CP-violating Majorana phases, lepton-conserving processes and final state interactions

Abstract

The CP-violating phases associated with Majorana neutrinos can give rise to CP-violating effects even in processes that conserve total Lepton number, such as μ-> eee+, μ+ e -> e + e and others. After explaining the reasons that make this happen, we consider the calculation of the rates for the process of the form \ell_a + \ell_b -> \ell_a + \ell_c, and its conjugate \bar\ell_a + \bar\ell_b -> \bar\ell_a + \bar\ell_c, where \ell_a, \ell_b and \ell_c denote charged leptons of different flavors. In the context of the Standard Model with Majorana neutrinos, we show that the difference in the rates depends on such phases. Our calculations illustrate in detail the mechanics that operate behind the scene, and set the stage for carrying out the analogous, more complicated (as we explain), calculations for other processes such as μ-> eee+ and its conjugate.