Simple symmetries in EPR-correlated decays of kaon and B-meson pairs with CP violation

Abstract

Simple general results are derived using a “quasispin” formalism with the two neutral meson states classified in a quasispin doublet and changes of basis described as quasispin rotations. Coherent decays of a neutral kaon or B-meson pair at times t 1 and t 2 respectively, after production in an eigenstate of charge conjugation with eigenvalue C are shown to depend on time only as a function of t 1 + Ct 2, except for an overall exponential decay factor depending on t 1 + t 2. Additional results are obtained for the B 0- B 0 system with the conventional approximation of neglecting the difference in lifetimes between the two eigenstates. EPR-correlated decays of meson pairs are described as quasispin polarization correlations and classified by time dependence and order in the CP-violation parameter. Charge asymmetries suggested for tests of CP violation in correlated decays where one meson decays into a CP eigenstate while the other decays into modes allowed only for B 0 or B 0 respectively, are shown to have a time dependence which averages out in any experiment which integrates over time. The explicit time dependence for the oscillations from an initial B 0- B 0 state is obtained.