BINARY SYSTEMS OF NEUTRAL MESONS IN QUANTUM FIELD THEORY

Abstract

Quasidegenerate binary systems of neutral mesons of the kaon type are investigated in Quantum Field Theory (QFT). General constraints cast by analyticity and discrete symmetries P, C, CP, TCP on the propagator (and on its spectral function) are deduced. Its poles are the physical masses; this unambiguously defines the propagating eigenstates. It is diagonalized and its spectrum thoroughly investigated. The role of "spurious" states, of zero norm at the poles, is emphasized, in particular for unitarity and for the realization of TCP symmetry. The KL-KS mass splitting triggers a tiny difference between their CP violating parameters ∊L and ∊S, without any violation of TCP. A constant mass matrix like used in Quantum Mechanics (QM) can only be introduced in a linear approximation to the inverse propagator, which respects its analyticity and positivity properties; it is however unable to faithfully describe all features of neutral mesons as we determine them in QFT, nor to provide any sensible parametrization of eventual effects of TCP violation. The suitable way to diagonalize the propagator makes use of a bi-orthogonal basis; it is inequivalent to a bi-unitary transformation (unless the propagator is normal, which cannot occur here). Problems linked with the existence of different "in" and "out" eigenstates are smoothed out. We study phenomenological consequences of the differences between the QFT and QM treatments; the nonvanishing of the semileptonic asymmetry δS - δL, does not signal, unlike usually claimed, TCP violation, while ATCP keeps vanishing when TCP is realized. We provide expressions invariant by the rephasing of K0 and [Formula: see text].