全国第四届重味物理和CP破坏研讨会

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,全国第四届重味物理和CP破坏研讨会,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,全国第四届重味物理和CP破坏研讨会,*,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,全国第四届重味物理和CP破坏研讨会,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,全国第四届重味物理和CP破坏研讨会,*,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.D73:034005,2006,2024/10/3,1,全国第四届重味物理和CP破坏研讨会,There are many different editions of Final State Interactions(,FSIs,)in the literature.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),2024/10/3,2,全国第四届重味物理和CP破坏研讨会,Outline,Motivation,Framework of,FSIs,FSIs,in B to KK and discussion,Summary,2024/10/3,3,全国第四届重味物理和CP破坏研讨会,FSIs,can provide an approach to solve many puzzles.To be,self-consistent,a good approach should also accommodate,with the data for other channels.,Motivation,2024/10/3,4,全国第四届重味物理和CP破坏研讨会,Motivation,is a pure annihilation process and the amplitude,is totally from,FSIs,.This process is quite helpful to detect,the dynamics of strong interactions.,2024/10/3,5,全国第四届重味物理和CP破坏研讨会,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,channels so that they can be treated as,one-particle-exchange graphs.,Framework of,FSIs,2024/10/3,6,全国第四届重味物理和CP破坏研讨会,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 distance),contribution:,2024/10/3,7,全国第四届重味物理和CP破坏研讨会,At the quark level,final state,rescattering,can occur through quark annihilation and quark exchange,：,Framework of,FSIs,2024/10/3,8,全国第四届重味物理和CP破坏研讨会,At,hadron,level,that is s-channel and t-channel,rescattering,:,Due to the lack of the existence 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,2024/10/3,9,全国第四届重味物理和CP破坏研讨会,Framework of,FSIs,Using cutting rule,we can get the,absportive,part of the magnitude:,2024/10/3,10,全国第四届重味物理和CP破坏研讨会,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 involved in the strong interaction vertex.,2024/10/3,11,全国第四届重味物理和CP破坏研讨会,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 the complication from integrations.So the dispersive part is neglected except in modes.,Including the absorptive contribution,the amplitude is:,2024/10/3,12,全国第四届重味物理和CP破坏研讨会,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 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,FSIs,2024/10/3,13,全国第四届重味物理和CP破坏研讨会,FSIs,in B to KK,Nave factorization gives the contribution as:,2024/10/3,14,全国第四届重味物理和CP破坏研讨会,FSIs,in B to KK,For intermediate states,we consider those channels favored by CKM and Wilson coefficients:,2024/10/3,15,全国第四届重味物理和CP破坏研讨会,FSIs,in B to KK,In order to avoid the 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.,2024/10/3,16,全国第四届重味物理和CP破坏研讨会,Only short distance and absorptive contribution:,2024/10/3,17,全国第四届重味物理和CP破坏研讨会,FSIs,in B to KK,2024/10/3,18,全国第四届重味物理和CP破坏研讨会,FSIs,in B to KK,Results from,PQCD:,Results from QCDF,:,2024/10/3,19,全国第四届重味物理和CP破坏研讨会,FSIs,in B to KK,Comparisons with these approaches:,For the branching ratio,with the errors,all the calculations 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.,2024/10/3,20,全国第四届重味物理和CP破坏研讨会,Including meson annihilation:,2024/10/3,21,全国第四届重味物理和CP破坏研讨会,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-channel Final State Interactions which is consistent with PQCD.,We test the