We examine the polarized doubly-virtual Compton scattering (VVCS) off the nucleon using chiral perturbation theory ($\chi$PT). The polarized VVCS contains a wealth of information on the spin structure of the nucleon which is relevant to the calculation of the two-photon-exchange effects in atomic spectroscopy and electron scattering. We report on a complete next-to-leading-order (NLO) calculation of the polarized VVCS amplitudes $S_1(\nu ,Q^2)$ and $S_2(\nu ,Q^2)$, and the corresponding polarized spin structure functions $g_1(x,Q^2)$ and $g_2(x,Q^2)$. Our results for the moments of polarized structure functions, partially related to different spin polarizabilities, are compared to other theoretical predictions and “data-driven’’ evaluations, as well as to the recent Jefferson Lab measurements. By expanding the results in powers of the inverse nucleon mass, we reproduce the known”heavy-baryon’’ expressions. This serves as a check of our calculation, as well as demonstrates the differences between the manifestly Lorentz-invariant baryon $\chi$PT (B$\chi$PT) and heavy-baryon (HB$\chi$PT) frameworks.

中文翻译：

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在手性摄动理论中，双虚拟康普顿从核子中向前散射。二。自旋极化率和极化结构函数的矩

我们使用手性扰动理论检查了核子的极化双虚拟康普顿散射（VVCS）（$\chi$PT）。极化的VVCS包含有关核子自旋结构的大量信息，这些信息与原子光谱和电子散射中双光子交换效应的计算有关。我们报告了极化VVCS幅度的完整的下一阶（NLO）计算${\mathrm{小号}}_{\mathrm{1个}}（\nu ，{问}^2）$ 和 ${\mathrm{小号}}_2（\nu ，{问}^2）$，以及相应的极化自旋结构函数 $G_{\mathrm{1个}}（X，{问}^2）$ 和 $G_2（X，{问}^2）$。我们将部分与不同自旋极化率相关的极化结构函数矩的结果与其他理论预测和“数据驱动”评估以及最近的Jefferson Lab测量进行了比较。通过扩大反核子质量幂的结果，我们重现了已知的“重质子”表达式。这是对我们计算的一种检验，并证明了明显的洛伦兹不变重子之间的差异$\chi$PT（B$\chi$PT）和重磅（HB$\chi$PT）框架。