Google  

Yasue Laboratory For Elementary Particle Theory 

Home What's New Site Map

CP-Violation and Masses

Up Non-Abelian Bipair: Charged Leptons CP-Violation and Masses leptogenesis

English page is HERE

Phases of Flavor Neutrino Masses and CP Violation

  • published in Phys. Lett. B 718, No. 1 (2012) 153-159 (Received date: July 2012).
Share.gif (14997 ???)arXiv:1207.2318

For flavor neutrino masses M^{PDG}_{ij} (i,j=e,mu,tau) compatible 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 by using these corrections. If possible neutrino 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 {m}_1 approx -{m}_2, where {m}_i=m_ie^{-i varphi_i} (i=1,2) stands for a neutrino mass m_i accompanied by a Majorana phase varphi_i for varphi_{1,2,3} giving two CP-violating Majorana phases. 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 {m}_1 approx {m}_2. For specific flavor neutrino masses M_{ij} whose phases arise from M_{e mu,e tau,tau tau}, these phases can be connected with arg(M_{ij}^{PDG}) (i,j=e,mu,tau). As a result, numerical analysis suggests that Dirac CP-violation becomes maximal as |arg(M_{e mu})| approaches to pi/2 for the inverted mass hierarchy with {m}_1 approx {m}_2 and for the degenerate mass pattern satisfying the inverted mass ordering 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. Alternative CP-violation induced by three CP-violating Dirac phases is compared with the conventional one induced by delta{CP} and two CP-violating Majorana phases.


Prev Home Next

This Web site is maximally optimized for Internet Explorer of Version 3.0 or higher versions.

Internet Explorer

If you have any comments on this Web site (since Dec. 1st, 1997), please let us know: Mail.gif (4196 ???)yasue.
Copyright (c) 1997-2016/01 M. Yasue, Department of Physics, Tokai University.
Last update: 2016/01/14

Microsoft Front Page98