Noncyclic phase for neutrino oscillation

Abstract

We provide explicit formulas for the noncyclic phases or Pancharatnam phases of neutrino oscillations. Since the Pancharatnam phase is a generalization of the Berry phase, our results generalize the previous findings for the Berry phase in a recent paper [M. Blasone, P. A. Henning, and G. Vitiello, Phys. Lett. B 466 262 (1999)]. Unlike the Berry phase, the noncyclic phase offers a distinctive advantage in terms of measurement and prediction. In particular, for three-flavor mixing, our explicit formula offers an alternative means of determining the CP-violating phase. Our results can also be extended easily to explore the noncyclic phase associated with neutron-antineutron oscillations. © 2001 The American Physical Society.