Particle Physics Booklet - Particle Data Group - Lawrence Berkeley ...

13. Neutrino mixing 199
V. Three neutrino mixing. All compelling data on neutrino oscillations
can be described assuming 3-flavour neutrino mixing in vacuum. In this
case U can be parametrised as
⎡
c12c13 s12c13 s13e
U = ⎣
−iδ
−s12c23 − c12s23s13eiδ c12c23 − s12s23s13eiδ s23c13
s12s23 − c12c23s13eiδ −c12s23 − s12c23s13eiδ ⎤
⎦
c23c13
× diag(1, e i α21 2 , e i α31 2 ) . (13.77)
where cij =cosθij, sij =sinθij, the angles θij =[0,π/2], δ =[0, 2π] isthe
Dirac CP violation phase and α21, α31 are the two Majorana phases. The
existing neutrino oscillation data allow us to determine the parameters
which drive the solar νe and the dominant atmospheric νμ → ντ
oscillations, Δm2 21 > 0, sin2 θ12, and|Δm2 31 |,sin22θ23, with a relatively
good precision, and to obtain rather stringent limit on the angle θ13:
Δm2 21 ∼ = 7.65 × 10−5 eV 2 ,sin2θ12 ∼ = 0.304, |Δm2 31 | ∼ = 2.40 × 10−3 eV 2 ,
sin2 2θ23 ∼ = 1, sin2 θ13 < 0.056 (at 3σ). These results imply that
Δm2 21 ≪|Δm2 31 | and that θ23 ∼ = π/4, θ12 ∼ = π/5.4 andθ13