论文标题
$ {\ cal n} = 4 $ super-yang-mills的一个不错的两循环近代到次要振幅
A nice two-loop next-to-next-to-MHV amplitude in ${\cal N}=4$ super-Yang-Mills
论文作者
论文摘要
我们研究了8点近隔至最大的甲基竞争（n $ {}^2 $ MHV）的标量组件，在$ {\ cal n} = 4 $ super-yang-mills理论中以两环级别为单位。它具有与四个盒平方根的倒数成正比的领先奇异性，并且仅从两种类型的非平凡积分的贡献中，具有单环红外（IR）差异。我们通过采用某些有限的，双符号不变的积分来计算这种两环的8点积分，并在减去差异后很好地赋予了IR-SAVE比率函数。作为第一个真正的两环n $ {}^2 $ MHV振幅明确计算出来，我们在其符号和字母中发现了出色的结构：与近代的MHV（NMHV）情况相似，仍然有9个代数字母与正方形相关，后者也成为第一次的字母;与NMHV案例不同，此类代数字母出现在第二，第三和最后一个条件的一个或全部，带有三个奇数字母的部分特别简单。
We study a scalar component of the 8-point next-to-next-to-maximally-helicity-violating (N${}^2$MHV) amplitude at two-loop level in ${\cal N}=4$ super-Yang-Mills theory; it has a leading singularity proportional to the inverse of the four-mass-box square root and receives contributions from only two types of non-trivial integrals with one-loop infrared (IR) divergences. We compute such two-loop 8-point integrals by taking (double-)collinear limits of certain finite, dual-conformal-invariant integrals, and they nicely give the IR-safe ratio function after subtracting divergences. As the first genuine two-loop N${}^2$MHV amplitude computed explicitly, we find remarkable structures in its symbol and alphabet: similar to the next-to-MHV (NMHV) case, there are still 9 algebraic letters associated with the square root, and the latter also becomes a letter for the first time; unlike the NMHV case, such algebraic letters appear at either one or all of the second, third and last entry, and the part with three odd letters is particularly simple.
