CP 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 = (lf)− (lf) (l+f) + (l−f) . (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 lν̄D that tags pure B̄ state, while fb is a CP eigenstate (e.g. ψKS, ππ, ππ ...), then the rate is given by [5] Rate(B(t1)B̄ (t2)→ fafb) ∼ e 12{[1 + cos(∆m(t1 − t2)]|A(fb)Ā(fa)| 2 + [1− cos(∆m(t1 − t2))]| q p ||Ā(fb)Ā(fa)| 2 − 2sin∆m(t1 − t2)|A(fb)Ā(fa)| Im ( q p Ā(fb) A(fb) ) } (2)