September 24, 2007 Walter Winter Phenomenology of q13 q13 half-day meeting Oxford, UK September 24, 2007 Walter Winter Universität Würzburg

Contents Introduction The measurement of q13: Reactor versus beam experiments Performance indicators for q13 … and comparison of experiments The “farer” future: what if q13 is very small? Beyond q13: Mass hierarchy and CP violation Summary Sept. 24, 2007 Oxford 2007 - Walter Winter

Neutrino mixing ( ) ( ) ( ) Use standard parameterization - as for CKM matrix: (sij = sin qij cij = cos qij) ( ) ( ) ( ) = x Three mixing angles q13, q12, q23; one CP phase dCP Difference to quarks: Two mixing angles large: q12, q23 Sept. 24, 2007 Oxford 2007 - Walter Winter

Neutrino mass Mass hierarchy: Normal or inverted? Theory: Dirac or Majorana mass terms? To independent mass squared differences relevant for oscillations: |Dm212 | << |Dm312| |a| = Dm212/|Dm312| ~ 3% 8 8 Mass spectra: Difference to origin? Degenerate masses? Sept. 24, 2007 Oxford 2007 - Walter Winter

Neutrino oscillations with two flavors Mixing and mass squared difference: na “disappearance”: nb “appearance”: ~Frequency Amplitude Baseline: Source - Detector Energy Sept. 24, 2007 Oxford 2007 - 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 Use ne transitions on atmospheric oscillation scale (“Oscillation maximum”) Magnitude of q13 is key to “subleading” effects: Mass hierarchy determination CP violation Sept. 24, 2007 Oxford 2007 - Walter Winter

Matter effects in n-oscillations (MSW) Ordinary matter contains electrons, but no m, t 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 Hamiltonian in matter: The matter potential is not CP-inv.! Source of many problems! (Wolfenstein, 1978; Mikheyev, Smirnov, 1985) Y: electron fraction ~ 0.5 (electrons per nucleon) Sept. 24, 2007 Oxford 2007 - Walter Winter

The measurement of q13 Experiment classes

Experiment classes by source Production … and Detection Limitations L <E> Reactor Systematics 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 b-beam Source luminosity 100-2,000 km 0.3 – 10 GeV For leading atm. params Signal prop. sin22q13 Contamination Sept. 24, 2007 Oxford 2007 - Walter Winter

Disappearance measurements Use expansions in small parameters: Short baseline reactor experiments: 2nd term small for sin22q13 >> 10-3! Long baseline accelerator experiments: D31 = Dm312 L/(4E) No dCP, No mass hierarchy! (see e.g. Akhmedov et al., hep-ph/0402175) Sept. 24, 2007 Oxford 2007 - Walter Winter

A multi-detector reactor experiment … for a “clean” measurement of q13 See also Lisa Falk-Harris‘ talk! Identical detectors, L ~ 1.1-1.7 km Daya Bay size Unknown systematics important for large luminosity NB: No sensitivity to dCP and mass hierarchy! Double Chooz size (Minakata et al, 2002; Huber, Lindner, Schwetz, Winter, 2003) Sept. 24, 2007 Oxford 2007 - Walter Winter

Appearance channels: nm ne Antineutrinos (Cervera et al. 2000; Freund, Huber, Lindner, 2000; Freund, 2001) Complicated, but all interesting information there: q13, dCP, mass hierarchy (via A) Sept. 24, 2007 Oxford 2007 - Walter Winter

Neutrino beams nb? Accelerator-based neutrino source na Far detector See also Dave Wark‘s talk! nb? Accelerator-based neutrino source na Far detector Often: near detector (measures flux times cross sections) Baseline: L ~ E/Dm312 (Osc. length) Sept. 24, 2007 Oxford 2007 - Walter Winter

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

q13 performance indicators …and comparison of experiments q13 exclusion/sensitivity limit q13 discovery potential

Predictions for future experiments Existing experiments: Future experiments: ? Simulated data Fit parameters to data: Precision of quantity of interest Input parameters Data Fit parameters to data: Precision of quantity of interest Performance indicators depend on input param. hypothesis! Sept. 24, 2007 Oxford 2007 - Walter Winter

