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

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

2006-07-31

arxiv.org/abs/hep-ph/0607335v1

Phys.Lett.B641:372-380,2006

Physics

High Energy Physics

High Energy Physics - Phenomenology

18 pages latex, 0 figures

Scientific paper

10.1016/j.physletb.2006.09.005

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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