Time Dependence of Coherent $P^{0}\bar{P}^{0}$ Decays and CP Violation at Asymmetric $B$ Factories

TL;DR

This paper develops a formalism for analyzing time-dependent and time-integrated decays of coherent neutral meson pairs, enabling improved measurements of CP violation and mixing parameters at asymmetric B factories.

Contribution

It introduces a general formalism applicable to various neutral meson systems and reanalyzes CP violation signals in B meson transitions, highlighting measurement advantages.

Findings

Proper time cuts improve measurement accuracy.

Direct and indirect CP asymmetries are distinguishable.

Potential to detect CP-forbidden processes at the $S$ resonance.

Abstract

A generic formalism is presented for the time-dependent or time-integrated decays of any coherent $P^{0}\bar{P}^{0}$ system ($P^{0} = K^{0}, D^{0}, B^{0}_{d}$, or $B^{0}_{s}$). To meet various possible measurements at asymmetric $B$ factories, we reanalyze some typical signals of CP violation in the coherent $B^{0}_{d}\bar{B}^ {0}_{d}$ transitions. The advantage of proper time cuts is illustrated for measuring mixing parameters and CP violation. We show that the direct and indirect CP asymmetries are distinguishable in neutral B decays to CP eigenstates. The possibility to detect the CP- forbidden processes at the $\Upsilon (4S)$ resonance is explored in some detail.