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Phenomenology of  13  13 half-day meeting Oxford, UK September 24, 2007 Walter Winter Universität Würzburg.

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Presentation on theme: "Phenomenology of  13  13 half-day meeting Oxford, UK September 24, 2007 Walter Winter Universität Würzburg."— Presentation transcript:

1 Phenomenology of  13  13 half-day meeting Oxford, UK September 24, 2007 Walter Winter Universität Würzburg

2 Sept. 24, 2007Oxford 2007 - Walter Winter2 Contents Introduction Introduction The measurement of  13 : Reactor versus beam experiments The measurement of  13 : Reactor versus beam experiments Performance indicators for  13 … and comparison of experiments Performance indicators for  13 … and comparison of experiments The “farer” future: what if  13 is very small? The “farer” future: what if  13 is very small? Beyond  13 : Mass hierarchy and CP violation Beyond  13 : Mass hierarchy and CP violation Summary Summary

3 Sept. 24, 2007Oxford 2007 - 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 Sept. 24, 2007Oxford 2007 - Walter Winter4 Neutrino mass To independent mass squared differences relevant for oscillations: |  m 21 2 | << |  m 31 2 | |  =  m 21 2 /|  m 31 2 | ~ 3% To independent mass squared differences relevant for oscillations: |  m 21 2 | << |  m 31 2 | |  =  m 21 2 /|  m 31 2 | ~ 3% Mass spectra: Difference to origin? Degenerate masses? Mass spectra: Difference to origin? Degenerate masses? Mass hierarchy: Normal or inverted? Mass hierarchy: Normal or inverted? Theory: Dirac or Majorana mass terms? Theory: Dirac or Majorana mass terms? 8 8

5 Sept. 24, 2007Oxford 2007 - Walter Winter5 Neutrino oscillations with two flavors Mixing and mass squared difference:  “disappearance”:  “appearance”: Amplitude ~Frequency Baseline: Source - Detector Energy

6 Sept. 24, 2007Oxford 2007 - Walter Winter6 Picture of three-flavor oscillations Magnitude of  13 is key to “subleading” effects: Mass hierarchy determination CP violation Use e transitions on atmospheric oscillation scale (“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 Sept. 24, 2007Oxford 2007 - Walter Winter7 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 because of CC (rel. phase shift) Coherent forward scattering in matter has net effect on electron flavor because of CC (rel. phase shift) Matter effects proportional to electron density and baseline Matter effects proportional to electron density and baseline Hamiltonian in matter: Hamiltonian in matter: The matter potential is not CP-inv.! Source of many problems! The matter potential is not CP-inv.! Source of many problems! Y: electron fraction ~ 0.5 (electrons per nucleon) (Wolfenstein, 1978; Mikheyev, Smirnov, 1985)

8 The measurement of  13 Experiment classes

9 Sept. 24, 2007Oxford 2007 - Walter Winter9 Experiment classes by source Source Production … and Detection LimitationsL<E> ReactorSystematics 1-2 km ~4 MeV Super- beam Intrinsic beam BG, systematics 100- 2,500 km 0.5 – 5 GeV Neutrino factory Charge identification, NC BG 700- 7,500 km 5-50 GeV  -beam Source luminosity 100- 2,000 km 0.3 – 10 GeV For leading atm. params Signal prop. sin 2 2  13 Contamination

10 Sept. 24, 2007Oxford 2007 - Walter Winter10 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!  31 =  m 31 2 L/(4E)

11 Sept. 24, 2007Oxford 2007 - Walter Winter11 A multi-detector reactor experiment … for a “clean” measurement of  13 Double Chooz size Daya Bay size (Minakata et al, 2002; Huber, Lindner, Schwetz, Winter, 2003) Identical detectors, L ~ 1.1-1.7 km Unknown systematics important for large luminosity NB: No sensitivity to  CP and mass hierarchy! See also Lisa Falk-Harris‘ talk!

12 Sept. 24, 2007Oxford 2007 - Walter Winter12 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) Antineutrinos

13 Sept. 24, 2007Oxford 2007 - Walter Winter13 Neutrino beams Accelerator- based neutrino source Often: near detector (measures flux times cross sections) Far detector Baseline: L ~ E/  m 31 2 (Osc. length)   ? See also Dave Wark‘s talk!

14 Sept. 24, 2007Oxford 2007 - Walter Winter14 Running example: MINOS Measurement of atmospheric parameters with high precision Measurement of atmospheric parameters with high precision Flavor conversion ? Flavor conversion ? Fermilab - Soudan L ~ 735 km Far detector: 5400 t Near detector: 980 t 735 km Beam line

15  13 performance indicators …and comparison of experiments  13 exclusion/sensitivity limit  13 discovery potential

16 Sept. 24, 2007Oxford 2007 - Walter Winter16 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 ? Performance indicators depend on input param. hypothesis!

