Finite volume effects for the pion mass at two loops

Abstract

We evaluate the pion mass in finite volume to two loops within Chiral Perturbation Theory. The results are compared with a recently proposed extension of the asymptotic formula of Luscher. We find that contributions, which were neglected in the latter, are numerically very small at the two-loop level and conclude that for Mpi*L>2, L>2fm the finite volume effects in the meson sector are analytically well under control.

26 pages, 6 figures

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• Thermodynamic Properties of Strongly Interacting Matter in a Finite Volume using the Polyakov-Nambu-Jona-Lasinio model
• Electromagnetic form factor of the pion from twisted-mass lattice QCD at Nf=2
• The Low Energy Constants of $SU(2)$ Partially Quenched Chiral Perturbation Theory from $N_f=2+1$ Domain Wall QCD
• High Statistics Analysis using Anisotropic Clover Lattices: (IV) Volume Dependence of Light Hadron Masses
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• Uncertainty Quantification in Lattice QCD Calculations for Nuclear Physics
• Chiral perturbation theory in a theta vacuum
• Chiral logs in twisted mass lattice QCD with large isospin breaking
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• Twisted Mass Finite Volume Effects
• External Momentum, Volume Effects, and the Nucleon Magnetic Moment
• Finite Volume Dependence of the Quark-Antiquark Vacuum Expectation Value
• Two-loop Sunset Integrals at Finite Volume
• The expansion by regions in pi K scattering
• The epsilon expansion at next-to-next-to-leading order with small imaginary chemical potential
• Modeling pion physics in the $\epsilon$-regime of two-flavor QCD using strong coupling lattice QED
• Setting the scale for nHYP fermions with the Lüscher-Weisz gauge action
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• 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
• Pion mass dependence of the $K_{l3}$ semileptonic scalar form factor within finite volume
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• Role of the $\sigma$-resonance in determining the convergence of chiral perturbation theory
• Sunset integrals at finite volume