Comment on: "Geometric phase of neutrinos: differences between Dirac and Majorana neutrinos" [Phys. Lett. B 780, 216 (2018)]

Abstract

In [Phys. Lett. B 780, 216 (2018)], Capolupo et al. calculate the noncyclic geometric phases associated with neutrino flavor transitions in the two-neutrino scenario, and claim that the results depend on the choice of representations of neutrino mixing matrix thus can be use to distinguish between Dirac and Majorana neutrinos. In this paper, we show that their calculation is flawed due to incorrect application of the definition of noncyclic geometric phase and the omission of one term in Wolfenstein effective Hamiltonian. Their results are neither gauge invariant nor lepton field rephasing invariant. We present an alternative calculation, which is solely in order to demonstrate that the Majorana CP-violating phase enters the geometric phase essentially by lepton field rephasing transformation. We point out that the seemingly nontrivial dependence of geometric phase on Majorana CP-violating phase presented in [Phys. Lett. B 780, 216 (2018)] is unphysical and thus unmeasurable.