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| Autori principali: | , , , |
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| Natura: | Preprint |
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2024
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| Accesso online: | https://arxiv.org/abs/2401.04731 |
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| _version_ | 1866911752586788864 |
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| author | Bartsch, Christoph Kampf, Karol Novotny, Jiri Trnka, Jaroslav |
| author_facet | Bartsch, Christoph Kampf, Karol Novotny, Jiri Trnka, Jaroslav |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04731 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An All-loop Soft Theorem for Pions Bartsch, Christoph Kampf, Karol Novotny, Jiri Trnka, Jaroslav High Energy Physics - Theory High Energy Physics - Phenomenology 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. |
| title | An All-loop Soft Theorem for Pions |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2401.04731 |