论文标题
树级形式和散射幅度的新关系
New relations for tree-level form factors and scattering amplitudes
论文作者
论文摘要
我们表明，Yang-Mills-scalar（YMS）理论中具有长度的两个操作员的树级形式的形式表现出与胶子和标量的散射幅度非常相似的结构，这导致了它们之间的新关系。就像振幅一样，$ n $ - 点杨米尔的形式是用$ {\ rm tr}（f^2）$ operator分解成$ {\ rm tr}（ϕ^2）$操作员和$ r $外部标量的yms理论的线性组合，在yms理论中，该系数由$ lorerentz ulorentz ul lororentz ul loreNTERS $ lorente $ rorefiend $ rore $ r lorefients ul loreNTERS。此外，我们表明，任何此类$ n $ n $点的形式均为$ {\ rm tr}（ϕ^2）$ operator可以进一步扩展到$（n {+} 1）$ - 点yms振幅，并具有额外的外壳标量腿。除了揭开隐藏的结构外，我们的结果还提供了一种有效的算法，用于计算任何维度的所有多重长度两个形式，以及通过YMS幅度的cachazo-He-yuan公式。
We show that tree-level form factors with length-two operators in Yang-Mills-scalar (YMS) theory exhibit structures very similar to scattering amplitudes of gluons and scalars, which leads to new relations between them. Just like amplitudes, $n$-point Yang-Mills form factors with ${\rm tr}(F^2)$ operator can be decomposed as a linear combination of form factors with ${\rm tr}(ϕ^2)$ operator and $r$ external scalars in YMS theory, where the coefficients are given by Lorentz products of the $r$ linearized field strengths. Moreover, we show that any such $n$-point form factor of ${\rm tr}(ϕ^2)$ operator can be further expanded into $(n{+}1)$-point YMS amplitudes with an additional off-shell scalar leg. In addition to unravelling hidden structures, our results provide an efficient algorithm for computing all-multiplicity length-two form factors in any dimension, as well as their Cachazo-He-Yuan formulae via those of the YMS amplitudes.
