Radiative corrections to the leptonic DiracCP-violating phase

Abstract

Since the smallest leptonic mixing angle θ 13 has been measured to be relatively large, it is quite promising to constrain or determine the leptonic Dirac CP-violating phase δ in future neutrino oscillation experiments. Given some typical values of δ = π/2, π, and 3π/2 at the low-energy scale, as well as current experimental results of the other neutrino parameters, we perform a systematic study of the radiative corrections to δ by using the one-loop renormalization group equations in the minimal supersymmetric standard model and the universal extra-dimensional model. It turns out that δ is rather stable against radiative corrections in both models, except for the minimal supersymmetric standard model with a very large value of tan β. Both cases of Majorana and Dirac neutrinos are discussed. In addition, we use the preliminary indication of δ = (1.08 +0.28 −0.31 ) π or δ = (1.67 +0.37 −0.77 ) π from the latest global-fit analyses of data from neutrino oscillation experiments to illustrate how it will be modified by radiative corrections. * Electronic address: tohlsson@kth.se † Electronic address: hzhang@mpi-hd.mpg.de ‡ Electronic address: shunzhou@kth.se

Applicability of second-order expansion in s13 to explore δCP in small and medium baseline ν experiments

“…38. Due to the CP-asymmetric nature of Earth, particle transition probability is not same to that of antiparticle one, which introduces a nonvanishing ∆P CP αβ even if δ CP = 0.…”

Leptonic CP Violation in Neutrino Oscillation Experiments

“…In Fig. 2, we calculate A m µe in the NH case by using the PREM model of the earth matter density [13]. In the left plot, one can observe that the large values appear in the region of low neutrino energies.…”

“…The coefficients α κ and C κ are flavor universal, and have been explicitly given in Appendix A of Ref. [7] for the SM, the MSSM, and the Universal Extra-Dimensional Model (UEDM).…”

“…In the flavor basis where the charged-lepton Yukawa matrix is diagonal Y l = diag(y e , y µ , y τ ) and in the limit of y e ≪ y µ ≪ y τ , the renormalization-group equation of δ approximates to [7] δ ≈ − C The enhancement may arise from the factor m 2 1 /∆m 2 21 , implying that the running effect will be significant for a nearly-degenerate neutrino mass spectrum; (c) The running behavior depends crucially on the difference between two Majorana-type CP-violating phases.…”

“…For a constant matter density, we can expand the oscillation probabilities in terms of s 2 13 and α ≡ ∆m 2 21 /∆m 2 31 . More explicitly, we have [13] ∆a ≈ +8αs 12 c 12 s 23 c 23 s 13 To describe the intrinsic CP violation and remove the fake CP effects induced by matter, we define ∆A CP µe (δ ) ≡ A CP µe (δ ) − A CP µe (0), which obviously vanishes for δ = 0. In addition, another working observable A m µe ≡ max{A CP µe (δ )} − min{A CP µe (δ )} can be introduced to measure the experimental sensitivity to δ , where the maximum and minimum have been found by varying δ in [0, 2π).…”