Soft theorems from effective field theory
Name
Larkoski-2015-Soft theorems from e.pdf
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1.88 MB
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059e13bf9df5592ddeabe199393c78e3
Author(s)
Larkoski, Andrew
Neill, Duff Austin
Stewart, Iain
Date Issued
June 2015
Journal
Journal of High Energy Physics
Publisher
Springer-Verlag
Citation
Larkoski, Andrew J., Duff Neill, and Iain W. Stewart. “Soft Theorems from Effective Field Theory.” J. High Energ. Phys. 2015, no. 6 (June 2015).
Version
Final published version
Abstract
The singular limits of massless gauge theory amplitudes are described by an effective theory, called soft-collinear effective theory (SCET), which has been applied most successfully to make all-orders predictions for observables in collider physics and weak decays. At tree-level, the emission of a soft gauge boson at subleading order in its energy is given by the Low-Burnett-Kroll theorem, with the angular momentum operator acting on a lower-point amplitude. For well separated particles at tree-level, we prove the Low-Burnett-Kroll theorem using matrix elements of subleading SCET Lagrangian and operator insertions which are individually gauge invariant. These contributions are uniquely determined by gauge invariance and the reparametrization invariance (RPI) symmetry of SCET. RPI in SCET is connected to the infinite-dimensional asymptotic symmetries of the S-matrix. The Low-Burnett-Kroll theorem is generically spoiled by on-shell corrections, including collinear loops and collinear emissions. We demonstrate this explicitly both at tree-level and at one-loop. The effective theory correctly describes these configurations, and we generalize the Low-Burnett-Kroll theorem into a new one-loop subleading soft theorem for amplitudes. Our analysis is presented in a manner that illustrates the wider utility of using effective theory techniques to understand the perturbative S-matrix.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Physics
Massachusetts Institute of Technology. Laboratory for Nuclear Science
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DOI of Published Version
https://doi.org/10.1007/jhep06(2015)077
