论文标题
更高级别的HADRONIC真空极化函数扰动扩展系数的重新归一化组关系的复发形式
Recurrent form of the renormalization group relations for the higher-order hadronic vacuum polarization function perturbative expansion coefficients
论文作者
论文摘要
研究了更高阶的辐射真空极化函数扰动扩展系数的重新归一化组关系。获得了这种关系的折叠复发和展开的明确形式。系数的显式表达式（将$π^{2} $ - 术语的贡献纳入了电子 - 彼斯特朗歼灭的r-Ratio中的$π^{2} $ - 术语的贡献是在任意的环上得出的。获得的结果可以用作辐射真空极化函数的高阶扰动计算的独立交叉检查，以及在相关物理可观察物中的重新规范量表设置的研究中。
The renormalization group relations for the higher-order hadronic vacuum polarization function perturbative expansion coefficients are studied. The folded recurrent and unfolded explicit forms of such relations are obtained. The explicit expression for the coefficients, which incorporate the contributions of the $π^{2}$-terms in the perturbative expansion of the R-ratio of electron-positron annihilation into hadrons, is derived at an arbitrary loop level. The obtained results can be employed as an independent crosscheck of the higher-order perturbative calculations of the hadronic vacuum polarization function and in the studies of the renormalization scale setting in the relevant physical observables.
