Mixing in B Decay

1. Mixing in B Decay Ying Li Yonsei and YTU

2. Outline • Some story in 2006-2008

3. 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.

4. 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.

5. This process should be suppressed strongly by the OZI rules • In the April of 2008, Y Liu email 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:

6. 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.

7. 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.B666:185-188,2008 • 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?

10. Very small branching ratio about 10-11

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

15. 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 VtbVtd* 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.

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

17. Naïve Factorization

18. QCD Factorization Vertex corrections and the hard spectator diagram involved

19. Long distance contribution

20. Phi-omega mixing

24. No Summary

25. Thank You!