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The quest for q 13 : Parameter space and performance indicators

The quest for q 13 : Parameter space and performance indicators. Proton Driver General Meeting At Fermilab April 27, 2005 Walter Winter Institute for Advanced Study, Princeton. Contents. Introduction Simulation of future experiments Performance indicators for q 13

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The quest for q 13 : Parameter space and performance indicators

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  1. The quest for q13: Parameter space and performance indicators Proton Driver General Meeting At Fermilab April 27, 2005 Walter Winter Institute for Advanced Study, Princeton

  2. Contents • Introduction • Simulation of future experiments • Performance indicators for q13 • What is “Fraction of dCP”? • PD News: Neutrino oscillation landscapes • Some implications: Examples for q13 cases • Summary PD General Meeting - Walter Winter

  3. ( ) ( ) ( ) = x x Neutrino mixing Use standard parameterization - as for CKM matrix: (sij = sin qij cij = cos qij) • Three mixing angles q13, q12,q23; one CP phase dCP • Difference to quarks: Two mixing angles large: q12,q23 PD General Meeting - Walter Winter

  4. Neutrino mass • From oscillations: We know that neutrinos have mass! • Dirac or Majorana? • Absolute neutrino mass scale? Now: < eV • Mass schemes: Degenerate or hierarchical? • Mass hierarchy:Normal or inverted?In addition: Hierarchy is good model discriminator! Better mass bounds from cosmology, 0nbb-decay Adiabatic conversion in SN PD General Meeting - Walter Winter

  5. Neutrino oscillations with two flavors Mixing and mass squared difference:na “disappearance”:nb “appearance”: ~Frequency Amplitude Baseline: Source - Detector Energy PD General Meeting - Walter Winter

  6. Picture of three-flavor oscillations Atmosphericoscillation:Amplitude: q23Frequency: Dm312 Solaroscillation:Amplitude: q12Frequency: Dm212 Sub-leading effect: dCP Coupling strength: q13 Magnitude of q13is key to “subleading” effects: • Mass hierarchy determination • CP violation nm ne flavor transitions in atmospheric oscillations (“Oscillation maximum”) PD General Meeting - Walter Winter

  7. Some “man-made” neutrino sources For leading atm. params Signal prop. sin22q13 Contamination PD General Meeting - Walter Winter

  8. Disappearance measurements • Use expansions in small parameters: • Short baseline reactor experiments: 2nd term small for sin22q13 >> 10-3! • Long baseline accelerator experiments: No dCP, No mass hierarchy! (see e.g. Akhmedov et al., hep-ph/0402175) PD General Meeting - Walter Winter

  9. Appearance channels: nmne • Complicated, but all interesting information there: q13, dCP, mass hierarchy (via A) (Cervera et al. 2000; Freund, Huber, Lindner, 2000; Freund, 2001) PD General Meeting - Walter Winter

  10. Existing experiments: Future experiments: Input parameters Data Simulated data Fit parameters to data:Precision of quantity of interest Fit parameters to data:Precision of quantity of interest Predictions for future experiments ? Simulation of future experiments = “Hypothesis testing” PD General Meeting - Walter Winter

  11. Determine the precision of the quantity 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! Simulated versus fit parameters Fit parameters Simulated/true params PD General Meeting - Walter Winter

  12. q13 exclusion limit (1) • Describes the new q13 limit for the hyopthesis of no signal (q13=0) • Define as largest fit value of q13=0, which fits true q13=0 • Straightfoward inclusion of correlations and degeneracies • Does not depend on the simulated dCPand mass hierarchy! (Huber et al hep-ph/0403068) PD General Meeting - Walter Winter

  13. Simulated parameters:q13=0, dCP meaningless Relatively “simple” parameter dependencies No dependence on dCP, mass hierarchy Fit parameters:All six parameters Correlations and degeneracies affect this performance indicator Small for NOvA etc.;Rate ~ 0 q13 exclusion limit (2) Look for any combination of parameters which “fake” the smallest rate PD General Meeting - Walter Winter

  14. Simulated parameters:Hypothesis:Certain q13, dCP, mass hierarchy Can we find a signal for this hypothesis? Maximize parameter space for discovery Fit parameters:Relatively simple as long as “solar term” negligible Small impact of correlations Small for NOvA etc.;Rate ~ 0 q13 discovery limit Simulated rate depends on all parameters PD General Meeting - Walter Winter

