Studying indirect violation of CP, T and CPT in a B-factory

Abstract

In this work we analyze the observable asymmetries one can build from entangled B-meson states, in order to extract information on the parameters ε and δ which govern indirect violation of discrete symmetries. The traditionally proposed observables, based on flavour tags, are not helpful for the study of the B d -system, where the tiny value of ∆Γ clears up such asymmetry effects. Our study makes instead use of CP tags in order to build new asymmetries where the different parameters can be separated out. For this separation, it is decisive to achieve a good time resolution in the measurement of entangled state decays. Nevertheless, even with no temporal information, as would be the case in a symmetric factory, it is still possible to extract some information on the symmetries of the system. We discuss both non-genuine and genuine observables, depending on whether absorptive parts can mimic or not asymmetry effects.

Probing violations of CPT with $B_d$ mesons

“…The original proposal of [2,3] to observe T violation independently of CP violation, implemented by BaBar [1] after [4], contained three ingredients:…”

“…(3.9), f 2 = J/ψK + and f 2 = J/ψK − were proposed in [2][3][4] and used by BaBar in [1], where K ± are the neutral kaon states filtered by the CP eigenstate decay channels. Consequently, the states B ∓ are well defined and given by equation (3.4) for each of the two decay channels.…”

“…The essential quantum mechanical ingredients involved are (i) the entanglement of the B 0 d -B 0 d pair in a B-Factory before the first decay, (ii) the use of decays as filtering measurements to (a) prepare the initial, and (b) detection the final, B meson states participating in the transition, (iii) the time dependence of the double decay rates. The concept behind this approach originates in [2,3] while the application to an actual experimental analysis was addressed in [4], avoiding, in particular, the need of the T-reversal of the decay (since, as emphasized by L.Wolfenstein [5], the T-reverse of a decaying state is not a physical state). The considered transitions are between Flavour and CP eigenstate decay products.…”

Discrete Symmetries CP, T, CPT

“…The problem is then the filtering of definite initial and final states of the neutral meson for the Reference and T-reverse transitions, something impossible for decaying particles. The solution [10][11][12][13][14] arises from the quantum mechanical properties imposed by the EPR entanglement [15,16] There are 8 experimentally independent Intensities for this kind of pairs of decay channels: 2 for Flavour X 2 for CP X 2 for the time-ordering of the decay channels. The four TRV independent raw symmetries measured by the BABAR experiment [17] are given in figure 4.…”

Spontaneous Breakdown of the Time Reversal Symmetry

“…This is obviously an irrealistic undertaking since the entropy is strongly increased by the decay, rendering the preparation of the initial state for the recombination process too difficult. The proposal to use the entanglement between the neutral B meson pairs, generated by the Υ(4S) decay, to tag the initial and the final states of the B 0 −B 0 oscillation [48][49][50] led finally to a convincing demonstration of the T-violating nature of the weak interactions [51]. It is believed that the T-violation of the weak interactions can not be responsible of the other time arrows.…”