From tree- to loop-simplicity in affine Toda theories I: Landau singularities and their subleading coefficients

Dorey, Patrick; Polvara, Davide

doi:10.1007/jhep09(2022)220

Cited by 5 publications

(1 citation statement)

References 30 publications

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“…In that paper, a complete proof of the tree-level perturbative integrability of these theories was provided by showing that combinations of Feynman diagrams contributing to non-elastic processes always sum to zero at the tree level. At the loop level, partial results were obtained in [19,[44][45][46][47][48][49]: while many nice features of these models were shown, the results were based on a case-by-case study performed over different theories and a proof of the vanishing of inelastic one-loop amplitudes has so far been missing. In this section, we extend the results of [15] to the one-loop order in perturbation theory: using the techniques developed in the previous sections we show how integrability manifests itself in one-loop computations in affine Toda field theories.…”

Section: Sufficient Conditions For Absence Of Inelasticity At One-loopmentioning

confidence: 99%

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

Polvara¹

2023

Preprint

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We investigate the perturbative integrability of different quantum field theories in 1+1 dimensions at one loop. Starting from massive bosonic Lagrangians with polynomiallike 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.

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Section: Sufficient Conditions For Absence Of Inelasticity At One-loopmentioning

confidence: 99%

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

Polvara¹

2023

Preprint

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

Polvara

2023

J. High Energ. Phys.

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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.

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

Fabri,

Polvara

2024

J. High Energ. Phys.

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In this paper we extend the study initiated in [1] to the computation of one-loop elastic amplitudes. We consider 1+1 dimensional massive bosonic Lagrangians with polynomial-like potentials and absence of inelastic processes at the tree level; starting from these assumptions we show how to write sums of one-loop diagrams as products and integrals of tree-level amplitudes. We derive in this way a universal formula for the one-loop two-to-two S-matrices in terms of tree S-matrices. We test our results on different integrable theories, such as sinh-Gordon, Bullough-Dodd and the full class of simply-laced affine Toda theories, finding perfect agreement with the bootstrapped S-matrices known in the literature. We show how Landau singularities in amplitudes are naturally captured by our universal formula while they are lost in results based on unitarity-cut methods implemented in the past [2, 3].

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From tree- to loop-simplicity in affine Toda theories I: Landau singularities and their subleading coefficients

Cited by 5 publications

References 30 publications

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

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

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

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

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