Two-loop Sunset Integrals at Finite Volume

Abstract

We show how to compute the two-loop sunset integrals at finite volume, for non-degenerate masses and non-zero momentum. We present results for all integrals that appear in the Chiral Perturbation Therory ($\chi$PT) calculation of the pseudoscalar meson masses and decay constants at NNLO, including the case of Partially Quenched $\chi$PT. We also provide numerical implementations of the finite-volume sunset integrals, and review the results for one-loop integrals at finite volume.

45 pages

References in corpus (5)

• BOKASUN: a fast and precise numerical program to calculate the Master Integrals of the two-loop sunrise diagrams
• Finite volume effects for the pion mass at two loops
• Three-Flavor Partially Quenched Chiral Perturbation Theory at NNLO for Meson Masses and Decay Constants
• Two-loop Sunset Integrals at Finite Volume
• Applications of Chiral Perturbation theory to lattice QCD

Cited by in corpus (17)

• FLAG Review 2019
• Finite-volume effects due to spatially non-local operators
• Vector two-point functions in finite volume using partially quenched chiral perturbation theory
• Finite Volume at Two-loops in Chiral Perturbation Theory
• Two-loop Sunset Integrals at Finite Volume
• Geometrically confined thermal field theory: Finite size corrections and phase transitions
• CHIRON: a package for ChPT numerical results at two loops
• Masses, Decay Constants and Electromagnetic Form-factors with Twisted Boundary Conditions
• Massless sunset diagrams in finite asymmetric volumes
• Finite volume corrections to forward Compton scattering off the nucleon
• Finite Volume for Three-Flavour Partially Quenched Chiral Perturbation Theory through NNLO in the Meson Sector
• A unified formulation of one-loop tensor integrals for finite volume effects
• Critical Probability Distributions of the order parameter at two loops I: Ising universality class
• Status of Chiral Meson Physics
• Critical Probability Distributions of the order parameter at two loops II: $O(n)$ universality class
• Pion scattering in finite volume within the Inverse Amplitude Method
• Chiral Perturbation Theory at Finite Volume and/or with Twisted Boundary Conditions