neutrino oscillation

neutrino oscillation

Theory of neutrino oscillation 1. Neutrino oscillation in vacuum 2. Neutrino oscillation in matter Neutrinos come from at least three flavors The known three flavors: each of these is associated with the corresponding charged-lepton flavor The meaning of this association 1. Neutrino oscillation in vacuum Over short distance, neutrinos do not change flavor: Does not occur But if neutrinos are massive, and mixed, neutrino flavor changes do occur during long journeys Let us assume neutrino have mass and leptons mix When W + decays: The produced neutrino state |n a > is Neutrino of flavor a Neutrino of definite mass m i Lepton mixing matrix Another way to look at W boson decay A given l a + can be accompanied by any n i , and The neutrino state |n a > produced together with l a + is According to the Standard Model, extended to include neutrino mass and leptonic mixing É The number of different n i is the same as the number of different l a (3). É The mixing matrix U is 3 x 3 and unitary: UU † = U † U = 1 From |n a > = Σ i U* ai |n i > and the unitarity of U, The flavor-α fraction of n i is Neutrino Flavor Change (Oscillation) in Vacuum What is Propagator (n i ) ª Prop(n i )? Neutrino sources are ~ constant in time. Averaged over time of the interference is Unless E 1 = E 2 Only neutrino mass eigenstates with a common energy E are coherent. |, exp[( )]|,0 iiii LiEtpL       For each mass eigenstate 2 |, exp[ /2]|,0 iii LimLE     Probability for Neutrino Oscillation in Vacuum [...]... Two Mass Eigenstates 2) The oscillations of neutrinos in matter Hamiltonian of a neutrino in a medium: H = H0 + V, V = VNC + VCC º const.*I + VeCC (Up to small higher-order corrections) 2 n oscillation in constant-density matter — Comments — 1) Mikheyev - Smirnov - Wolfenstein (MSW) resonance: 2) For anti-neutrinos, VeCC changes sign, hence there is no MSW resonance for anti-neutrinos 3) Matter effects...For Antineutrinos: We assume the world is CPT invariant — Comments — 1 If all mi = 0, so that all Δmij2 = 0, Flavor changes ï n mass 2 If there is no mixing, Flavor changes ⇒ Mixing 3 P (na → nb) depends only on squared-mass splitting Oscillation experiments cannot tell us the absolute scale of neutrino mass 4 Neutrino flavor change does not change the total... Comments — 1) Mikheyev - Smirnov - Wolfenstein (MSW) resonance: 2) For anti-neutrinos, VeCC changes sign, hence there is no MSW resonance for anti-neutrinos 3) Matter effects induces the CP violation for 2n oscillation in a medium . Theory of neutrino oscillation 1. Neutrino oscillation in vacuum 2. Neutrino oscillation in matter Neutrinos come from at least three flavors The known. meaning of this association 1. Neutrino oscillation in vacuum Over short distance, neutrinos do not change flavor: Does not occur But if neutrinos are massive, and mixed, neutrino flavor changes. occur during long journeys Let us assume neutrino have mass and leptons mix When W + decays: The produced neutrino state |n a > is Neutrino of flavor a Neutrino of definite mass m i Lepton