17 Sept. 24, 2007Oxford 2007 - Walter Winter17 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

18 Sept. 24, 2007Oxford 2007 - Walter Winter18  13 exclusion/sensitivity limit (1) Describes the new  13 limit for the simulation of no signal (  13 =0) Describes the new  13 limit for the simulation of no signal (  13 =0) Define as largest fit value of  13, which fits true  13 =0 Define as largest fit value of  13, which fits true  13 =0  Straightforward 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! (from hep-ph/0403068, App. C)

19 Sept. 24, 2007Oxford 2007 - Walter Winter19  13 exclusion/sensitivity 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 T2K etc.; Rate ~ 0 Look for any combination of parameters which “fake” the smallest rate

20 Sept. 24, 2007Oxford 2007 - Walter Winter20  13 exclusion: Problems with degeneracies Connected (green) or disconnected (yellow) degenerate solutions in parameter space Connected (green) or disconnected (yellow) degenerate solutions in parameter space Affect measurements Example:  13 -sensitivity (exclusion limit) Affect measurements Example:  13 -sensitivity (exclusion limit) (Huber, Lindner, Winter, 2002) Discrete degeneracies: ( ,  13 )-degeneracy (Burguet-Castell et al, 2001) sgn-degeneracy (Minakata, Nunokawa, 2001) (  23,  /2-  23 )-degeneracy (Fogli, Lisi, 1996) Discrete degeneracies: ( ,  13 )-degeneracy (Burguet-Castell et al, 2001) sgn-degeneracy (Minakata, Nunokawa, 2001) (  23,  /2-  23 )-degeneracy (Fogli, Lisi, 1996) Degeneracy resolution important topic in recent years! Example: Neutrino factory (later)

21 Sept. 24, 2007Oxford 2007 - Walter Winter21  13 discovery limit Simulated parameters: Hypothesis: Certain  13 >0,  CP, mass hierarchy Simulated parameters: Hypothesis: Certain  13 >0,  CP, mass hierarchy Can we establish  13 >0 for this hypothesis? Can we establish  13 >0 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

22 Sept. 24, 2007Oxford 2007 - Walter Winter22  13 discovery: 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 Read: For sin 2 2  13 =0.04, we expect a discovery for 20% of all values of  CP “Typical  CP ”: CP fraction 50%

23 Sept. 24, 2007Oxford 2007 - Walter Winter23 Evolution of  13 discovery limit? Specific scenario Specific scenario Bands reflect dependence on  CP Bands reflect dependence on  CP (from: FNAL Proton Driver Study) GLoBES 2005 (NOvA)

24 Sept. 24, 2007Oxford 2007 - Walter Winter24 Discovery versus exclusion power Beams: discovery machines?Reactor experiments: Exclusion instruments? (Huber, Kopp, Lindner, Rolinec, Winter, 2006)

25 The „farer“ future? Experiments for very small  13

26 Sept. 24, 2007Oxford 2007 - Walter Winter26 Superbeam upgrades: Examples Bands reflect variation of systematical errors: 2%-5%-10% Bands reflect variation of systematical errors: 2%-5%-10% Dots: Nominal L Dots: Nominal L Typical  CP, 3  Typical  CP, 3  Discovery of sin 2 2  13 downto ~10 -3 Discovery of sin 2 2  13 downto ~10 -3 (Barger, Huber, Marfatia, Winter, hep-ph/0610301, hep-ph/0703029) discovery

27 Sept. 24, 2007Oxford 2007 - Walter Winter27 Neutrino factory Ultimate “high precision” instrument!? Ultimate “high precision” instrument!? Muon decays in straight sections of storage ring Muon decays in straight sections of storage ring Technical challenges: Target power, muon cooling, charge identification, maybe steep decay tunnels Technical challenges: Target power, muon cooling, charge identification, maybe steep decay tunnels (from: CERN Yellow Report ) p Target , K  Decays  -Accelerator  Cooling “Right sign” “Wrong sign” “Right sign” “Wrong sign” (Geer, 1997; de Rujula, Gavela, Hernandez, 1998; Cervera et al, 2000)

28 Sept. 24, 2007Oxford 2007 - Walter Winter28 IDS-NF launched at NuFact 07 International design study for a neutrino factory Successor of the International Scoping Study for a „future neutrino factory and superbeam facility“: Physics case made in physics WG report (~368 pp) http://www.hep.ph.ic.ac.uk/ids Successor of the International Scoping Study for a „future neutrino factory and superbeam facility“: Physics case made in physics WG report (~368 pp) http://www.hep.ph.ic.ac.uk/ids http://www.hep.ph.ic.ac.uk/ids Initiative from ~ 2007-2012 to present a design report, schedule, cost estimate, risk assessment for a neutrino factory Initiative from ~ 2007-2012 to present a design report, schedule, cost estimate, risk assessment for a neutrino factory In Europe: Close connection to „Euro us“ proposal within the FP 07; currently ranked #1, negotiating contract In Europe: Close connection to „Euro us“ proposal within the FP 07; currently ranked #1, negotiating contract In the US: „Muon collider task force“ How can a neutrino factory be „upgraded“ to a muon collider? In the US: „Muon collider task force“ How can a neutrino factory be „upgraded“ to a muon collider? Ken Long (Imperial, RAL)

