter Winter38 Density measurement: Geography Something else than water in “core shadow”? Inner core shadow Outer core shadow

39. April 13, 2005KTH Stockholm - Walter Winter39 “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

40. April 13, 2005KTH Stockholm - Walter Winter40 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 In some cases: Option to add VL baseline later (or replace existing baseline) could be interesting approaches In some cases: Option to add VL baseline later (or replace existing baseline) could be interesting approaches