NLO finite system size corrections to $2\to2$ scattering in $\phi^4$ theory using newly derived sum of sinc functions

TL;DR

This paper calculates finite system size corrections to $2\to2$ scattering in massive $\phi^4$ theory at NLO, using a new sum of sinc functions formula, and shows these corrections preserve unitarity, relevant for lattice gauge theory predictions.

Contribution

It introduces a novel formula for sums of sinc functions in arbitrary dimensions and applies it to compute finite size corrections in $\phi^4$ theory at NLO, ensuring unitarity is maintained.

Findings

Finite size corrections are computed at NLO for $\phi^4$ theory.

The new sinc sum formula is validated in the context of finite volume corrections.

Unitarity is preserved in the finite size corrected scattering amplitudes.

Abstract

Previously an equation of state for the relativistic hydrodynamics encountered in heavy-ion collisions at the LHC and RHIC has been calculated using lattice gauge theory methods. This leads to a prediction of very low viscosity, due to the calculated trace anomaly. Finite system corrections to this trace anomaly could challenge this calculation, since the lattice calculation was done in an effectively infinite system. In order to verify this trace anomaly it is sensible to add phenomenologically relevant finite system corrections. We investigate massive $\phi^4$ theory with periodic boundary conditions on $n$ of the 3 spatial dimensions. $2\to2$ NLO scattering is then computed. Using a newly derived formula for an arbitrary dimensional sum of sinc functions, we show that the NLO finite size corrections preserve unitarity.