On the use of the reciprocal basis in neutral meson mixing

Details On the use of the reciprocal basis in neutral meson mixing On the use of the reciprocal basis in neutral meson mixing

2000-07-09

arxiv.org/abs/hep-ph/0007075v1

Phys.Rev. D62 (2000) 116008

Physics

High Energy Physics

High Energy Physics - Phenomenology

15 pages, no figures

Scientific paper

10.1103/PhysRevD.62.116008

In the presence of CP violation, the effective Hamiltonian matrix describing a neutral meson anti-meson system does not commute with its hermitian conjugate. As a result, this matrix cannot be diagonalized by a unitary transformation and one needs to introduce a reciprocal basis. Although known, this fact is seldom discussed and almost never used. Here, we use this concept to highlight a parametrization of the Hamiltonian matrix in terms of physical observables, and we show that using it reduces a number of long and tedious derivations into simple matrix multiplications. These results have a straightforward application for propagation in matter. We also comment on the (mathematical) relation with neutrino oscillations.

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