Neutrino phenomenology Lecture 2: Precision physics with neutrinos Winter school Schladming 2010 Masses and constants 01.03.2010 Walter Winter Universität Würzburg ν
Contents (overall) Lecture 1: Testing neutrino mass and flavor mixing Lecture 2: Precision physics with neutrinos Lecture 3: Aspects of neutrino astrophysics 2
Contents (lecture 2) Repetition Matter effects in neutrino oscillations CP violation phenomenology Mass hierarchy measurement Experiments: The near future Experiments for precision. Example: Neutrino factory New physics searches (some examples) Summary 3
Repetition from yesterday
Three flavor oscillation summary With three flavors: six parameters (three mixing angles, one phase, two mass squared differences) Atmospheric oscillations: Amplitude: θ 23 Frequency: Δm 31 2 Coupling: θ 13 Solar oscillations: Amplitude: θ 12 Frequency: Δm 21 2 Suppressed effect: δ CP (Super-K, 1998; Chooz, 1999; SNO 2001+2002; KamLAND 2002) Established by two flavor subsector measurements In the future: measure unknown θ 13 and δ CP, MH 5
Global fits 90%CL, 3σ 1σ Schwetz, Tortola, Valle, 2008 6
A new ingredient: Matter effects in neutrino oscillations
Ordinary matter: electrons, but no µ, τ Coherent forward scattering in matter: Net effect on electron flavor Matter effects proportional to electron density n e and baseline Hamiltonian in matter (matrix form, flavor space): Matter effect (MSW) (Wolfenstein, 1978; Mikheyev, Smirnov, 1985) Y: electron fraction ~ 0.5 (electrons per nucleon) 8
Numerical evaluation Evolution operator method: H(ρ j ) is the Hamiltonian in constant density Note that in general Additional information by interference effects compared to pure absorption phenomena 9
Matter profile of the Earth as seen by a neutrino Core Inner core (PREM: Preliminary Reference Earth Model) 10
Two flavor limit (ρ=const.) Multiplied out, two flavors, global phase substracted: Compare to vacuum Idea: write matter Hamiltonian in same form as in vacuum with effective parameters 11
Parameter mapping Oscillation probabilities in vacuum: matter: Matter resonance: In this case: - Effective mixing maximal - Effective osc. frequency minimal Resonance energy: ρ ~ 4.5 g/cm 3 (Earth s mantle) Solar osc.: E ~ 100 MeV!!! Atm osc.: E ~ 6.5 GeV 12
Mass hierarchy Matter resonance for Neutrinos/Antineutrinos Will be used in the future to determine the mass ordering: 8 Normal Inverted 8 Neutrinos Resonance Suppression Antineutrinos Suppression Resonance Normal Δm 31 2 >0 Inverted Δm 31 2 <0 13
Three flavor effects: CPV phenomenology
Terminology Any value of δ CP (except for 0 and π) violates CP Sensitivity to CPV: Exclude CP-conserving solutions 0 and π for any choice of the other oscillation parameters in their allowed ranges Why interesting? Lecture Xing! 15
Three flavor effects Antineutrinos: Magic baseline: Silver: Platinum, T-inv.: (Cervera et al. 2000; Freund, Huber, Lindner, 2000; Huber, Winter, 2003; Akhmedov et al, 2004) 16
Degeneracies Iso-probability curves Neutrinos Antineutrinos Best-fit 17
Intrinsic vs. extrinsic CPV The dilemma: Strong matter effects (high E, long L), but Earth matter violates CP Intrinsic CPV (δ CP ) has to be disentangled from extrinsic CPV (from matter effects) Example: π-transit Fake sign-solution crosses CP conserving solution Typical ways out: T-inverted channel? (e.g. beta beam+superbeam, platinum channel at NF, NF+SB) Second (magic) baseline Fit True δ CP (violates CP maximally) Critical range True NuFact, L=3000 km Degeneracy above 2σ (excluded) (Huber, Lindner, Winter, hep-ph/0204352) 18
The magic baseline 19
CP violation discovery in (true) sin 2 2θ 13 and δ CP Best performance close to max. CPV (δ CP = π/2 or 3π/2) δ CP values now stacked for each θ 13 Sensitive region as a function of true θ 13 and δ CP No CPV discovery if δ CP too close to 0 or π 3σ No CPV discovery for all values of δ CP Read: If sin 2 2θ 13 =10-3, we expect a discovery for 80% of all values of δ CP ~ Cabibbo-angle precision at 2σ BENCHMARK! 20
Mass hierarchy measurement
