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The quest for 13 : Parameter space and performance indicators Proton Driver General Meeting At Fermilab April 27, 2005 Walter Winter Institute for Advanced Study, Princeton
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April 27, 2005PD General Meeting - Walter Winter2 Contents Introduction Introduction Simulation of future experiments Simulation of future experiments Performance indicators for 13 Performance indicators for 13 What is “Fraction of CP ”? What is “Fraction of CP ”? PD News: Neutrino oscillation landscapes PD News: Neutrino oscillation landscapes Some implications: Examples for 13 cases Some implications: Examples for 13 cases Summary Summary
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April 27, 2005PD General Meeting - Walter Winter3 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 )
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April 27, 2005PD General Meeting - Walter Winter4 Neutrino mass From oscillations: We know that neutrinos have mass! From oscillations: We know that neutrinos have mass! Dirac or Majorana? Dirac or Majorana? Absolute neutrino mass scale? Now: < eV Absolute neutrino mass scale? Now: < eV Mass schemes: Degenerate or hierarchical? Mass schemes: Degenerate or hierarchical? Mass hierarchy: Normal or inverted? In addition: Hierarchy is good model discriminator! Mass hierarchy: Normal or inverted? In addition: Hierarchy is good model discriminator! Adiabatic conversion in SN Better mass bounds from cosmology, 0 -decay
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April 27, 2005PD General Meeting - Walter Winter5 Neutrino oscillations with two flavors Mixing and mass squared difference: “disappearance”: “appearance”: Amplitude ~Frequency Baseline: Source - Detector Energy
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April 27, 2005PD General Meeting - Walter Winter6 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
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April 27, 2005PD General Meeting - Walter Winter7 Some “man-made” neutrino sources Source Production … and Detection “Limitation”L<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
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April 27, 2005PD General Meeting - Walter Winter8 Disappearance measurements Use expansions in small parameters: Use expansions in small parameters: Short baseline reactor experiments: 2 nd term small for sin 2 2 13 >> 10 -3 ! Short baseline reactor experiments: 2 nd term small for sin 2 2 13 >> 10 -3 ! Long baseline accelerator experiments: Long baseline accelerator experiments: (see e.g. Akhmedov et al., hep-ph/0402175) No CP, No mass hierarchy!
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April 27, 2005PD General Meeting - Walter Winter9 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)
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April 27, 2005PD General Meeting - Walter Winter10 Predictions for future experiments Existing experiments: Existing experiments: Future experiments: Data Fit parameters to data: Precision of quantity of interest Simulated data Fit parameters to data: Precision of quantity of interest Input parameters ? Simulation of future experiments = “Hypothesis testing”
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April 27, 2005PD General Meeting - Walter Winter11 Simulated versus fit parameters Determine the precision of the quantity of interest Determine the precision of the quantity of interest “Unused” parameteres are usually marginalized over (projection onto axis/plane of interest) “Unused” parameteres are usually marginalized over (projection onto axis/plane of interest) Source of correlations! Represent the values implemented by nature Known within current limits Change the event rates, top. Have to be interpreted like “If the value of … is …, then the performance will be …” - Luck or not luck? Used for risk minimization! Fit parametersSimulated/true params
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April 27, 2005PD General Meeting - Walter Winter12 13 exclusion limit (1) Describes the new 13 limit for the hyopthesis of no signal ( 13 =0) Describes the new 13 limit for the hyopthesis of no signal ( 13 =0) Define as largest fit value of 13 =0, which fits true 13 =0 Define as largest fit value of 13 =0, which fits true 13 =0 Straightfoward inclusion of correlations and degeneracies Does not depend on the simulated CP and mass hierarchy! Does not depend on the simulated CP and mass hierarchy! (Huber et al hep-ph/0403068)
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April 27, 2005PD General Meeting - Walter Winter13 13 exclusion limit (2) Simulated parameters: 13 =0, CP meaningless Simulated parameters: 13 =0, CP meaningless Relatively “simple” parameter dependencies Relatively “simple” parameter dependencies No dependence on CP, mass hierarchy No dependence on CP, mass hierarchy Fit parameters: All six parameters Correlations and degeneracies affect this performance indicator Small for NOvA etc.; Rate ~ 0 Look for any combination of parameters which “fake” the smallest rate
