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Strasbourg Anselmo Meregaglia - IPHC Strasbourg Neutrino Oscillation Physics Neutrino Oscillations (1)

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Strasbourg Anselmo Meregaglia - IPHC Strasbourg Neutrino Oscillation Physics Neutrino Oscillations (1) Liquid Argon TPCs for T2K experiment and future long baseline neutrino experiments 20th February 2009 - Strasbourg Anselmo Meregaglia - IPHC Strasbourg Neutrino oscillation physics Neutrino oscillations (1) • Neutrino 3-flavour oscillation is well established both at the solar and atmospheric scale. • This means that mass eigenstates and flavour eigenstates are different. • Neutrinos are produced in weak interactions i.e. as flavour eigenstates and propagate as mass eigenstates (Hamiltonian eigenstates). • The relationship between the two eigenstate bases can be expressed with a matrix equation: • The matrix can be written in terms of 3 mixing angles (θij) and 1 complex (δ) phase as: sij = sin(θij) cij = cos(θij) Atmospheric scale Interference Solar scale A.Meregaglia - IPHC 3 Neutrino oscillations (2) • Using the standard plane wave approximation we can write the neutrino propagation as: • Knowing that neutrinos are relativistic we can use the approximation: • It results that the oscillation probability has terms proportional to: L = baseline (normally distance between where ν source and detector) E = ν energy • The probability of oscillation from a flavour to a different one can be expressed as a function of the 3 mixing angles (θ12, θ13, θ23), the complex phase (δ) and 2 2 2 neutrino mass differences (Δm 21, Δm 31). NOTE: neutrino oscillations are NOT sensitive to absolute masses but only to mass differences. A.Meregaglia - IPHC 4 Neutrino oscillations (3) • As an example we take the 2-flavour case. The mixing matrix can be written as: 1 Equazioni • The probability of oscillation from neutrino “a” to neutrino “b” is: 2 2 2 ∆m L Pab = sin 2θ sin (1) ! 4E " 2nd maximum of oscillation Baseline L = 295 km 2 -3 2 b Δm = 2.5 × 10 eV ! 1 " a ! P st 0.8 1 maximum of oscillation 0.6 sin2(2θ) 1st minimum of 0.4 oscillation 0.2 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 E (GeV) A.Meregaglia - IPHC 5 1 Neutrino oscillations (4) • The presence of matter affects neutrino oscillations since the mass eigenstates (i.e. the ones relevant for the propagation) are different, due to a new potential term present in the system Hamiltonian. • The probability of oscillation of neutrinos and antineutrinos is affected in a different way: this “fakes” a CP violation effect. • In order to measure intrinsic CP violation due to δCP phase we need to disentangle the two phenomena and this can be done in 2 ways: 1. Measuring the same maximum of oscillation at different baselines. 2. Measuring two maxima of oscillation at the same baseline. A.Meregaglia - IPHC 6 Neutrino oscillations (5) 2 • The fact that mass hierarchy (i.e. Sign (Δm 31)) is unknown makes things harder since changing hierarchy the effects of matter on neutrino and antineutrino are swapped. Normal hierarchy Inverted hierarchy νe ν3 νe 2 ν2 ∆m sol νµ νµ 2 ∆m atm ν1 ντ ντ 2 ∆m atm ν2 2 ∆m sol ν1 ν3 • To measure the hierarchy the best option would be to have a very long baseline (a few thousands km) so that matter effect is strong and it is easy to measure if neutrino oscillations are enhanced or reduced. A.Meregaglia - IPHC 7 Present knowledge Present knowledge Parameter Channel Experiments Future (90% C.L.) 2 θ23 sin (2θ23) ≥ 0.92 P(νµ→νµ) SK, (K2K, MINOS) T2K 2 Solar ν + θ12 0.82 ≤ sin (2θ12) ≤ 0.89 SK, SNO, KamLAND P(anti νe → anti νe) 2 P(anti νe → anti νe) T2K, Double CHOOZ θ13 sin (2θ13) ≤ 0.19 CHOOZ P(νµ→νe) Future LBL 2 2 -5 2 Solar ν + Δm 21 7.7 ≤ Δm 21 / 10 eV ≤ 8.3 SK, SNO, KamLAND P(anti νe → anti νe) 2 2 -3 2 Δm 31 1.9 ≤ Δm 31 / 10 eV ≤ 3.0 P(νµ→νµ) SK, MINOS MINOS, T2K 2 P(νµ→νe) Vs Sign (Δm 31) Unknown Future LBL P(anti νµ→ anti νe) P(νµ→νe) Vs T2K+Reactor δCP Unknown P(anti νµ→ anti νe) Future LBL A.Meregaglia - IPHC 8 Goals • The goal of long baseline neutrino oscillation experiments is to precisely measure the relevant parameters and answer to important questions such as: Is θ23 mixing maximal? Is θ13 different from zero? Is there CP violation in the leptonic sector? (i.e. is δ≠0?) 2 Is there normal or inverted hierarchy? (i.e. which is the sign of ∆m 31?) A.Meregaglia - IPHC 9 Strategy (1) • The goal of long baseline neutrino oscillation experiments is to precisely measure the relevant parameters and answer to important questions such as: νμ disappearance 4 2 2 2 Is θ23 mixing maximal? P(νμ→νx) ~ cos θ13 sin (2θ23) sin (∆m 32 L/(4Eν)) Is θ13 different from zero? Is there CP violation in the leptonic sector? (i.e. is δ≠0?) 