arXiv 1006.06792010-06-03hep-ph

单圈Feynman张量积分约化的一些变形

Some variations of the reduction of one-loop Feynman tensor integrals

Jochem Fleischer, Tord Riemann

备注：: 8 pages, 1figure, 1 table, submitted to PoS(ACAT2010)074
发表信息：: PoS ACAT2010:074,2010

摘要：

提出了一种新的算法，将带$n\leq 4$外支的单圈\emph{tensor} Feynman积分约化为在$D$维上带$n=3,4$支的\emph{scalar} Feynman积分$I_n^D$，其中$D=d+2l$具有整数$l \geq 0$和泛维$d=4-2ε$，从而避免了逆Gram行列式$()_4$的出现.只要$()_4\neq 0$，$I_{3,4}^D$与$D>d$的积分可以进一步用通常的维数正则化标量函数$I_{2,3,4}^d$表示.积分$I_{4}^D$在$()_4 \equiv 0$是已知的，因此我们可以通过应用维数递归关系将数值扩展到小的、非零的$()_4$。最后给出了一个数值算例。再加上递归减少6点和5点的功能，推导出较早，计算计划允许一个稳定的减少$n$点功能与$n\leq 6$在任意相空间点。该算法是对秩为$R\leq n$的张量显式地给出的。

英文摘要：

We present a new algorithm for the reduction of one-loop \emph{tensor} Feynman integrals with $n\leq 4$ external legs to \emph{scalar} Feynman integrals $I_n^D$ with $n=3,4$ legs in $D$ dimensions, where $D=d+2l$ with integer $l \geq 0$ and generic dimension $d=4-2ε$, thus avoiding the appearance of inverse Gram determinants $()_4$. As long as $()_4\neq 0$, the integrals $I_{3,4}^D$ with $D>d$ may be further expressed by the usual dimensionally regularized scalar functions $I_{2,3,4}^d$. The integrals $I_{4}^D$ are known at $()_4 \equiv 0$, so that we may extend the numerics to small, non-vanishing $()_4$ by applying a dimensional recurrence relation. A numerical example is worked out. Together with a recursive reduction of 6- and 5-point functions, derived earlier, the calculational scheme allows a stabilized reduction of $n$-point functions with $n\leq 6$ at arbitrary phase space points. The algorithm is worked out explicitely for tensors of rank $R\leq n$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文