全国第四届重味物理和CP破坏研讨会.ppt

Wei Wang Institute of High Energy PhysicsInstitute of High Energy PhysicsFinal State Interactions in B to KK modesBased on:Cai-dian Lv,Yue-Long Shen and Wei Wang,Phys.Rev.D73:034005,2006 2022/12/241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)2022/12/242全国第四届重味物理和CP破坏研讨会OutlineMotivationFramework of FSIs FSIs in B to KK and discussionSummary2022/12/243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.Motivation2022/12/244全国第四届重味物理和CP破坏研讨会Motivation is a pure annihilation process and the amplitudeis totally from FSIs.This process is quite helpful to detect the dynamics of strong interactions.2022/12/245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 FSIs2022/12/246全国第四届重味物理和CP破坏研讨会Framework of FSIsIn 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:2022/12/247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 FSIs2022/12/248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 FSIs2022/12/249全国第四届重味物理和CP破坏研讨会Framework of FSIsUsing cutting rule,we can get the absportive part of the magnitude:2022/12/2410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.2022/12/2411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:2022/12/2412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 FSIs2022/12/2413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:2022/12/242022/12/241414全国第四届重味物理和全国第四届重味物理和CPCP破坏研讨会破坏研讨会FSIs in B to KK For intermediate states,we consider those channels favored by CKM and Wilson coefficients:2022/12/242022/12/241515全国第四届重味物理和全国第四届重味物理和CPCP破坏研讨会破坏研讨会FSIs in B to KKIn 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.2022/12/242022/12/241616全国第四届重味物理和全国第四届重味物理和CPCP破坏研讨会破坏研讨会Only short distance and absorptive contribution:2022/12/242022/12/241717全国第四届重味物理和全国第四届重味物理和CPCP破坏研讨会破坏研讨会FSIs in B to KK2022/12/242022/12/241818全国第四届重味物理和全国第四届重味物理和CPCP破坏研讨会破坏研讨会FSIs in B to KKResults from PQCD:Results from QCDF:2022/12/242022/12/241919全国第四届重味物理和全国第四届重味物理和CPCP破坏研讨会破坏研讨会FSIs in B to KKComparisons 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.2022/12/242022/12/242020全国第四届重味物理和全国第四届重味物理和CPCP破坏研讨会破坏研讨会Including meson annihilation:2022/12/242022/12/242121全国第四届重味物理和全国第四届重味物理和CPCP破坏研讨会破坏研讨会SummaryFinal state interactions can not change the branching ratioof and sizably if we considerThe 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 contribution from the annihilation diagram and find it not favored by the data.So new mechanism is needed to explain this process.2022/12/2422全国第四届重味物理和CP破坏研讨会Thank you!2022/12/2423全国第四届重味物理和CP破坏研讨会