2 Is there normal or inverted hierarchy? (i.e. which is the sign of ∆m 31?) νe appearance νμ→ νe oscillation A.Meregaglia - IPHC 10 Strategy (2) • The full 3-flavour neutrino oscillation probability for νμ→ νe is given by: Atmospheric term Solar term Interference terms Baseline = 1000km 2 -3 sin (2θ13) = 3.16x10 2 -3 2 ∆m31 = 2.6x10 eV • θ13 is crucial for the atmospheric part of the oscillation, and it must be proved to be non- zero. • In case of a value of θ13 different from zero, the oscillation probability depends strongly on the value of δ. 2 • The so far unknown sign of ∆m31 also affects the oscillation probability and mass hierarchy must be determined. A.Meregaglia - IPHC 11 T2K experiment T2K goals Using a conventional neutrino beam (mainly νμ with a contamination of 0.4% νe at peak) the goals are: νμ disappearance: 2 • sin 2θ23 4 2 2 2 P(νμ→νx) ~ cos θ13 sin (2θ23) sin (∆m 32 L/(4Eν)) 2 Sensitivity: δ(sin (2θ23)) ~ 0.01 (≈1%) 2 -5 2 δ(∆m 32) ≤3 × 10 eV (≈1%) 2 ∆m 32 Eν (MeV) νe appearance: • 90% C.L. δBG = 20% This measurement will allow to discover a non-zero value δBG = 10% δBG = 5% or set a smaller limit on the θ13 mixing angle. sin22 ~0.008 (90%) sensitivity θ13 13 θ 2 2 -3 2 Sensitivity: sin (2θ13) ≤ 8 × 10 (90% C.L.) sin Exposure (22.5kt × 1021 p.o.t) A.Meregaglia - IPHC 13 T2K experiment 2km complex Super-K µ monitor (beam ν energy spectrum Same spectrum as SK, direction and intensity) and intensity BG measurement • Long baseline (295 km) neutrino oscillation experiment. • Low E (less than 1 GeV) Super Beam: ~ 1021 p.o.t./year. • Off axis by 2.5 degrees. • Start in 2009 aiming to reach a power of 0.75 MW from a 30 GeV proton synchrotron (upgrades to 1.6 MW and 4 MW under study). A.Meregaglia - IPHC 14 T2K experiment: 2 km complex 2 km complex layout incoming neutrino beam ≈ 15 m ≈ 28 m • The 2 km complex has been proposed but not approved yet, it is not foreseen before ∼ 2012. • This detector complex would be located off axis at 2km from the target. • It is made up of a 100 ton LAr TPC (fine grained detector), a 1 kton Water Cerenkov detector and a muon range detector. A.Meregaglia - IPHC 15 Far/Near ratio F/N ratio • Both appearance and disappearance analyses rely on the neutrino spectra measured at SK (far detector) and the spectra extrapolated at SK from the near detector measurement (ND280): extrapolated at ΦSK(E )=R (E ) ΦND(E ) measured at the far detector µ,e ν µ,e ν × µ,e ν near detector Far to Near (F/N) ratio νμ Flux (normalised to SK) F/N ratio (νμ) • In case of a point-like and isotropic neutrino source, the ratio is given by 280m / 295km the solid angle (i.e. it scales as L-2 where L is the baseline). • In practice, due to the finite size of the source, the F/N ratio depends on the neutrino energy. A.Meregaglia - IPHC 17 Requirements on F/N ratio π0 e • The background in νe appearance NBG = NBG + NBG 0 i s m ainly due to νμ N C π SK π0 SK e = Φµ σNCπ0 εSK + Φe σe εSK interactions and intrinsic beam νe: ·ND · π0 · ND· e =RΦ σ 0 ε + R Φ σ ε µ µ · NCπ · SK e e · e · SK • To achieve the goals of the experiment the systematics should be no more than 10%, therefore δ(NBG) ≤10%. SK νµCC Nsig(Eν)=Posc Φ (Eν) σνµCC(Eν) ε (Eν) • The νμ disappearance · µ · · SK oscillation is measured as: = P R ΦND(E ) σ (E ) ενµCC(E ) osc · µ µ ν · νµCC ν · SK ν • MC studies on how systematics on F/N ratio affects the precision of T2K measurements showed that if δ(Rμ,e) ≈ 2 - 3% the contribution to the systematics is negligible compared to other contributions (due to ND280 spectrum measurements, cross sections, efficiencies, etc.) and it results into: 2 -5 2 2 δ(NBG) ≈ 2% δ(Δm 32) ≈ ±1.5 x 10 eV δ(sin 2θ23) ≈ ± 0.005 A.Meregaglia - IPHC 18 F/N ratio measurement • No data for p+C interaction at 30 GeV exist, therefore the only way to evaluate F/N ratio is to rely on MC simulation. • No model has been validated in this range, therefore we can assume as systematic error on F/N ratio the difference between MARS and G-FLUKA models i.e.: F/N ratio comparison for different hadron production models G-FLUKA / FLUKA MARS / G-FLUKA • This corresponds to the following error on the N/F ratio: δ(Rμ) ≈ 20% A.Meregaglia - IPHC 19 F/N ratio measurement (2) • The error on F/N ratio of ≈ 20% corresponds to: 2 δ(sin 2θ23) ≈ ± 0.015 - 0.030 Larger than T2K goal: 2 δ(sin (2θ23)) ~ 0.01 2 -5 2 2 -5 2 δ(Δm 32) ≈ ±(5 - 10) x 10 eV δ(∆m 32) ≤3 × 10 eV Larger than the required δ(NBG) ≈ 15% error on background: δ(NBG) ≤10%.
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