Testing the Weisskopf–Wigner approximation by using neutral-meson–antimeson correlated states

Abstract

We phenomenologically decompose the Weisskopf-Wigner approximation, as applied to the neutral flavoured meson complexes, into three pieces and propose tests for these pieces. Our tests hold for general decay amplitudes and M 0 -M 0 mixing parameters. We concentrate on C-odd M 0M 0 states and stress the importance of such tests in view of the variety of physics extracted from measurements on such complexes. Studying the feasibility of the tests confines one to the K 0K 0 system at present. In particular, we show that the time dependence of the correlated decay φ → K 0K 0 → 2(π + π − ) is determined solely by the WWA and provides thus a clean test of it.

The fundamental symmetries in the neutral kaon system—a pedagogical choice

“…The experiments have achieved precisions which may open the capability to explore the validity of some of the often tacitly assumed hypotheses. Some examples are: (i) the quantum-mechanical result for the correlation among two distant particles in an entangled state, rather than a weaker correlation limited by the assumption of Local Realism [110][111][112], (ii) the perturbation expansion of the Schrödinger equation [113,114] leading to the two dimensional spinor representation with the exponential decay law, (iii) the unitarity relations [115], (iv) the complementarity of CP parity and strangeness [116][117][118], (v) that the K 0 and the K 0 from φ decay are exact CPT conjugates [84], (vi) the conservation of the purity of states of isolated particles, manifested by the long time coherence of the kaon matter wave [65,66]. On the last subject, data from the CPLEAR Collaboration in combination with earlier data from the CERN-HEIDELBERG Collaboration achieve a sensitivity of ≈ 10 −21 GeV.…”

Plate with a hole obeys the averaged null energy condition

“…Some examples are: (i) the perturbation expansion of the Schrödinger equation [104,105] leading to the two dimensional spinor representation with the exponential decay law, (ii) the unitarity relations [106], (iii) the conservation of the purity of states of isolated particles, manifested by the long time coherence of the kaon matter wave [65,66]. A dedicated measurement on this subject has been performed at CERN.…”

Tests of CPT invariance for neutral flavored meson-antimeson mixing

“…(2.3) and (2.4), transition rates can be expressed as functions of only two amplitudes, say a and b; therefore, in any theory using the LVR (e.g., the LOY theory) these equations are often useful in algebraic manipulations. The remaining part of the WWA can be expressed as [7] 8) where both the real and imaginary parts of the phase-convention-independent parameter θ are in principle measurable and violate both CP and CPT; the quantity |q/p| − 1 is a measure of CP and T violation in mixing. Then we can write…”

“…where α and β are complex constants determined in terms of p H,L and q H,L : 3) and (2.4), transition rates can be expressed as functions of only two amplitudes, say a and b; therefore, in any theory using the LVR (e.g., the LOY theory) these equations are often useful in algebraic manipulations. The remaining part of the WWA can be expressed as [7] a…”

“…[6]). The purpose of this paper is to consider some tests of CPT invariance in the mixing of M 0 and M0 , at two levels [7] of the WWA. We will consider the following situations:…”