An asymptotic formula for the pion decay constant in a large volume

Abstract

We derive an asymptotic formula a la Luscher for the finite volume correction to the pion decay constant: this is expressed as an integral over the < 3 π| A_μ|0 > amplitude after proper subtraction of the pion pole contribution. We analyze the formula numerically at leading and next-to-leading order in the chiral expansion.

arXiv comment10 pages, 2 figures, v2: two references and a comment on the corresponding lattice results added

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• Twist-two matrix elements at finite and infinite volume
• Volume Dependence of the Pion Mass in the Quark-Meson-Model
• Finite-volume effects due to spatially non-local operators
• Influence of quark boundary conditions on the pion mass in finite volume
• Finite-Size Effects in Lattice QCD with Dynamical Wilson Fermions
• $F_K/F_{\pi }$ from Möbius domain-wall fermions solved on gradient-flowed HISQ ensembles
• Modeling Finite-Volume Effects and Chiral Symmetry Breaking in Two-Flavor QCD Thermodynamics
• Finite volume effects for nucleon and heavy meson masses
• Finite volume effects for the pion mass at two loops
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• Topological susceptibility on the lattice and the three-flavour quark condensate
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• Twisted Mass Finite Volume Effects
• Finite Volume at Two-loops in Chiral Perturbation Theory
• Extrapolation Formulas for Neutron EDM Calculations in Lattice QCD
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• Finite Volume Dependence of the Quark-Antiquark Vacuum Expectation Value
• Finite volume effects in chiral perturbation theory
• Volume dependences from lattice chiral perturbation theory
• Goldstone Boson Scattering with a Light Composite Scalar
• Modeling pion physics in the $\epsilon$-regime of two-flavor QCD using strong coupling lattice QED
• Finite-size scaling for the left-current correlator with non-degenerate quark masses
• Probing the chiral weak Hamiltonian at finite volumes
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• Pseudoscalar mesons in a finite cubic volume with twisted boundary conditions
• Hadron Spectrum from Dynamical Lattice QCD Simulations
• Pion mass dependence of the $K_{l3}$ semileptonic scalar form factor within finite volume
• A unified formulation of one-loop tensor integrals for finite volume effects
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• The pion mass in finite volume to two loops
• Finite volume effects using lattice chiral perturbation theory
• Phenomenology of static-light mesons from unquenched lattice QCD calculations