29 Sept. 24, 2007Oxford 2007 - Walter Winter29 Resolving degeneracies Example: „Magic“ baseline for NF L= ~ 4000 km (CP) + ~7500 km (degs) today baseline configuration of a neutrino factory (ISS study, 2006) L= ~ 4000 km (CP) + ~7500 km (degs) today baseline configuration of a neutrino factory (ISS study, 2006) (Huber, Winter, 2003)

30 Beyond  13 discovery Mass hierarchy and CP violation Precision measurements

31 Sept. 24, 2007Oxford 2007 - Walter Winter31 Perspectives for MH and  CP for the coming 5 to 10 years? A mass hierarchy or CP violation measurement will be unlikely or impossible from A mass hierarchy or CP violation measurement will be unlikely or impossible from –Beams+Reactor experiments –Any other source alone (supernova etc.) (from: Huber, Lindner, Rolinec, Schwetz, Winter, 2004)

32 Sept. 24, 2007Oxford 2007 - Walter Winter32 Help from outer space? Astrophysical neutrino sources produce certain flavor ratios of neutrinos ( e :  :  ): Neutron decays: (1:0:0) Muon damped sources: (0:1:0) Pion decays: (1:2:0) Astrophysical neutrino sources produce certain flavor ratios of neutrinos ( e :  :  ): Neutron decays: (1:0:0) Muon damped sources: (0:1:0) Pion decays: (1:2:0) These ratios are changed at Earth through averaged neutrino oscillations: These ratios are changed at Earth through averaged neutrino oscillations: Measure muon track to shower ratio at neutrino telescope: R =   /(  e   ) (conservative, since in future also flavors!?) Measure muon track to shower ratio at neutrino telescope: R =   /(  e   ) (conservative, since in future also flavors!?) ~ cos 

33 Sept. 24, 2007Oxford 2007 - Walter Winter33 Complementarity to beams Use R to obtain information on osc. parameters? Difficult, since Use R to obtain information on osc. parameters? Difficult, since –Low statistics –No spectral info (Serpico, Kachelriess, 2005; Serpico, 2005) But: Complementary dependence on  CP But: Complementary dependence on  CP Combine the information from multiple low statistics exps? Combine the information from multiple low statistics exps? (Winter, 2006) R Total Rates

34 Sept. 24, 2007Oxford 2007 - Walter Winter34 Early measurement of  CP... using Double Chooz? Double Chooz might be the first experiment to observe  CP Double Chooz might be the first experiment to observe  CP If more information: possibly even CP violation measurement: If more information: possibly even CP violation measurement: (Winter, 2006) (Blum, Nir, Waxman, 2007)

35 Sept. 24, 2007Oxford 2007 - Walter Winter35 Future discovery of MH and  CP Mass hierarchy discoveryCP violation discovery (ISS study) Left end of band: Optimistic setup Right end of band: Conservative setup

36 Sept. 24, 2007Oxford 2007 - Walter Winter36 Beyond discovery: Precision measurements at a NF (Gandhi, Winter, 2006)(Huber, Lindner, Winter, 2004)  CP precision  13 precision  CP dep. 33

37 Sept. 24, 2007Oxford 2007 - Walter Winter37 Summary  13 will be tested in the near future by reactor experiments and superbeams  13 will be tested in the near future by reactor experiments and superbeams Reactor experiments provide very good limits on  13, while a discovery may be more likely at a beam experiment Reactor experiments provide very good limits on  13, while a discovery may be more likely at a beam experiment If not found, neutrino factories may probe sin 2 2  13 down to the level of 10 -4 or 10 -5 If not found, neutrino factories may probe sin 2 2  13 down to the level of 10 -4 or 10 -5 The measurements of the mass hierarchy and  CP will require the next generation of experiments The measurements of the mass hierarchy and  CP will require the next generation of experiments

38 Backup

39 Sept. 24, 2007Oxford 2007 - Walter Winter39 Matter effects (two flavors,  const.) Parameter mapping (same form): Vacuum: Matter: Parameter mapping (same form): Vacuum: Matter: “Matter resonance”: In this case: - Effective mixing maximal - Effective osc. frequency min.  ~ 4.5 g/cm 3 (Earth’s mantle) LBL osc.: E ~ 6.5 GeV Resonance energy: Describes e –  transitions to 0 th order in     13  m 2   m 31 2 (except factor 0.5)

40 Sept. 24, 2007Oxford 2007 - Walter Winter40 Curves: Errors on R 5% 10% 20% No constraint Early mass hierarchy measurement? Fake solution is running in  CP as function of  13 Fake solution is running in  CP as function of  13 Astrophysical source may help mass hierarchy measurement by constraining this running Astrophysical source may help mass hierarchy measurement by constraining this running (Winter, 2006) MINOS+Double Chooz+T2K+NOvA

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