Motivation 8 8 Normal Inverted Specific models typically come together with specific MH prediction (e.g. textures are very different) Good model discriminator (Albright, Chen, hep-ph/0608137) 22
Matter effects (Cervera et al. 2000; Freund, Huber, Lindner, 2000; Huber, Winter, 2003; Akhmedov et al, 2004) Magic baseline: Restore two flavor limit (ξ ~ 1 A for small θ 13 ) Resonance: 1-A 0 (NH: ν, IH: anti-ν) Damping: sign(a)=-1 (NH: anti-ν, IH: ν) Energy close to resonance energy helps (~ 7 GeV) To first approximation: P eµ ~ L 2 (e.g. at resonance) Baseline length helps (compensates 1/L 2 flux drop) 23
Baseline dependence Comparison matter (solid) and vacuum (dashed) Matter effects (hierarchy dependent) increase with L Event rate (ν, NH) hardly drops with L Go to long L! Event rates (A.U.) Peak neutrino energy ~ 14 GeV (Δm 2 21 0) NH matter effect Vacuum, NH or IH NH matter effect (Freund, Lindner, Petcov, Romanino, 1999) 24
Experiments: The near future
Artificial neutrino sources There are three possibilities to artificially produce neutrinos Beta decay: Example: Nuclear reactors Pion decay: From accelerators: Protonen Pions Muons, neutrinos Neutrinos Target Selection, focusing Decay tunnel Absorber Muon decay: Muons produced by pion decays! 26
New reactor experiments Examples: Double Chooz, Daya Bay Identical detectors, L ~ 1.1 km (Quelle: S. Peeters, NOW 2008) 27
Spin-off: Nuclear monitoring? Idea: The event rate N close to the reactor is high, Ν ~ 1/R 2 A few thousand events/day for small detector ~ 25 m away from reactor core Anticipated precision: ~ O (10) kg for extraction of radioactive material ν 28
Narrow band superbeams Off-axis technology to suppress backgrounds Beam spectrum more narrow Examples: T2K NOνA T2K beam OA 1 degree OA 2 degrees OA 3 degrees (hep-ex/0106019) 29
Simulation of future experiments GLoBES AEDL Abstract Experiment Definition Language Define and modify experiments AEDL files User Interface C library, reads AEDL files Functionality for experiment simulation (Huber, Lindner, Winter, 2004; Huber, Kopp, Lindner, Rolinec, Winter, 2007) http://www.mpi-hd.mpg.de/ lin/globes/ Application software linked with user interface Calculate sensitivities Comes with a 180 pages manual with step-by-step intro! 30
Calculation of event rates In practice: Secondary particles integrated out Detector response R(E,E ) E E 31
Next generation CPV reach Includes Double Chooz, Daya Bay, T2K, NOvA 90% CL (Huber, Lindner, Schwetz, Winter, arxiv:0907.1896) 32
Experiments for precision Example: Neutrino factory
Neutrino factory: International Design Study (IDS-NF) Muons decay in straight sections of a storage ring (Geer, 1997; de Rujula, Gavela, Hernandez, 1998; Cervera et al, 2000) Signal prop. sin 2 2θ 13 Contamination ISS IDS-NF: Initiative from ~ 2007-2012 to present a design report, schedule, cost estimate, risk assessment for a neutrino factory In Europe: Close connection to Euroνus proposal within the FP 07 In the US: Muon collider task force 34
IDS-NF baseline setup 1.0 Two decay rings E µ =25 GeV 5x10 20 useful muon decays per baseline (both polarities!) Two baselines: ~4000 + 7500 km Two MIND, 50kt each Currently: MECC at shorter baseline 35
NF physics potential Excellent θ 13, MH, CPV discovery reaches (IDS-NF, 2007) Robust optimum for ~ 4000 + 7500 km Optimization even robust under non-standard physics (dashed curves) (Kopp, Ota, Winter, arxiv:0804.2261; see also: Gandhi, Winter, 2007) 36
Steve Geer s vision 37
Science fiction or science fact? http://www.fnal.gov/pub/muon_collider/ 38
New physics searches (some examples, using neutrino factory near detectors)
New physics from heavy mediators Effective operator picture if mediators integrated out: ν mass d=6, 8, 10,...: NSI, NU, CLFV, Describes additions to the SM in a gauge-inv. way! Example: TeV-scale new physics d=6: ~ (100 GeV/1 TeV) 2 ~ 10-2 compared to the SM d=8: ~ (100 GeV/1 TeV) 4 ~ 10-4 compared to the SM Interesting dimension six operators Fermion-mediated Non-unitarity (NU) Scalar or vector mediated Non-standard int. (NSI) 40
