The axial-vector form factor of the nucleon in a finite box

Abstract

We consider the axial-vector form factor of the nucleon in a finite box. Starting from the chiral Lagrangian with nucleon and Delta-isobar degrees of freedom, we address, at the one-loop level, the impact of two types of finite-volume effects. On the one hand, there are the implicit effects from the in-box values of the nucleon and Delta-isobar masses. On the other hand, there are the explicit effects caused by computing the in-box loop integrals with the values of the nucleon and Delta-isobar masses obtained in the infinite-volume limit. Selected numerical results are shown for three lattice ensembles. We show that the implicit effects dominate the in-box form factor. Our results are presented in terms of a set of basis functions that generalize the Passarino-Veltman reduction scheme to the finite-box case, such that only scalar loop integrals have to be performed. The techniques we developed are more generally relevant for lattice studies of hadronic quantities.

arXiv comment36 pages, 2 figures and 2 tables, revised version in print

References in corpus (41)

• Relativistic chiral SU(3) symmetry, large N_c sum rules and meson-baryon scattering
• Renormalization of relativistic baryon chiral perturbation theory and power counting
• The form factors of the nucleon at small momentum transfer
• Isovector Charges of the Nucleon from 2+1+1-flavor Lattice QCD
• Pion--Nucleon Scattering in a New Approach to Chiral Perturbation Theory
• Nucleon isovector couplings from $N_f=2$ lattice QCD
• Nucleon axial form factors using lattice QCD simulations with a physical value of the pion mass
• Analyses of pion-nucleon elastic scattering amplitudes up to $O(p^4)$ in extended-on-mass-shell subtraction scheme
• Axial Nucleon form factors from lattice QCD
• Light baryon masses with dynamical twisted mass fermions
• Axial, induced pseudoscalar, and pion-nucleon form factors in manifestly Lorentz-invariant chiral perturbation theory
• Axial coupling constant of the nucleon for two flavours of dynamical quarks in finite and infinite volume
• Quark mass dependence of the nucleon axial-vector coupling constant
• Baryon Axial Charge in a Finite Volume
• Threshold Pion Electroproduction in Chiral Perturbation Theory
• Iso-vector axial form factors of the nucleon in two-flavour lattice QCD
• Nucleon isovector charges and twist-2 matrix elements with $N_f=2+1$ dynamical Wilson quarks
• Muon capture by a proton in heavy baryon chiral perturbation theory
• Nucleon electromagnetic form factors in two-flavour QCD
• Dynamical coupled-channel approaches on a momentum lattice
• On finite volume effects in the chiral extrapolation of baryon masses
• Solving the PCAC puzzle for nucleon axial and pseudoscalar form factors
• Baryon self energies in the chiral loop expansion
• The nucleon and Delta(1232) form factors at low momentum-transfer and small pion masses
• Chiral extrapolation of g_A with explicit Delta(1232) degrees of freedom
• Extraction of nucleon axial charge and radius from lattice QCD results using baryon chiral perturbation theory
• On the convergence of the chiral expansion for the baryon ground-state masses
• Nucleon Form Factors of the Isovector Axial-Vector Current: Situation of Experiments and Theory
• Octet baryon isovector charges from $N_f=2+1$ lattice QCD
• Pion electroproduction, PCAC, chiral Ward identities, and the axial form factor revisited
• Split Dimensional Regularization for the Coulomb Gauge
• Ordinary muon capture on a proton in manifestly Lorentz invariant baryon chiral perturbation theory
• On the axial-vector form factor of the nucleon and chiral symmetry
• Leading order mesonic and baryonic SU(3) low energy constants from $N_f=3$ lattice QCD
• Axial-vector form factors of the baryon octet and chiral symmetry
• Finite volume corrections to the electromagnetic current of the nucleon
• Light-quark mass dependence of the nucleon axial charge and pion-nucleon scattering phenomenology
• Low-energy constants in the chiral Lagrangian with baryon octet and decuplet fields from Lattice QCD data on CLS ensembles
• Finite volume corrections to forward Compton scattering off the nucleon
• The chiral Lagrangian with three flavors and large-Nc sum rules
• A unified formulation of one-loop tensor integrals for finite volume effects