Pions的一个全圈软定理
An All-loop Soft Theorem for Pions
AI总结：
本文针对$SU(N)$ NLSM平面极限下圈积分被积函数的Adler零在两圈及以上被破坏的问题，提出并验证了一个适用于任意圈数和腿数的非零“代数软定理”及其在壳版本。
摘要：
在这封信中，我们讨论了将Adler零推广到$SU(N)$非线性sigma模型（NLSM）平面极限下的圈积分被积函数。尽管在单圈时可以保持，但被积函数的Adler零从两圈阶开始被破坏，并且只有在积分后才被恢复。在此，我们提出了一个由任意圈数和腿数的圈积分被积函数满足的非零软定理。这需要将NLSM被积函数推广到具有特定变形运动学的离壳框架。通过定义“代数软极限”，我们识别出被积函数一种特别简单的非消失软行为，我们称之为“代数软定理”。我们发现，所提出的软定理由Arkani-Hamed、Cao、Dong、Figueiredo和He的“曲面”被积函数所满足，该被积函数由位移后的${\ m Tr}ϕ^3$曲面多面体被积函数获得。最后，我们推导了代数软定理的在壳版本，该版本在pions和标量的混合理论中以传播子重整化因子和低圈被积函数的形式呈现出有趣的形式。
英文摘要：
In this letter, we discuss a generalization of the Adler zero to loop integrands in the planar limit of the $SU(N)$ non-linear sigma model (NLSM). While possible to maintain at one-loop, the Adler zero for integrands is violated starting at the two-loop order and is only recovered after integration. Here we propose a non-zero soft theorem satisfied by loop integrands with any number of loops and legs. This requires a generalization of NLSM integrands to an off-shell framework with certain deformed kinematics. Defining an `algebraic soft limit', we identify a particularly simple non-vanishing soft behavior of integrands, which we call the `algebraic soft theorem'. We find that the proposed soft theorem is satisfied by the `surface' integrand of Arkani-Hamed, Cao, Dong, Figueiredo and He, which is obtained from the shifted ${\rm Tr}ϕ^3$ surfacehedron integrand. Finally, we derive an on-shell version of the algebraic soft theorem that takes an interesting form in terms of propagator renormalization factors and lower-loop integrands in a mixed theory of pions and scalars.
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。
