Investigating The Kaon Twist-3Distribution Amplitudes With QCD Sum Rules In The Background Field Approach

In this paper, I investigate the kaon twist-3two-partical distribution amplitudes（DAs） with SVZ sum rules in the background field approach. The sum rules of the zeromoment normalization parameters and the first two moments of the DAsφ_p,σ^Kareobtained. I make use of the quak and gluon parapogaters in the background field, whichare expressed in the momentum space, to calculate the operator product expansion （OPE）of the correlation functions, all the calculation is proceeded in the momentum space,some common perturbative calculation technique, such as the momentum integration ofthe two point function, is adopted in my calculation. Because the mass effects in thequark propagator are retained completely, it is convenient to study the SU（3）-breakingeffects.My investigation about the kaon twist-3DAs φ_p,σ^K,σis based on the fact that, thequark in the meson is off-shell. Be different from using the motion function of theon-shell quark to esteimate the normalization parameters of the DASφ_p,σ^K, which isobtained direct with sum rules approach. After considering the uncertainty originatingfrom all of the input parameters, I obtained:μ-p^K|_1GeV=1.188_0.043^+0.039GeV，μ_σ^K|_1GeV=1.021_0.055^+0.036)GeV，〔ξ_p¹〕_k|_1GeV=-0.126_-0.049^+0.034，〔ξ_p²〕_K|_1GeV=0.428_-0.066^+0.031〔ξ_σ¹〕_K|_1GeV=-0.096_-0.044^+0.031，〔ξ_σ²〕_K|_1GeV=0.324_-0.050^+0.055 The DAsφ_p,σ^Kcan be expanded as the Gegenbaular polynomial series, and usually the first few termsare retained, the expanding coefficients are known as Gegenbaular moments. With thevalues of〔ξ_p,σ^1,2_K I obtain:a_K,p¹（1GeV）=-0.376_-0.148^+0.103, a_K,p²（1GeV）=0.701_-0.491^+0.481,a_K,σ¹1GeV)=-0.160_-0.074^+0.051a_K,σ¹（1GeV）=0.369_-0.149^+0.163。the key input parameters applying QCDfactorization approach and the QCD light cone sum rules （LCSR） to the exclusiveprocess. Because of the asymptotic behaviorφ_p^K,AS=1, the end-point singularity wouldbe appeared. Based on the first two Gegenbaular moments ofφ_p,σ^K, the improved modelof the kaon twist-3DAs is established, which have nice end-point behavior.The B to K transition form factor f_BK⁺is the key input parameter making use ofthe exclusive process to extract the CKM matrix element. For studying the influence ofthe kaon twist-3DAs to f_BK⁺, I adopt appropriate chiral current correlation function,with QCD LCSR, and obtain the expression only including the kaon twist-3DAs ofwhich. And the NLO correction is considered.