Mixing in B Decay Ying Li Yonsei and YTU

Outline Some story in

In 2006, there is summer school on particle physics in Nasu, Japan. The students are comes for Japan, Korea, China, Thailand, India, Indonesia, and so on.

There, we not only discussed the physics, but also enjoyed the traditional Japan food. At that time, I also know some friends such as Ardi and Yang Liu from Belle.

In the April of 2008, Y Liu to me that he had found some event of decay. Actually, this channel should be measured easily in experimental side. He asked me to estimate this branching ratio theoretically. Y. Liu, K. Trabelsi, et al, Phys.Rev.D78:011106,2008 In the strong interaction, this quark diagram can drawn like: This process should be suppressed strongly by the OZI rules

At the same time, Prof. Sakai, Liu’s supervisor asked Prof. Hagiwara for help. Prof Hagiwara also think this process should be suppressed. So he send the same question to Hai-Yang Cheng. In the May, I meet Hai-Yang in IHEP in Beijing. At that time, we found that we were thinking the same questions. After some discussion, we think if this process have a large branching ratio, it should come from the final states interaction.

So, we planed to calculated this process theoretically with considering all contribution. However, in the June, M. Gronau and J.L. Rosner posted one paper where they agued that this larger branching ratio is comes from the phi-omega mixing. M.Gronau, J.L. Rosner, Phys.Lett.B666: ,2008 This paper promoted our work. However, when we finish the calculation, we found the final states interaction is very small. So our results proved that the Gronau and Rosner’s conclusion is correct. Since the mixing contribution is so large, does it contribute to another channel as B  phi pi?

Very small branching ratio about

The experimentalists have reported the following measurements Or 60% Confidence 90% Confidence

At the quark level, these decays proceed via b  dss, which is a flavor changing neutral current (FCNC) process. The FCNC transition is induced by the loop effects and the relevant Wilson coefficients are very small. The Cabibbo-Kobayashi-Maskawa (CKM) matrix elements for this transition V tb V td * is very tiny. In order to produce a phi-meson from the vacuum, at least three gluons are required, which suppresses these channels further. Feynmann diagrams for these decays are often referred to the hairpin diagram. Because of the tiny branching ratio in the SM, it is usually considered as an ideal place to search for the possible new physics.

Contributions in the naive factorization Radiative corrections (vertex corrections and the hard spectator diagram), Long-distance contributions Contributions due to the omega-phi- mixing. Before we turn to the new physics scenario, it is logical to investigate all possible contributions in the SM

Naïve Factorization

QCD Factorization Vertex corrections and the hard spectator diagram involved

Long distance contribution

Phi-omega mixing

No Summary

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