Non-cyclic phase for 4-flavor neutrino oscillation

The non-cyclic phase for neutrino oscillation is calculated, taking into consideration a possible 4th sterile flavor. This extends the results derived in the paper by Xiang-Bin Wang et al. [X.-B. Wang, L.C. Kwek, Y. Liu, C.H. Oh, Phys. Rev. D 63 (2001) 053003] that discussed the non-cyclic phase in 3-flavor neutrino oscillation. A mathematical simplification is also introduced, making use of some of the transformation properties of the 4-flavor mixing matrix. The restriction that CPT symmetry imposes on the non-cyclic phase of neutrinos is also discussed briefly, with the possibility of further simplification of these phases. The scheme that we introduced is also applicable to 3-flavor neutrinos, and could yield more insights in 3-flavor mixing. Extending our result to ν to ν¯ oscillation could also help in resolving the issue concerning the Majorana or Dirac nature of neutrinos.