标题： 关于$e^+ e^-$湮灭纵向截面的红外灵敏度 显示英文标题

标题： On the infrared sensitivity of the longitudinal cross section in $e^+ e^-$ annihilation

摘要： 我们计算了与$\beta_0^n\alpha_s^{n+1}$成正比的纵向碎裂函数在$e^+e^-$粒子湮灭中所有阶微扰理论的贡献。我们利用这一结果来估计纵向截面$\sigma_L$的高阶微扰修正和非微扰修正，并讨论从$\sigma_L$中确定$\alpha_s$的前景。 红外重整化群的结构表明，在微扰展开中，具有固定动量分数$x$的强子产生纵向截面会受到阶为$1/(x^2Q^2)$的非微扰贡献，而总截面则有更大的阶为$1/Q$的修正。 此修正来源于非常大的纵向距离，并与固定$x$的截面的Borel积分在Borel参数较大时的行为有关。 显示英文摘要

摘要： We have calculated the contributions proportional to $\beta_0^n\alpha_s^{n+1}$ to the longitudinal fragmentation function in $e^+e^-$ annihilation to all orders of perturbation theory. We use this result to estimate higher-order perturbative corrections and nonperturbative corrections to the longitudinal cross section $\sigma_L$ and discuss the prospects of determining $\alpha_s$ from $\sigma_L$. The structure of infrared renormalons in the perturbative expansion suggests that the longitudinal cross section for hadron production with fixed momentum fraction $x$ receives nonperturbative contributions of order $1/(x^2Q^2)$, whereas the total cross section has a larger, $1/Q$ correction. This correction arises from very large longitudinal distances and is related to the behaviour of the Borel integral for the cross section with fixed $x$ at large values of the Borel parameter.