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

by J. F. Du Plessis, W. A. Horowitz

Submission summary

Authors (as registered SciPost users): Jean Du Plessis
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-07-04
Date submitted: 2022-10-03 09:30
Submitted by: Du Plessis, Jean
Submitted to: SciPost Physics Proceedings
Proceedings issue: 51st International Symposium on Multiparticle Dynamics (ISMD2022)
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


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.

Current status:
Accepted in target Journal

Editorial decision: For Journal SciPost Physics Proceedings: Publish
(status: Editorial decision fixed and (if required) accepted by authors)

Submission & Refereeing History

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Submission 2209.15309v1 on 3 October 2022

Reports on this Submission

Anonymous Report 1 on 2023-1-7 (Invited Report)


This report is a representative summary of the poster the author presented at ISMD 2022, and hence the publication criteria have been met. I found it to be a clear discussion of an interesting result which has possible future applications.

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