再论$k_T$分解公式中的Rho-pion跃迁形状因子
Rho-pion transition form factors in the $k_T$ factorization formulism revisited
摘要：
在$k_T$因子分解定理的框架下，我们重新评估了类空和类时$ρπ$跃迁形状因子$F_{ρπ}(Q^2)$和$G_{ρπ}(Q^2)$，并加入了次领先阶（NLO）QCD贡献。红外发散被外价夸克携带的横动量正则化，并最终被介子波函数吸收。在$ Q^2 \leqslant 2 \, \textrm{GeV}^2 $区域，当PQCD因子分解方法适用时，非线性光学贡献对类空形状因子$F_{ρπ}(Q^2)$的增强不超过$ 35\%$.对于在运动学交换对称性下导出的类时形状因子，当动量转移平方足够大时，这种贡献也是可控的。我们还考虑了格点QCD的结果，将我们的预言扩展到小$Q^2$区域，从而得到了耦合$g_{ρπγ} = G_{ρπ}(0)=0.596$。
英文摘要：
We revisit the evaluations for the spacelike and timelike $ρπ$ transition form factors $F_{ρπ}(Q^2)$ and $G_{ρπ}(Q^2)$ with the inclusion of the the next-to-leading order (NLO) QCD contributions in the framework of the $k_T$ factorization theorem. The infrared divergence is regularized by the transversal momentum carried by external valence quarks, and ultimately absorbed into the meson wave functions. In the region of $ Q^2 \leqslant 2 \, \textrm{GeV}^2 $, where PQCD factorization apporach applicable, the NLO contribution can bring no larger than $ 35\%$ enhancement to the spacelike form factor $F_{ρπ}(Q^2)$. For the timelike form factor derived under the kinematic exchanging symmetry, this contribution is also under control when the momentum transfer squared is large enough. We also prolong our prediction into the small $Q^2$ region by taking the Lattice QCD results into account, and subsequently obtain the coupling $g_{ρπγ} = G_{ρπ}(0)=0.596$.
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