The Infrared Structure of Nonlinear Sigma Model Amplitudes

Yin, Zhewei

doi:https://doi.org/10.21985/n2-qrbz-vp90

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The Infrared Structure of Nonlinear Sigma Model Amplitudes

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On-shell formulations of scattering amplitudes for quantum field theories, without utilizating the local descriptions of Lagrangian and Feynman diagrams, have become increasingly useful and important in recent years for both formal and practical reasons. The nonlinear sigma model (NLSM), which describes the interactions between Nambu-Goldstone bosons, is an ideal testing ground for the applications of the on-shell methods to effective field theories (EFT's). We present progresses in understanding the on-shell amplitudes of the NLSM, with a focus on the low energy behavior and the infrared universality. We review the construction of the NLSM Lagrangian from both the ultraviolet and the infrared perspectives. Basic properties of the NLSM amplitudes are then discussed, including the general flavor decomposition in the trace basis, the pair basis for the NLSM of the SO(N) fundamental representation, as well as the Cachazo-He-Yuan representation of the leading-order tree level amplitudes. We then perform a systematic survey of the soft theorems for NLSM amplitudes. We derive the leading and subleading single soft theorems using the Ward identity corresponding to the shift symmetry, and study the form of the local interactions for the emergent extended theories. We then present a most general double soft theorem valid up to all orders in the derivative expansion of the EFT and all loops, as well as a subleading triple soft theorem that also involves the extended theory. Next, we study the method of the soft bootstrap, which utilizes the single soft behavior of the amplitudes to construct the NLSM in a completely on-shell manner. We bootstrap the tree level NLSM amplitudes up to the 4-derivative level, recovering all degrees of freedom for the Wilson coefficient in the local Lagrangian.

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