  15. q13 exclusion vs. q13 discovery • Two different performance indicators • q13 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 q13? • q13 discovery interesting for PD era:In what cases could we discover something? • Completely risk-minimized discovery potential corresponds approximately to q13 exclusion limit • Discovery limit has to be interpreted with care! • Correlations and degeneracies in one case translate into dependence on dCP and mass hierarchy in the other PD General Meeting - Walter Winter

  16. q13 exclusion limit at PD startup • q13 may or may not have been discovered at PD startup: Need substantially more thanexisting beamline + detectorBut: superbeams way to go Conceptual casesin PD study Probably need neutrino factory Could work on CP violation+mass hierarchywith existing beamline + det. NUE=“NuMI Up-graded Experiment” ~ NOvA Scenario 3:Discovery unlikely until PD startup Scenario 1:Certainly discovereduntil PD startup Scenario 2:Discovery likely before PD startup PD General Meeting - Walter Winter

  17. q13 discovery and CP fraction plots Read: For sin22q13=0.04, we expect a discovery for 20% of all values of dCP Sensitive region as function of true q13 and dCP New primer in PD-NOD! Fraction of dCP for successful discovery dCP values now stacked for each q13 PD General Meeting - Walter Winter

  18. “Fraction of dCP”= Measure for luck? No luck needed; works for all d, hier. • Discovery potential depends on true dCP, mass hierarchy • For uniform distribution in dCP:Fraction of dCP = Probability to discoverdCP • Remember: dCP comes from a complex phase factor eid in the mixing matrix Thus: a distribution in sin d would be theoretically “unnatural” “Typical” d;50-50 chance Best case d, hierarchy (FNAL Proton Driver study, to appear in 2005) PD General Meeting - Walter Winter

  19. Discovery limit landscapes: q13 • Assume that each experiment runs five years (most in neutrino mode only) • Characterize dependence on dCP as bands reflecting all possible chases • Choose starting times as close as possible to values in respective LOIs/proposals • Include statistics+systematics+correlations • Assume that disappearance channels give best information on leading atmospheric params PD General Meeting - Walter Winter

  20. Evolution of q13 discovery limit Proton driver + NUE(NuMI Upgraded Experiment): Pass branching point almost for sure Superbeamshave a better discovery potential than reactor exps for a large number of CP values! Branching point between Scenarios 2 and 3 (not for PD!) MINOS and CNGSHave approximately equal performance(depends somewhat onassumptions) Reactor experiments:No dependence on dCP! Reactor-IIcorresponds to “large” reactor experiment(Braidwood or similar). Actual performance depends on control of systematics! 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) PD General Meeting - Walter Winter

  21. Evolution of q13 discovery limit • Obviously different generations of experiments • New generation will quickly determine potential • Reactor experiments provide complementary information! • Antineutrino running could help for risk minimization • For inverted hierarchy: Beam limits shift somewhat down! (from: FNAL Proton Driver Study, to appear in 2005) PD General Meeting - Walter Winter

  22. Examples for q13 cases (1) ~2012-2013: q13 signal likely at superbeams or reactor experiments • Assume: Actual value of sin22q13 = 0.03 PD+NUE+2nd NUE very competitiveFast+cost efficient alternative to T2HK!? (from: FNAL Proton Driver Study, to appear in 2005) PD General Meeting - Walter Winter

  23. Examples for q13 cases (2) Discovery of q13 unlikely without PD and impossible for T2K If no PD at Fermilab, probably no further superbeam program! • Assume: Actual value of sin22q13 = 0.007 But: One could have done almost of all the physics with a superbeam program! (from: FNAL Proton Driver Study, to appear in 2005) PD General Meeting - Walter Winter

  24. Summary • NUE discovery potential for q13 greatly increased by Proton Driver • NUE and NUE+PD have “very likely” better q13 discovery potential then reactor experiments • Predictions for reactor experiments more robust: Do not depend on dCP and mass hierarchyThus: Very competitive exclusion limits expected (if no signal) • Dependence of Pme on dCP and mass hierarchy implies that genuine potential of PD-based experiments in these quantities PD General Meeting - Walter Winter

  25. Special topic: Why does worst-case limit hardly improve for superbeam upgrades? • Assume oscillation maximum, neglect solar term • Then for one specific value of dCP (typically p/2): • This means: For sin2q13 ~ a (or sin22q13 ~ a2 ~ 0.001) Pme is very small independent of the total number of events • Therefore: The closer the experiment performance to sin22q13 = 0.001, the broader the band and the more unaffected the lower end of the band (equivalent to good performance in dCP!) PD General Meeting - Walter Winter

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