Partial wave decomposition is one of the main tools within the modern S-matrix studies. We present a method to compute partial waves for 2 → 2 scattering of spinning particles in arbitrary spacetime dimension. We identify partial waves as matrix elements of the rotation group with definite covariance properties under a subgroup. This allows to use a variety of techniques from harmonic analysis in order to construct a novel algebra of weight-shifting operators. All spinning partial waves are generated by the action of these operators on a set of known scalar seeds. The text is accompanied by a Mathematica notebook to automatically generate partial waves. These results pave the way to a systematic studies of spinning S-matrix bootstrap and positivity bounds.

Spinning partial waves for scattering amplitudes in d dimensions

Buric, Ilija
;
Russo, Francesco
;
Vichi, Alessandro
2023-01-01

Abstract

Partial wave decomposition is one of the main tools within the modern S-matrix studies. We present a method to compute partial waves for 2 → 2 scattering of spinning particles in arbitrary spacetime dimension. We identify partial waves as matrix elements of the rotation group with definite covariance properties under a subgroup. This allows to use a variety of techniques from harmonic analysis in order to construct a novel algebra of weight-shifting operators. All spinning partial waves are generated by the action of these operators on a set of known scalar seeds. The text is accompanied by a Mathematica notebook to automatically generate partial waves. These results pave the way to a systematic studies of spinning S-matrix bootstrap and positivity bounds.
2023
Buric, Ilija; Russo, Francesco; Vichi, Alessandro
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1220569
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