Scattering Amplitudes from Euclidean Correlators: Haag-Ruelle theory and approximation formulae

TL;DR

This paper develops a non-perturbative method to extract scattering amplitudes from Euclidean correlators using Haag-Ruelle theory, providing formulae suitable for numerical lattice QCD calculations.

Contribution

It generalizes previous results by deriving approximation formulae for scattering amplitudes from Euclidean correlators within the Haag-Ruelle framework, enabling potential non-perturbative QCD computations.

Findings

Provides explicit approximation formulae for scattering amplitudes

Extends previous theoretical results to broader applicability

Lays groundwork for numerical implementation in lattice QCD

Abstract

In this work we provide a non-perturbative solution to the theoretical problem of extracting scattering amplitudes from Euclidean correlators in infinite volume. We work within the solid axiomatic framework of the Haag-Ruelle scattering theory and derive formulae which can be used to approximate scattering amplitudes arbitrarily well in terms of linear combinations of Euclidean correlators at discrete time separations. Our result generalizes and extends the range of applicability of a result previously obtained by Barata and Fredenhagen [Commun. Math. Phys. 138 (1991) 507-520]. We provide a concrete procedure to construct such approximations, making our formulae ready to be used in numerical calculations of non-perturbative QCD scattering amplitudes. A detailed numerical investigation is needed to assess whether the proposed strategy can lead to the calculation of scattering amplitudes with phenomenologically satisfactory precision with presently available lattice QCD data. This will be the subject of future work. Nevertheless, the numerical accuracy and precision of lattice simulations is systematically improvable, and we have little doubts that our approach will become useful in the future.