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Previously an equation of state for the relativistic hydrodynamicsencountered in heavy-ion collisions at the LHC and RHIC has been calculatedusing lattice gauge theory methods. This leads to a prediction of very lowviscosity, due to the calculated trace anomaly. Finite system corrections tothis trace anomaly could challenge this calculation, since the latticecalculation was done in an effectively infinite system. In order to verify thistrace anomaly it is sensible to add phenomenologically relevant finite systemcorrections. We investigate massive $\phi^4$ theory with periodic boundaryconditions on $n$ of the 3 spatial dimensions. $2\to2$ NLO scattering is thencomputed. Using a newly derived formula for an arbitrary dimensional sum ofsinc functions, we show that the NLO finite size corrections preserveunitarity.

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