Erratum:CPviolation in the seesaw model [Phys. Rev. D64,013006 (2001)]

Abstract

We have overlooked a Feyman diagram which contributes to the lepton number asymmetry. In Fig. 1, in the self-energy diagram, there is a loop diagram coming from neutrino and neutral Higgs boson.In order to evaluate the diagram, we have to include the interaction term for neutral Higgs boson in Eq. ͑15͒:where 0 is a neutral complex scalar which forms SU͑2͒ doublet with ϩ , T ϭ( ϩ ,v/ͱ2ϩ 0 ). In the exact calculation, we have to keep all the six neutrinos. However, the mixings among heavy neutrinos are suppressed as v 2 /M 2 , where M denotes the heavy neutrino mass. Therefore, to a good approximation, we can keep only light three neutrinos inside the loop. By evaluating the mixing matrix and using the approximate 3ϫ3 unitarity, i.e., ͚ jϭ1 3 V lЈ j* V l j Ӎ␦ lЈl , the contribution from ( 0 , L ) loop is the same as ( ϩ ,l L Ϫ ) loop in the limit of vanishing masses for Higgs bosons, light neutrinos, and charged leptons. As a result, we need to multiply a factor of 2 to the self-energy contribution. The changes are summarized in Table I below. We also correct some notational errors.

Flavor physics of leptons and dipole moments

“…A third possible parameterization of the neutrino Yukawa coupling uses the Gram-Schmidt decomposition, in order to cast the Yukawa coupling as a product of a unitary matrix and a lower triangular matrix [240]:…”

On the connection of leptogenesis with low energyCPviolation and lepton flavor violating charged lepton decays

“…The mounting evidence in favor of neutrino oscillations (see, e.g., [3,4,5,6]) gave analyzes of these two mechanisms a firmer phenomenological basis. Establishing a connection between the low energy (neutrino mixing) and high energy (leptogenesis) parameters has gathered much attention in recent years [7,8,9,10,11,12,13,14,15]. However, the number of parameters of the see-saw mechanism is significantly larger than the number of quantities measurable in the "low energy" neutrino experiments.…”

“…This parametrization relies on the property that any complex matrix can be written as a product of a unitary and a lower triangular matrix [14]:…”

Numerical study on the correlation between CP violation in neutrino oscillations and baryogenesis

“…In the previous paper [1] we have identified the CP violating phases of the seesaw model and found six independent phases. In the case where the heavy right-handed Majorana mass has a strong hierarchy in the diagonal basis M 1 ≫ M 2 ≫ M 3 , the diagonalization of the seesaw matrix is possible under the assumption that the elements in Yukawa-Dirac mass matrix are rather universal.…”

“…In the non-decoupling case [1]and by using the mass eigenstate for charged lepton, the V MN S matrix is the submatrix 3×6 of V itself. General analysis on this extended 3×6 MNS matrix results in six independent CP phases.…”