Simulated versus fit parameters Simulated/true params 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! Determine the precision of the quantity of interest “Unused” parameteres are usually marginalized over (projection onto axis/plane of interest) Source of correlations! Sept. 24, 2007 Oxford 2007 - Walter Winter

q13 exclusion/sensitivity limit (1) Describes the new q13 limit for the simulation of no signal (q13=0) Define as largest fit value of q13, which fits true q13=0 Straightforward inclusion of correlations and degeneracies Does not depend on the simulated dCP and mass hierarchy! (from hep-ph/0403068, App. C) Sept. 24, 2007 Oxford 2007 - Walter Winter

q13 exclusion/sensitivity limit (2) 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 Look for any combination of parameters which “fake” the smallest rate Small for T2K etc.; Rate ~ 0 Sept. 24, 2007 Oxford 2007 - Walter Winter

q13 exclusion: Problems with degeneracies Connected (green) or disconnected (yellow) degenerate solutions in parameter space Affect measurements Example: q13-sensitivity (exclusion limit) Discrete degeneracies: (d,q13)-degeneracy (Burguet-Castell et al, 2001) sgn-degeneracy (Minakata, Nunokawa, 2001) (q23,p/2-q23)-degeneracy (Fogli, Lisi, 1996) (Huber, Lindner, Winter, 2002) Degeneracy resolution important topic in recent years! Example: Neutrino factory (later) Sept. 24, 2007 Oxford 2007 - Walter Winter

q13 discovery limit Simulated parameters: Hypothesis: Certain q13>0, dCP, mass hierarchy Can we establish q13>0 for this hypothesis? 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 Sept. 24, 2007 Oxford 2007 - Walter Winter

q13 discovery: 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 “Typical dCP”: CP fraction 50% Fraction of dCP for successful discovery dCP values now stacked for each q13 Sept. 24, 2007 Oxford 2007 - Walter Winter

Evolution of q13 discovery limit? Specific scenario Bands reflect dependence on dCP GLoBES 2005 (NOvA) (from: FNAL Proton Driver Study) Sept. 24, 2007 Oxford 2007 - Walter Winter

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

Experiments for very small q13 The „farer“ future? Experiments for very small q13

Superbeam upgrades: Examples Bands reflect variation of systematical errors: 2%-5%-10% Dots: Nominal L Typical dCP, 3s Discovery of sin22q13 downto ~10-3 discovery (Barger, Huber, Marfatia, Winter, hep-ph/0610301, hep-ph/0703029) Sept. 24, 2007 Oxford 2007 - Walter Winter

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

Ken Long (Imperial, RAL) 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 Initiative from ~ 2007-2012 to present a design report, schedule, cost estimate, risk assessment for a neutrino factory In Europe: Close connection to „Euronus“ 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? Ken Long (Imperial, RAL) Sept. 24, 2007 Oxford 2007 - Walter Winter

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

Mass hierarchy and CP violation Precision measurements Beyond q13 discovery Mass hierarchy and CP violation Precision measurements

Perspectives for MH and dCP for the coming 5 to 10 years? 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) Sept. 24, 2007 Oxford 2007 - Walter Winter

Help from outer space? Astrophysical neutrino sources produce certain flavor ratios of neutrinos (ne:nm:nt): 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: Measure muon track to shower ratio at neutrino telescope: R = fm/(fe+ft) (conservative, since in future also flavors!?) ~ cosd Sept. 24, 2007 Oxford 2007 - Walter Winter

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

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

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

Beyond discovery: Precision measurements at a NF dCP precision q13 precision 3s dCP dep. (Huber, Lindner, Winter, 2004) (Gandhi, Winter, 2006) Sept. 24, 2007 Oxford 2007 - Walter Winter

Summary q13 will be tested in the near future by reactor experiments and superbeams Reactor experiments provide very good limits on q13, while a discovery may be more likely at a beam experiment If not found, neutrino factories may probe sin22q13 down to the level of 10-4 or 10-5 The measurements of the mass hierarchy and dCP will require the next generation of experiments Sept. 24, 2007 Oxford 2007 - Walter Winter

Backup

Matter effects (two flavors, r const.) Parameter mapping (same form): Vacuum: Matter: Describes ne – nm transitions to 0th order in a: q  q13 Dm2  Dm312 (except factor 0.5) “Matter resonance”: In this case: - Effective mixing maximal - Effective osc. frequency min. r ~ 4.5 g/cm3 (Earth’s mantle) LBL osc.: E ~ 6.5 GeV Resonance energy: Sept. 24, 2007 Oxford 2007 - Walter Winter

Early mass hierarchy measurement? Fake solution is running in dCP as function of q13 Astrophysical source may help mass hierarchy measurement by constraining this running Curves: Errors on R 5% 10% 20% No constraint MINOS+Double Chooz+T2K+NOvA (Winter, 2006) Sept. 24, 2007 Oxford 2007 - Walter Winter