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arXiv · hep-ph/0607335

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

P. F. Harrison·W. G. Scott·T. J. Weiler
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Abstract

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.

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P. F. Harrison, W. G. Scott, T. J. Weiler. 2006-07-31. Real Invariant Matrices and Flavour-Symmetric Mixing Variables with Emphasis on Neutrino Oscillations. https://doi.org/10.1016/j.physletb.2006.09.005

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