1. 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

2. 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

3. 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 )

4. 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

5. 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

6. 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

7. 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

8. 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!

9. 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)

10. 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”

11. 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

12. 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)

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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!

21. 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)

22. 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)

23. 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)

24. 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

25. 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 !)