Journal of High Energy Physics (May 2024)

Electroweak three-body decays in the presence of two- and three-body bound states

  • Raul A. Briceño,
  • Andrew W. Jackura,
  • Dimitra A. Pefkou,
  • Fernando Romero-López

DOI
https://doi.org/10.1007/JHEP05(2024)279
Journal volume & issue
Vol. 2024, no. 5
pp. 1 – 34

Abstract

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Abstract Recently, formalism has been derived for studying electroweak transition amplitudes for three-body systems both in infinite and finite volumes. The formalism provides exact relations that the infinite-volume amplitudes must satisfy, as well as a relationship between physical amplitudes and finite-volume matrix elements, which can be constrained from lattice QCD calculations. This formalism poses additional challenges when compared with the analogous well-studied two-body equivalent one, including the necessary step of solving integral equations of singular functions. In this work, we provide some non-trivial analytical and numerical tests on the aforementioned formalism. In particular, we consider a case where the three-particle system can have three-body bound states as well as bound states in the two-body subsystem. For kinematics below the three-body threshold, we demonstrate that the scattering amplitudes satisfy unitarity. We also check that for these kinematics the finite-volume matrix elements are accurately described by the formalism for two-body systems up to exponentially suppressed corrections. Finally, we verify that in the case of the three-body bound state, the finite-volume matrix element is equal to the infinite-volume coupling of the bound state, up to exponentially suppressed errors.

Keywords