Neutral pion to two-photons transition form factor revisited

M. Atif Sultan, Jiayin Kang, Adnan Bashir, Lei Chang
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Abstract

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.
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中性先驱到双光子转变形式因子再探讨
基于量子色动力学(QCD)中施温格-戴森方程和贝特-萨尔佩特方程的组合形式主义,我们提出了一种QCD同类代数模型,用于敷装夸克传播者、夸克的贝特-萨尔佩特振幅以及电磁夸克-光子相互作用顶点。然后,我们计算了光子动量转移平方$Q^2$范围内的$\gamma^{*}\pi^0\gamma$过渡形式因子$G^{gamma^{*}\pi^0\gamma}(Q^2)$。夸克传播者以其微扰函数形式展开,但具有动态生成的穿戴夸克质量。它在复动量平面上具有复共轭极点奇异性,这是由夸克间隙方程与施文格-戴森方程无穷集彩虹梯截断的解法激发的。夸克传播者的这种复极性结构可以与阻止夸克成为稳定渐近态的束缚信号联系起来。贝特-萨尔佩特振幅的表达没有谱密度函数,而谱密度函数囊括了其低动量和大动量行为。我们在描述夸克-光子顶点时加入了夸克反常磁矩的影响,众所周知,夸克-光子顶点的红外增强会影响强子特性。在构建了QCD同类模型之后,我们计算了形式因子$G^{\gamma^{*}\pi^0\gamma}(Q^2)$,发现它与基于QCD的直接研究以及大多数可用的实验数据相一致。它略微超出了大$Q^2$时的共形极限,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先驱衰变宽度与实验数据相一致。
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