Testing the threshold expansion for three-particle energies at fourth order in ϕ4 theory

Stephen R. Sharpe
Phys. Rev. D 96, 054515 – Published 26 September 2017; Erratum Phys. Rev. D 98, 099901 (2018)

Abstract

A relativistic formalism for relating the energies of the states of three scalar particles in finite volume to infinite volume scattering amplitudes has recently been developed. This formalism has been used to predict the energy of the state closest to threshold in an expansion in powers of 1/L, with L the box length. This expansion has been tested previously by a perturbative calculation of the threshold energy in λϕ4 theory, working to third order in λ and up to O(1/L6) in the volume expansion. However, several aspects of the predicted threshold behavior do not enter until fourth (three-loop) order in perturbation theory. Here I extend the perturbative calculation to fourth order and find agreement with the general prediction. This check also requires a two-loop calculation of the infinite-volume off-shell two-particle scattering amplitude near threshold. As a spin-off, I check the threshold expansion for two particles to the same order, finding agreement with the result that follows from Lüscher’s formalism.

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  • Received 24 July 2017

DOI:https://doi.org/10.1103/PhysRevD.96.054515

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Particles & FieldsNuclear Physics

Erratum

Authors & Affiliations

Stephen R. Sharpe*

  • Physics Department, University of Washington, Seattle, Washington 98195-1560, USA

  • *srsharpe@uw.edu

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Issue

Vol. 96, Iss. 5 — 1 September 2017

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