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April 27, 2005PD General Meeting - Walter Winter14 13 discovery limit Simulated parameters: Hypothesis: Certain 13, CP, mass hierarchy Simulated parameters: Hypothesis: Certain 13, CP, mass hierarchy Can we find a signal for this hypothesis? Can we find a signal for this hypothesis? Maximize parameter space for discovery Maximize parameter space for discovery Fit parameters: Relatively simple as long as “solar term” negligible Small impact of correlations Simulated rate depends on all parameters Small for NOvA etc.; Rate ~ 0
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April 27, 2005PD General Meeting - Walter Winter15 13 exclusion vs. 13 discovery Two different performance indicators Two different performance indicators 13 exclusion interesting for pre-PD era: What will be the limits at PD startup? How far can we go for sure = can we exclude that we will not discover 13 ? 13 exclusion interesting for pre-PD era: What will be the limits at PD startup? How far can we go for sure = can we exclude that we will not discover 13 ? 13 discovery interesting for PD era: In what cases could we discover something? 13 discovery interesting for PD era: In what cases could we discover something? Completely risk-minimized discovery potential corresponds approximately to 13 exclusion limit Completely risk-minimized discovery potential corresponds approximately to 13 exclusion limit »Discovery limit has to be interpreted with care! Correlations and degeneracies in one case translate into dependence on CP and mass hierarchy in the other Correlations and degeneracies in one case translate into dependence on CP and mass hierarchy in the other
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April 27, 2005PD General Meeting - Walter Winter16 13 exclusion limit at PD startup 13 may or may not have been discovered at PD startup: 13 may or may not have been discovered at PD startup: Scenario 3: Discovery unlikely until PD startup Scenario 1: Certainly discovered until PD startup Scenario 2: Discovery likely before PD startup Could work on CP violation+ mass hierarchy with existing beamline + det. Need substantially more than existing beamline + detector But: superbeams way to go Probably need neutrino factory Conceptual cases in PD study NUE=“NuMI Up- graded Experiment” ~ NOvA
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April 27, 2005PD General Meeting - Walter Winter17 13 discovery and CP fraction plots Sensitive region as function of true 13 and CP CP values now stacked for each 13 Fraction of CP for successful discovery New primer in PD-NOD! Read: For sin 2 2 13 =0.04, we expect a discovery for 20% of all values of CP
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April 27, 2005PD General Meeting - Walter Winter18 “Fraction of CP ” = Measure for luck? Discovery potential depends on true CP, mass hierarchy Discovery potential depends on true CP, mass hierarchy For uniform distribution in CP : Fraction of CP = Probability to discover CP For uniform distribution in CP : Fraction of CP = Probability to discover CP Remember: CP comes from a complex phase factor e i in the mixing matrix Thus: a distribution in sin would be theoretically “unnatural” Remember: CP comes from a complex phase factor e i in the mixing matrix Thus: a distribution in sin would be theoretically “unnatural” (FNAL Proton Driver study, to appear in 2005) No luck needed; works for all hier. Best case , hierarchy “Typical” chance
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April 27, 2005PD General Meeting - Walter Winter19 Discovery limit landscapes: 13 Assume that each experiment runs five years (most in neutrino mode only) Assume that each experiment runs five years (most in neutrino mode only) Characterize dependence on CP as bands reflecting all possible chases Characterize dependence on CP as bands reflecting all possible chases Choose starting times as close as possible to values in respective LOIs/proposals Choose starting times as close as possible to values in respective LOIs/proposals Include statistics+systematics+correlations Include statistics+systematics+correlations Assume that disappearance channels give best information on leading atmospheric params Assume that disappearance channels give best information on leading atmospheric params
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April 27, 2005PD General Meeting - Walter Winter20 Evolution of 13 discovery limit Branching point between Scenarios 2 and 3 (not for PD!) MINOS and CNGS Have approximately equal performance (depends somewhat on assumptions) Reactor experiments: No dependence on CP ! Reactor-II corresponds to “large” reactor experiment (Braidwood or similar). Actual performance depends on control of systematics! Proton driver + NUE (NuMI Upgraded Experiment): Pass branching point almost for sure Based on T2HK; assume start 10 years after T2K starts Starts about 10 years after branching point; changes polarity after 2.5 years (normal mass hierarchy assumed) Superbeams have a better discovery potential than reactor exps for a large number of CP values!
