Genuine T, CP, CPT asymmetry parameters for the entangled $\boldsymbol{B_d}$ system

TL;DR

This paper establishes a precise connection between theoretical and experimental asymmetries in entangled B_d mesons, identifying genuine T, CP, CPT asymmetry parameters and analyzing their measurements and implications.

Contribution

It introduces a method to disentangle genuine asymmetry parameters from fake terms and provides a global fit to experimental data, revealing evidence of T and CP violation and setting limits on CPT violation.

Findings

Non-zero T and CP asymmetry parameters confirm violation.

Fake terms are compatible with zero, validating the method.

An upper limit on CPT violation parameter is established.

Abstract

The precise connection between the theoretical T, CP, CPT asymmetries, in terms of transition probabilities between the filtered neutral meson $B_d$ states and the experimental asymmetries between the double decay rate intensities for Flavour-CP eigenstate decay products in a B-factory of entangled states, is established. This allows the identification of genuine Asymmetry Parameters in the time distribution of the asymmetries and their measurability by disentangling genuine and possible fake terms. We express the nine asymmetry parameters -- three different observables for each one of the three symmetries -- in terms of the ingredients of the Weisskopf-Wigner dynamical description of the entangled $B_d$-meson states and we obtain a global fit to their values from the BaBar collaboration experimental results. The possible fake terms are all compatible with zero and the information content of the nine asymmetry parameters is indeed different. The non-vanishing $\Delta\mathscr S_c^{\rm T} =-0.687\pm 0.020 $ and $\Delta\mathscr S_c^{\rm CP}=-0.680\pm 0.021$ are impressive separate direct evidence of Time-Reversal-violation and CP-violation in these transitions and compatible with Standard Model expectations. An intriguing 2$\sigma$ effect for the Re($\theta$) parameter responsible of CPT-Violation appears which, interpreted as an upper limit, leads to $|M_{\bar B^0\bar B^0}-M_{B^0B^0}| < 4.0\times 10^{-5}$ eV at 95\% C.L. for the diagonal flavour terms of the mass matrix. It contributes to the CP-violating $\Delta\mathscr C_c^{\rm CP}$ asymmetry parameter in an unorthodox manner -- in its $\cos(\Delta M\,t)$ time dependence --, and it is accessible in facilities with non-entangled $B_d$'s, like the LHCb experiment.