All-loop soft theorem for pions

Journal Article · 07 August 2024 · Physical Review. D.

DOI: https://doi.org/10.1103/PhysRevD.110.045009 · OSTI ID:2426988

Bartsch, Christoph ; Kampf, Karol ; Novotný, Jiří ; Trnka, Jaroslav

In this paper we discuss a generalization of the Adler zero to loop integrands in the planar limit of the $SU\left(N\right)$ nonlinear sigma model (NLSM). The Adler zero for integrands is violated starting at the two-loop order and is only recovered after integration. Here we propose a 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 , we identify a simple nonvanishing soft behavior of integrands, which we call the . We find that the proposed soft theorem is satisfied by the “surface” integrand of Arkani-Hamed and Figueiredo [], which is obtained from the shifted $\mathrm{Tr}{\phi }^3$ surfacehedron integrand. Finally, we derive an on shell version of the algebraic soft theorem that takes an interesting form in terms of self-energy factors and lower-loop integrands in a mixed theory of pions and scalars. Published by the American Physical Society 2024

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0009999
• OSTI ID: 2426988
• Journal Information: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 4 Vol. 110; ISSN PRVDAQ; ISSN 2470-0010
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English