Topological phase in two flavor neutrino oscillations and imprint of the CP phase

Abstract

We show that the coherent phase involved in the neutrino oscillation formalism can be decomposed into two parts, one corresponding to the usual energy-dependent dynamical phase and the other part being the achromatic geometric phase. This study was carried out specifically for (a) CP conserving two flavor case [P. Mehta. Topological phase in two flavor neutrino oscillations. Phys. Rev. D, 79:096013, 2009.] and (b) CP violating two flavor case [P. Mehta. Geometric imprint of cp violation in two flavor neutrino oscillations. arXiv:0907.0562 [hep-ph].]. We noted that the geometric phase is actually topological for case (a) irrespective of details of evolution while it can become geometric in case (b).