One-loop inelastic amplitudes from tree-level elasticity in 2d

Polvara, Davide

Abstract

We investigate the perturbative integrability of different quantum field theories in 1+1 dimensions at one loop. Starting from massive bosonic Lagrangians with polynomial-like potentials and absence of inelastic processes at the tree level, we derive a formula reproducing one-loop inelastic amplitudes for arbitrary numbers of external legs. We show that any one-loop inelastic amplitude is equal to its tree-level version, in which the masses of particles and propagators are corrected by one-loop bubble diagrams. These amplitudes are nonzero in general and counterterms need to be added to the Lagrangian to restore the integrability at one loop. For the class of simply-laced affine Toda theories, we show that the necessary counterterms are obtained by scaling the potential with an overall multiplicative factor, proving in this way the one-loop integrability of these models. Even though we focus on bosonic theories with polynomial-like interactions, we expect that the on-shell techniques used in this paper to compute amplitudes can be applied to several other models.

Citation

Polvara, D. (2023). One-loop inelastic amplitudes from tree-level elasticity in 2d. Journal of High Energy Physics, 2023(4), Article 20. https://doi.org/10.1007/jhep04%282023%29020

• Journal Article Type: Article
• Acceptance Date: Mar 26, 2023
• Online Publication Date: Apr 4, 2023
• Publication Date: 2023-04
• Deposit Date: Oct 2, 2023
• Publicly Available Date: Oct 3, 2023
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2023
• Issue: 4
• Article Number: 20
• DOI: https://doi.org/10.1007/jhep04%282023%29020
• Public URL: https://durham-repository.worktribe.com/output/1755038