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  • Open Access

Finite-volume formalism for physical processes with an electroweak loop integral

Xin-Yu Tuo1,2,* and Xu Feng1,3,4,†

  • *Contact author: xtuo@bnl.gov
  • †Contact author: xu.feng@pku.edu.cn
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Phys. Rev. D 112, 034512 – Published 28 August, 2025

DOI: https://doi.org/10.1103/4mn6-w366

Abstract

This study investigates finite-volume effects in physical processes that involve the combination of long-range hadronic matrix elements with electroweak loop integrals. We adopt the approach of implementing the electroweak part as the infinite-volume version, which is denoted as the EW∞ method in this work. A general approach is established for correcting finite-volume effects in cases where the hadronic intermediate states are dominated by either a single particle or two particles. For the single-particle case, this work derives the infinite volume reconstruction method from a new perspective. For the two-particle case, we provide the correction formulas for power-law finite-volume effects and unphysical terms with exponentially divergent time dependence. The finite-volume formalism developed in this study has broad applications, including the QED corrections in various processes and the two-photon exchange contribution in KL→μ+μ− or η→μ+μ− decays.

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Phys. Rev. D 112, 034512– Published 28 August, 2025
  • Received 8 August 2024
  • Accepted 5 August 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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