Abstract
BaBar collaboration announced that they observed time reversal (T) asymmetry through $B$ meson system. In the experiment, time dependencies of two distinctive processes, $B_- \rightarrow \bar{B^0}$ and $\bar{B^0}\rightarrow B_-$($-$ expresses CP value) are compared with each other. In our study, we examine event number difference of these two processes. In contrast to the BaBar asymmetry, the asymmetry of events number includes the overall normalization difference for rates. Time dependence of the asymmetry is more general and it includes terms absent in one used by BaBar collaboration. Both of the BaBar asymmetry and ours are naively thought to be T-odd since two processes compared are related with flipping time direction. We investigate the time reversal transformation property of our asymmetry. Using our notation, one can see that the asymmetry is not precisely a T-odd quantity, taking into account indirect CP and CPT violation of K meson systems. The effect of $\epsilon_K$ is extracted and gives rise to $\mathcal{O}(10^{-3})$ contribution. The introduced parameters are invariant under rephasing of quarks so that the coefficients of our asymmetry are expressed as phase convention independent quantities. Some combinations of the asymmetry enable us to extract parameters for wrong sign decays of $B_d$ meson, CPT violation, etc. We also study the reason why the T-even terms are allowed to contribute to the asymmetry, and find that several conditions are needed for the asymmetry to be a T-odd quantity.
Highlights
That they measured non-zero asymmetry and this observation is direct demonstration of T-violation
BaBar collaboration announced that they observed time reversal (T) asymmetry through B meson system
The ratio of the overall constants for the two decay rates is deviated from unity, and the deviation ∆NR = NR − 1 is taken into account in our analysis
Summary
In ref. [6], a formula for the time-dependent decay rate of the entangled BBsystem is derived. When f1 and f2 denote the final states of a tagging side and a signal side, respectively, it is written as, Γ(f1)⊥,f2 = e−Γ(t1+t2)N(1)⊥,2 κ(1)⊥,2 cosh(yΓt) + σ(1)⊥,2 sinh(yΓt). The expressions for N(1)⊥,2, κ(1)⊥,2, σ(1)⊥,2, C(1)⊥,2 and S(1)⊥,2 are given in ref. For the sake of completeness, we record their expressions in eqs. We evaluate an asymmetry including overall factor N(1)⊥,2κ(1)⊥,2 in eq (2.1). One obtains a generic formula for the event number asymmetry of the two distinctive sets for final states; (f1, f2) versus (f3, f4) as,. (2.3)–(2.6), contribution from different overall factors in eq (2.1) for two processes are taken into account. Taking the limit NR → 1 and y → 0 in eq (2.3), one finds an asymmetry whose overall normalization is eliminated, used in [4].
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