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

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

Picture of three-flavor oscillations Atmospheric oscillation: Amplitude: q23 Frequency: Dm312 Solar oscillation: Amplitude: q12 Frequency: Dm212 Sub-leading effect: dCP Coupling strength: q13 Magnitude of q13 is key to “subleading” effects: Mass hierarchy determination CP violation nm ne flavor transitions on atmospheric oscillation scale June 23, 2005 NuFact 05 - VLBL - Walter Winter

Appearance channels: nm ne (Cervera et al. 2000; Freund, Huber, Lindner, 2000; Freund, 2001) All interesting information there: q13, dCP, mass hier. Complicated: Problems with correlations and degs June 23, 2005 NuFact 05 - VLBL - Walter Winter

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

“Very long” (VL) baselines 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 Em = 50 GeV, L = 3,000 km (standard configuration) Running time: 4 years in each polarity = 8 years Detector: 50 kt magnetized iron calorimeter 1021 useful muon decays/ year (~ 4 MW target power) 10% prec. on solar params, 5% matter density uncertainty Atmospheric parameters best measured by disapp. channel (for details: Huber, Lindner, Winter, hep-ph/0204352) June 23, 2005 NuFact 05 - VLBL - Walter Winter

Phenomenology of VL baselines (1) Note: Pure baseline effect! A 1: Matter resonance Prop. To L2; compensated by flux prop. to 1/L2 (Factor 1)(Factor 2) (Factor 1)2 (Factor 2)2 June 23, 2005 NuFact 05 - VLBL - Walter Winter

Phenomenology of VL baselines (2) 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) (Dm312 = 0.0025, r=4.3 g/cm3, normal hierarchy) Factor 2 always suppresses CP and solar terms for very long baselines; note that these terms include 1/L2-dep.! June 23, 2005 NuFact 05 - VLBL - Walter Winter

Application 1: “Magic baseline” Idea: Factor 2=0 independent of E, osc. Params Purpose: “Clean” measurement of q13 and mass hierarchy Drawback: No dCP measurement at magic baseline combine with shorter baseline, such as L=3 000 km q13-range: 10-4 < sin22q13 < 10-2, where most problems with degeneracies are present June 23, 2005 NuFact 05 - VLBL - Walter Winter

Magic baseline: q13 sensitivity Use two-baseline space (L1,L2) with (25kt, 25kt) and compute q13 sensitivity including correlations and degeneracies: No CP violation measurement there! Animation in q13-dCP-space: Optimal performance for all quantities: Unstable: Disappears for different parameter values (Huber, Winter, PRD 68, 2003, 037301, hep-ph/0301257) June 23, 2005 NuFact 05 - VLBL - Walter Winter

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

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) June 23, 2005 NuFact 05 - VLBL - Walter Winter

Appl. 2: Matter effect sensitivity for q13=0 Idea: For q13=0 only “solar term” survives. Factor 2 is suppressed in matter vs. vacuum : Purpose: Verify MSW effect at high CL even for q13=0 Drawback: No mass hierarchy measurement (this term) q13-range: Interesting for sin22q13 < 10-3 Note: No 1/L2 suppression of solar term in vacuum! June 23, 2005 NuFact 05 - VLBL - Walter Winter

MSW sensitivity: q13-L-dependence (dCP=0) For sin22q13 >> a2 ~ 10-3: Depending on sin22q13, L=3 000 km might be sufficient For sin22q13 << a2 ~ 10-3: Independent of sin22q13, even works for sin22q13=0: L > 6 000 km required! No sensitivity here (Winter, PLB 613, 2005, 73, hep-ph/0411309) June 23, 2005 NuFact 05 - VLBL - Walter Winter

MSW effect vs. mass hierarchy (5s, dashed curve: no correlations ) Both qualitatively similar for large q13, but: matter effect sens. harder (Difference vacuum-matter < difference normal-inverted) Small q13: No mass hierarchy sensitivity whatsoever Some dependence on dCP, but L > 6 000 km safe (Winter, PLB 613, 2005, 73, hep-ph/0411309) June 23, 2005 NuFact 05 - VLBL - Walter Winter

Application 3: Measurement of the Earth’s core density Idea: Factor 1 does not drop prop. 1/L2 close to resonance But: The longer L, the sharper the change off the resonance Very sensitive to matter density especially for large L q13 large, A~1 (resonance) Purpose: Measure the absolute density of the Earth’s core Drawbacks: Not possible to measure dCP; “vertical” decay tunnel sophisticated q13-range: sin22q13 >> 10-3 June 23, 2005 NuFact 05 - VLBL - Walter Winter

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! June 23, 2005 NuFact 05 - VLBL - Walter Winter

Core density measurement: Results (Winter, hep-ph/0502097) First: consider “ideal” geographical setup: Measure rIC (inner core) with L=2 RE Combine with L=3000 km to measure oscillation parameters Key question: Does this measurement survive the correlations with the unknown oscillation parameters? For sin22q13 > 0.01 a precision at the per cent level is realistic For 0.001 < sin22q13 < 0.01: Correlations much worse without 3000 km baseline (1s, 2s, 3s, dCP=0, Dashed: no correlations) June 23, 2005 NuFact 05 - VLBL - Walter Winter

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

“Realistic geography” … and sin22q13=0.01. Examples for rIC: There are potential detector locations! Per cent level precision not unrealistic JHF BNL CERN (Winter, hep-ph/0502097) Inner core shadow June 23, 2005 NuFact 05 - VLBL - Walter Winter

Summary: VL baseline applications Excluded 10-1 10-2 10-3 10-4 10-5 10-6 sin22q13 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 Open question: Simultaneous or subsequent operation of VL baseline? Feasiblity study for storage ring configurations needed! June 23, 2005 NuFact 05 - VLBL - Walter Winter