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April 27, 2005PD General Meeting - Walter Winter21 Evolution of 13 discovery limit Obviously different generations of experiments Obviously different generations of experiments New generation will quickly determine potential New generation will quickly determine potential Reactor experiments provide complementary information! Reactor experiments provide complementary information! Antineutrino running could help for risk minimization Antineutrino running could help for risk minimization For inverted hierarchy: Beam limits shift somewhat down! For inverted hierarchy: Beam limits shift somewhat down! (from: FNAL Proton Driver Study, to appear in 2005)
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April 27, 2005PD General Meeting - Walter Winter22 Examples for 13 cases (1) Assume: Actual value of sin 2 2 13 = 0.03 Assume: Actual value of sin 2 2 13 = 0.03 ~2012-2013: 13 signal likely at superbeams or reactor experiments PD+NUE+2 nd NUE very competitive Fast+cost efficient alternative to T2HK!? (from: FNAL Proton Driver Study, to appear in 2005)
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April 27, 2005PD General Meeting - Walter Winter23 Examples for 13 cases (2) Assume: Actual value of sin 2 2 13 = 0.007 Assume: Actual value of sin 2 2 13 = 0.007 Discovery of 13 unlikely without PD and impossible for T2K But: One could have done almost of all the physics with a superbeam program! If no PD at Fermilab, probably no further superbeam program! (from: FNAL Proton Driver Study, to appear in 2005)
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April 27, 2005PD General Meeting - Walter Winter24 Summary NUE discovery potential for 13 greatly increased by Proton Driver NUE discovery potential for 13 greatly increased by Proton Driver NUE and NUE+PD have “very likely” better 13 discovery potential then reactor experiments NUE and NUE+PD have “very likely” better 13 discovery potential then reactor experiments Predictions for reactor experiments more robust: Do not depend on CP and mass hierarchy Thus: Very competitive exclusion limits expected (if no signal) Predictions for reactor experiments more robust: Do not depend on CP and mass hierarchy Thus: Very competitive exclusion limits expected (if no signal) Dependence of P e on CP and mass hierarchy implies that genuine potential of PD-based experiments in these quantities Dependence of P e on CP and mass hierarchy implies that genuine potential of PD-based experiments in these quantities
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April 27, 2005PD General Meeting - Walter Winter25 Special topic: Why does worst-case limit hardly improve for superbeam upgrades? Assume oscillation maximum, neglect solar term Assume oscillation maximum, neglect solar term Then for one specific value of CP (typically /2): Then for one specific value of CP (typically /2): This means: For sin2 13 ~ (or sin 2 2 13 ~ 2 ~ 0.001) P e is very small independent of the total number of events This means: For sin2 13 ~ (or sin 2 2 13 ~ 2 ~ 0.001) P e is very small independent of the total number of events Therefore: The closer the experiment performance to sin 2 2 13 = 0.001, the broader the band and the more unaffected the lower end of the band (equivalent to good performance in CP !) Therefore: The closer the experiment performance to sin 2 2 13 = 0.001, the broader the band and the more unaffected the lower end of the band (equivalent to good performance in CP !)
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