1207.2318 (Masaki Yasue)

Phases of Flavor Neutrino Masses and CP Violation    [PDF]

Masaki Yasue

For flavor neutrino masses M^{PDG}_{ij} (i,j=e,mu,tau) with the phase convention defined by Particle Data Group (PDG), if neutrino mixings are controlled by small corrections to those with sin\theta_{13}=0 denoted by sin\theta_{13}deltaM^{PDG}_{e tau} and sin\theta_{13}deltaM^{PDG}_{tau tau}, CP-violating Dirac phase delta_{CP} is calculated to be delta_{CP} \approx arg[M_{mu tau}^{PDG*}/tan\theta_{23}+M_{mu mu}^{PDG*})deltaM_{e tau}^{PDG}+M_{ee}^{PDG}deltaM_{e tau}^{PDG*}-tan\theta_{23}M_{e mu}^{PDG}deltaM_{tau tau}^{PDG*}] (mod pi), where \theta_{ij} (i,j=1,2,3) denotes an i-j mixing angle. If possible mass hierarchies are taken into account, the main source of delta_{CP} turns out to be deltaM_{e tau}^{PDG} except for the inverted mass hierarchy with {tilde m}_1\approx -{tilde m}_2, where {tilde m}_i=m_ie^{-i\varphi_i} (i=1,2) stands for a neutrino mass m_i and a Majorana phase \varphi_i. We can further derive that delta_{CP}\approx arg(M_{e mu}^{PDG})-arg(M_{mu mu}^{PDG}) with arg(M_{e mu}^{PDG})\approx arg(M_{e tau}^{PDG}) for the normal mass hierarchy and delta_{CP}\approx arg(M_{ee}^{PDG})-arg(M_{e tau}^{PDG})+pi for the inverted mass hierarchy with {tilde m}_1\approx{tilde m}_2. For specific flavor neutrino masses M_{ij}, whose phases are associated with M_{e mu,e tau,tau tau}, we obtain that arg({M_{e mu})=arg(M_{e mu}^{PDG})-[arg(M_{ee}^{PDG})+arg(M_{mu mu}^{PDG})]/2, arg(M_{e tau})=arg(M_{e tau}^{PDG)-[arg(M_{ee}^{PDG})-arg(M_{mu mu}^{PDG})]/2 and arg(M_{tau tau})=arg(M_{tau tau}^{PDG})+arg(M_{mu mu}^{PDG})-2arg(M_{mu tau}^{PDG}). Numerical analysis suggests that Dirac CP-violation becomes maximal as arg(M_{e mu})| approaches to pi/2 for the inverted mass hierarchy with {tilde m}\approx{tilde m}_2 and for the degenerate mass pattern and that Majorana CP-violation becomes maximal as |arg(M_{tau tau})| approaches to its maximal value around 0.5 for the normal mass hierarchy.

View original: http://arxiv.org/abs/1207.2318