标题： 中性π介子到两个光子的转换形式因子的重新研究 显示英文标题

标题： Neutral pion to two-photons transition form factor revisited

摘要： 基于量子色动力学（QCD）中施温格-戴森方程和贝塞尔-萨尔佩特定理的联合形式，我们提出了一种QCD类代数模型，用于描述带电夸克传播子、介子的贝塞尔-萨尔佩特定理振幅以及电磁夸克-光子相互作用顶点。 我们随后计算了$\gamma^{*}\pi^0\gamma$的转换形式因子$G^{\gamma^{*}\pi^0\gamma}(Q^2)$，在广泛的光子动量转移平方$Q^2$范围内进行计算。 夸克传播子以微扰函数形式展开，但具有动态生成的带电夸克质量。 它在复动量平面上具有共轭极点奇异性，这是由求解夸克间隙方程在雨伞-阶梯截断下的无限组施温格-戴森方程所得出的结果所激发的。 夸克传播子的这种复极点奇异性可以与禁闭信号相关联，这阻止了夸克成为稳定的渐近态。 贝塞尔-萨尔佩特定理振幅没有用谱密度函数来表示，其包含了低动量和高动量行为。 通过直接实现埃夫雷莫夫-拉杜什金-布罗德斯基-莱普奇进化方程，我们也把分布振幅的QCD演化纳入我们的模型中。 我们在描述夸克-光子顶点时考虑了夸克异常磁矩的影响，其红外增强已知决定了强子性质。 一旦构建了QCD类模型，我们计算了形式因子$G^{\gamma^{*}\pi^0\gamma}(Q^2)$，并发现其与基于QCD的直接研究以及大多数可用实验数据一致。 对于大的$Q^2$，它略微超过共形极限，这可能归因于QCD中的尺度违反。 相关的相互作用半径和中性π介子衰变宽度与实验数据相容。 显示英文摘要

摘要： Based upon a combined formalism of Schwinger-Dyson and Bethe-Salpeter equations in quantum chromodynamics (QCD), we propose a QCD kindred algebraic model for the dressed quark propagator, for the Bethe-Salpeter amplitude of the pion and the electromagnetic quark-photon interaction vertex. We then compute the $\gamma^{*}\pi^0\gamma$ transition form factor $G^{\gamma^{*}\pi^0\gamma}(Q^2)$ for a wide range of photon momentum transfer squared $Q^2$. The quark propagator is expanded out in its perturbative functional form but with dynamically generated dressed quark mass. It has complex conjugate pole singularities in the complex-momentum plane which is motivated by the solution of the quark gap equation with rainbow-ladder truncation of the infinite set of Schwinger-Dyson equations. This complex pole singularity structure of the quark propagator can be associated with a signal of confinement which prevents quarks to become stable asymptotic states. The Bethe-Salpeter amplitude is expressed without a spectral density function, which encapsulate its low and large momentum behaviour. The QCD evolution of the distribution amplitude is also incorporated into our model through the direct implementation of Efremov-Radyushkin-Brodsky-Lepage evolution equations. We include the effects of the quark anomalous magnetic moment in the description of the quark-photon vertex whose infrared enhancement is known to dictate hadronic properties. Once the QCD kindred model is constructed, we calculate the form factor $G^{\gamma^{*}\pi^0\gamma}(Q^2)$ and find it consistent with direct QCD-based studies as well as most available experimental data. It slightly exceeds the conformal limit for large $Q^2$ which might be attributed to the scaling violations in QCD. The associated interaction radius and neutral pion decay width turn out to be compatible with experimental data.