Inclusive reactions from finite Minkowski spacetime correlation functions

TL;DR

This paper advances methods to extract scattering amplitudes from finite Minkowski spacetime correlation functions, demonstrating improved accuracy and broader applicability of the estimator, and providing error estimates for real-time computational approaches.

Contribution

It extends previous conjectures on estimators for scattering amplitudes from finite-volume correlators to larger kinematic regions and introduces a new error estimation method for finite-time effects.

Findings

Estimator works for broader kinematic regions

Spacetime volume requirements for 10% accuracy identified

Error estimation method for finite-time effects developed

Abstract

The need to determine scattering amplitudes of few-hadron systems for arbitrary kinematics expands a broad set of subfields of modern-day nuclear and hadronic physics. In this work, we expand upon previous explorations on the use of real-time methods, like quantum computing or tensor networks, to determine few-body scattering amplitudes. Such calculations must be performed in a finite Minkowski spacetime, where scattering amplitudes are not well defined. Our previous work presented a conjecture of a systematically improvable estimator for scattering amplitudes constructed from finite-volume correlation functions. Here we provide further evidence that the prescription works for larger kinematic regions than previously explored as well as a broader class of scattering amplitudes. Finally, we devise a new method for estimating the order of magnitude of the error associated with finite time separations needed for such calculations. In units of the lightest mass of the theory, we find that to constrain amplitudes using real-time methods within $\mathcal{O}(10\%)$, the spacetime volumes must satisfy $mL \sim \mathcal{O}(10-10^2)$ and $ mT\sim \mathcal{O}(10^2-10^4)$.