Asymmetry In Neutral B System At Symmetric Colliders ∗

Contrary to the conventional belief, time integrated asymmetry are measurable in selected final states in the neutral B system at symmetric e+e− colliders. They occur due to the interplay of weak and strong phases of two different amplitudes in addition to the B0 − B̄0 mixing. Observation of these asymmetries would be evidence for direct CP violation in the decay amplitudes. Typeset using REVTEX Work supported in part by the Department of Energy Grant No. DE-FG06-85ER40224. 1 CP violation is one of the few remaining unresolved myseries in particle physics. The explanation in the Standard Model based on Cabibbo-Kobayashi-Maskawa (CKM) matrix is still not established. Although there is no conflict between the observation of CP violation in the K-system and theory [1], intriguing hints of other plausible explanations emerge from astrophysical considerartion of baryon to photon ratio in the universe [2]. Models based on additional Higgs bosons or gauge bosons can equally well explain the existing data [3]. It is for this reason that exploration of CP vioaltion in the B system is so crucial. The B system offers several final states that provide a rich source for the study of this phenomena [4]. The principle techniques at electron-positron colliders that will be used involves: (a) measurement of particle-antiparticle partial rate asymmetries, and (b) rate aysmmetries in the neutral B system with a lepton tag for one of the B mesons and the decay of the other B into a CP eigenstate f (e.g. f ψKS) [5], Asy = (l+f)− (lf) (l+f) + (lf) . (1) The rationale for building an asymmetric electron-position collider arises from the well known observation that time integrated asymmetries arising from B − B̄ production in C = −1 state are washed out due to quantum coherence of the initial state. On closer examination this is exactly correct only when the amplitude for the process B → f has a single weak phase. As we show below, when the amplitude is a mixture of two terms with different weak and strong phases, the asymmetry though diluted, still remains. Consider the deay of the coherent BB̄ state produced in C = −1 state as in the decay of Υ(4s). If t1 and t2 denote decay times of the states that were pure B 0 and B̄ at time zero, and fa is a flavor specific decay like l ν̄D that tags pure B̄ state, while fb is a CP eigenstate (e.g. ψKS, π π, ππ ...), then the rate is given by [5] Rate(B(t1)B̄ (t2) → fafb) ∼ e12{[1 + cos(∆m(t1 − t2)]|A(fb)Ā(fa)| + [1− cos(∆m(t1 − t2))]| q p ||Ā(fb)Ā(fa)| − 2sin∆m(t1 − t2)|A(fb)Ā(fa)|Im (