We present a calculation of $P\to {\gamma }^{(*)}{\gamma }^{(*)}$ processes, where $P={\pi }^0,\eta ,\eta \prime$, at the one-loop level up to and including next-to-next-to-leading order (NNLO) in large-$N_c$ chiral perturbation theory. The results are numerically evaluated successively at LO, NLO, and NNLO. The appearing low-energy constants are determined through fits to the available experimental data. We investigate the decay widths to real photons, the single-virtual transition form factors, and the widths of $P\to \gamma l^{+}{l}^{-}$, where $l=e,\mu$. Furthermore, we provide results for the slopes and curvatures of the transition form factors.

中文翻译：

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在大手性微扰理论中π0，η和η′的双光子衰变和跃迁形成因子

我们提出一个计算 $P\to {\gamma }^{（*）}{\gamma }^{（*）}$ 流程，在哪里 $P={\pi }^0，\eta ，\eta \prime$，在单循环级别上，直到并包括大到倒数第二个订单（NNLO）${ñ}_C$手性摄动理论。在LO，NLO和NNLO处依次对结果进行数值评估。出现的低能量常数是通过对可用实验数据进行拟合确定的。我们研究了实际光子的衰减宽度，单虚拟跃迁形状因数以及$P\to \gamma {升}^{+}{升}^{-}$，在哪里 $升=Ë，\mu$。此外，我们提供了过渡形状因数的斜率和曲率的结果。