全國第四屆重味物理和CP破壞研討會.ppt

1、全國第四屆重味物理和CP破壞研討會,1,2020/9/8,Wei Wang Institute of High Energy Physics,Final State Interactions in B to KK modes,Based on: Cai-dian Lv,Yue-Long Shen and Wei Wang, Phys.Rev.D73:034005,2006,全國第四屆重味物理和CP破壞研討會,2,2020/9/8,There are many different editions of Final State Interactions (FSIs) in the literat

2、ure. Here, we use the edition given by:,Final state interactions in hadronic B decays, H.Y.Cheng, C.K.Chua and A.Soni,Phys. Rev.D 71,014030(2005),2020/9/8,全國第四屆重味物理和CP破壞研討會,3,Outline,Motivation,Framework of FSIs,FSIs in B to KK and discussion,Summary,全國第四屆重味物理和CP破壞研討會,4,2020/9/8,FSIs can provide an

3、approach to solve many puzzles. To be self-consistent, a good approach should also accommodate with the data for other channels.,Motivation,全國第四屆重味物理和CP破壞研討會,5,2020/9/8,Motivation,is a pure annihilation process and the amplitude is totally from FSIs. This process is quite helpful to detect the dynam

4、ics of strong interactions.,2020/9/8,全國第四屆重味物理和CP破壞研討會,6,From the accumulated data at B factories and CLEO, there are many indications that FSIs may play a prominent role.,It is nonperturbative in nature. However, FSIs can be modeled as the soft rescattering of certain intermediate two-body hadronic

5、 channels so that they can be treated as one-particle-exchange graphs.,Framework of FSIs,2020/9/8,全國第四屆重味物理和CP破壞研討會,7,Framework of FSIs,In order to avoid the double counting problem, we use the leading order Wilson coefficients for the effective operators.,We use nave factorization for direct (short

6、 distance ) contribution:,2020/9/8,全國第四屆重味物理和CP破壞研討會,8,At the quark level, final state rescattering can occur through quark annihilation and quark exchange：,Framework of FSIs,2020/9/8,全國第四屆重味物理和CP破壞研討會,9,At hadron level, that is s-channel and t-channel rescattering:,Due to the lack of the existence

7、of resonances at energies close to B meson mass, the s-channel contribution is suppressed relative to the rescattering effect from quark exchange.,Framework of FSIs,2020/9/8,全國第四屆重味物理和CP破壞研討會,10,Framework of FSIs,Using cutting rule, we can get the absportive part of the magnitude:,2020/9/8,全國第四屆重味物理

8、和CP破壞研討會,11,Framework of FSIs,Because the t-channel exchanged particle is not on shell, a form-factor cutoff must be introduced to the vertex which is usually parametrized as:,where n=1 is preferred and The parameter depends not only on the exchanged particle but also on the external particles invol

9、ved in the strong interaction vertex.,2020/9/8,全國第四屆重味物理和CP破壞研討會,12,Framework of FSIs,The dispersive part of the amplitude can be obtained from the absorptive part using the dispersion relation:,However, the dispersive contribution suffers large uncertainties due to some possible subtractions and th

10、e complication from integrations. So the dispersive part is neglected except in modes.,Including the absorptive contribution, the amplitude is:,2020/9/8,全國第四屆重味物理和CP破壞研討會,13,As pointed out by C.K.Chua et al in Mod.Phys.Lett.A 18,1763(2003),there exist and meson annihilation diagrams in which the two

11、 initial quark pairs in the zero isospin configuration are destroyed and then created. These diagrams give a dispersive contribution to and . Cheng et al. finds that the following contribution can accommodate with the data of branching ratio and mixing-induced CP-violating parameter:,Framework of FS

12、Is,2020/9/8,全國第四屆重味物理和CP破壞研討會,14,FSIs in B to KK,Nave factorization gives the contribution as:,2020/9/8,全國第四屆重味物理和CP破壞研討會,15,FSIs in B to KK,For intermediate states, we consider those channels favored by CKM and Wilson coefficients:,2020/9/8,全國第四屆重味物理和CP破壞研討會,16,FSIs in B to KK,In order to avoid the

13、 double counting problem, we use the leading order Wilson coefficients for the effective operators.,Like in , meson annihilation diagrams give,a dispersive contribution to and .,We estimate this effect by taking the value from via SU(3) symmetry.,2020/9/8,全國第四屆重味物理和CP破壞研討會,17,Only short distance and

14、 absorptive contribution:,2020/9/8,全國第四屆重味物理和CP破壞研討會,18,FSIs in B to KK,2020/9/8,全國第四屆重味物理和CP破壞研討會,19,FSIs in B to KK,Results from PQCD:,Results from QCDF:,2020/9/8,全國第四屆重味物理和CP破壞研討會,20,FSIs in B to KK,Comparisons with these approaches:,For the branching ratio, with the errors, all the calculations

15、can be consistent. As for CP asymmetry, PQCD and QCDF have opposite sign. Our calculation is consistent with PQCD for while our result has the same sign with QCDF for So more experimental data are needed to test these different approaches.,2020/9/8,全國第四屆重味物理和CP破壞研討會,21,Including meson annihilation:,2020/9/8,全國第四屆重味物理和CP破壞研討會,22,Summary,Final state interactions can not change the branching ratio of and sizably if we consider The absorptive contribution.,The branch ratio of is at O(10-8) by purely t-cha