Geometric phase and neutrino mass hierarchy problem

We study the geometric phase for neutrinos at various man-made facilities, such as the reactor and accelerator neutrino experiments. The analysis is done for the three flavor neutrino scenario, in the presence of matter and for general, noncyclic paths. The geometric phase is seen to be sensitive to the CP violating phase in the leptonic sector and the sign ambiguity in Delta_{31}. We find that for neutrino experimental facilities where the geometric phase can complete one cycle, all the phase curves corresponding to different values of CP violating phase, converge to a single point, called the cluster point. There are two distinct cluster points for positive and negative signs of Delta_{31}. Thus the geometric phase can contribute to our understanding of the neutrino mass hierarchy problem.