Example 1: Non-standard interactions Typically described by effective four fermion interactions (here with leptons) May lead to matter NSI (for γ=δ=e) May also lead to source/detector NSI (e.g. NuFact: ε µβ s for α=δ=e, γ=µ) These source/det.nsi are process-dep.! 41
Lepton flavor violation and the story of SU(2) gauge invariance Ex.: CLFV e µ NSI (FCNC) ν e ν µ 4ν-NSI ν e (FCNC) ν µ e e e e ν e ν e Strong bounds Affects neutrino oscillations in matter (or neutrino production) Affects environments with high ν densities (supernovae) BUT: These phenomena are connected by SU(2) gauge invariance Difficult to construct large leptonic matter NSI with d=6 operators (Bergmann, Grossman, Pierce, hep-ph/9909390; Antusch, Baumann, Fernandez-Martinez, arxiv:0807.1003; Gavela, Hernandez, Ota, Winter,arXiv:0809.3451) Need d=8 effective operators,! Finding a model with large NSI is not trivial! 42
On current NSI bounds (Source NSI for NuFact) The bounds for the d=6 (e.g. scalar-mediated) operators are strong (CLFV, Lept. univ., etc.) (Antusch, Baumann, Fernandez-Martinez, arxiv:0807.1003) The model-independent bounds are much weaker (Biggio, Blennow, Fernandez-Martinez, arxiv:0907.0097) However: note that here the NSI have to come from d=8 (or loop d=6?) operators ε ~ (v/λ) 4 ~ 10-4 natural? NSI hierarchy problem? 43
Source NSI with ν τ at a NuFact Probably most interesting for near detectors: ε eτs, ε µτ s (no intrinsic beam BG) Near detectors measure zero-distance effect ~ ε s 2 Helps to resolve correlations ND5: OPERA-like ND at d=1 km, 90% CL (Tang, Winter, arxiv:0903.3039) This correlation is always present if: - NSI from d=6 operators - No CLFV (Gavela et al, arxiv:0809.3451; see also Schwetz, Ohlsson, Zhang, arxiv:0909.0455 for a particular model) 44
Example 2: also: MUV Non-unitarity of mixing matrix Integrating out heavy fermion fields (such as in a type-i TeV see-saw), one obtains neutrino mass and the d=6 operator (here: fermion singlets) Re-diagonalizing and re-normalizing the kinetic terms of the neutrinos, one has This can be described by an effective (non-unitary) mixing matrix ε with N=(1+ε) U Similar effect to NSI, but source, detector, and matter NSI are correlated in a particular, fundamental way (i.e., processindependent) 45
Impact of near detector Example: (Antusch, Blennow, Fernandez-Martinez, Lopez-Pavon, arxiv:0903.3986) Curves: 10kt, 1 kt, 100 t, no ND ν τ near detector important to detect zero-distance effect 46
Example 3: Search for sterile neutrinos 3+S schemes of neutrinos include (light) sterile states, i.e., neutral fermion states light enough to be produced The mixing with the active states must be small, the mass squared difference can be very different The effects on different oscillation channels depend on the model test all possible twoflavor short baseline (SBL) cases, which are standard oscillation-free Example: ν e disappearance 47
SBL ν e disappearance Averaging over straight important (dashed versus solid curves) Location matters: Depends on Δm 2 Two baseline setup? d=50 m d~2 km (as long as possible) 90% CL, 2 d.o.f., No systematics, m=200 kg (Giunti, Laveder, Winter, arxiv:0907.5487) 48
SBL systematics Systematics similar to reactor experiments: Use two detectors to cancel X-Sec errors 10% shape error arxiv:0907.3145 (Giunti, Laveder, Winter, arxiv:0907.5487) 49
Summary Matter effects key ingredient to measure the mass ordering How do neutrinos behave in environments with strongly varying matter density (Sun, Supernovae)? Man-made terrestrial sources can measure all of the remaining standard neutrino oscillation properties (θ 13, CPV, MH) even for very small θ 13 Are all parameters best measured using terrestrial sources? Where did the solar sector get its name from? Some new physics neutrino properties can be tested as well Are there neutrino properties which are best tested using astrophysical environments? Lecture 3 Lecture 3 Lecture 3 50
Matrix form in flavor space Transition amplitude in matrix form: For instance, φ in = (1,0,0) T for ν e With, we have or 51