Real Invariant Matrices and Flavour-Symmetric Mixing Variables with Emphasis on Neutrino Oscillations

Harrison, P. F.; Scott, W. G.; Weiler, T. J.

Real Invariant Matrices and Flavour-Symmetric Mixing Variables with Emphasis on Neutrino Oscillations

Authors

Harrison, P. F.

Scott, W. G.

Weiler, T. J.

Description

In fermion mixing phenomenology, the matrix of moduli squared, P=(|U|^2), is well-known to carry essentially the same information as the complex mixing matrix U itself, but with the advantage of being phase-convention independent. The matrix K (analogous to the Jarlskog CP-invariant J) formed from the real parts of the mixing matrix "plaquette" products is similarly invariant. In this paper, the P and K matrices are shown to be entirely equivalent, both being directly related (in the leptonic case) to the observable, locally L/E-averaged transition probabilities in neutrino oscillations. We study an (over-)complete set of flavour-symmetric Jarlskog-invariant functions of mass-matrix commutators, rewriting them simply as moment-transforms of such (real) invariant matrices.
18 pages latex, 0 figures