On the axial-vector form factor of the nucleon and chiral symmetry

Abstract

We consider the chiral Lagrangian with nucleon, isobar, and pion degrees of freedom. The baryon masses and the axial-vector form factor of the nucleon are derived at the one-loop level. We explore the impact of using on-shell baryon masses in the loop expressions. As compared to results from conventional chiral perturbation theory we find significant differences. An application to QCD lattice data is presented. We perform a global fit to the available lattice data sets for the baryon masses and the nucleon axial-vector form factor, and determine the low-energy constants relevant at $$\hbox {N}^3$$ N 3 LO for the baryon masses and at $$\hbox {N}^2$$ N 2 LO for the form factor. Partial finite-volume effects are considered. We point out that the use of on-shell masses in the loops results in non-analytic behavior of the baryon masses and the form factor as function of the pion mass, which becomes prominent for larger lattice volumes than presently used.

The chiral Lagrangian with three flavors and large-Nc sum rules

“…A novel framework for the latter was recently developed in Refs. [15,44], where particular emphasis was put on the importance to use on-shell masses for mesons and baryons in loop contributions from the chiral Lagrangian.…”

“…While in principle this can and should be done, a complete study of these contributions is outside the scope of our current study. Only recently, a promising novel framework, in which such computations can be performed is available [15,44]. The key element is the request to consider loop contributions with on-shell meson and baryon masses.…”

Light-quark mass dependence of the nucleon axial charge and pion-nucleon scattering phenomenology

“…The impact of setting the baryon masses in the loops to the values obtained by the LQCD simulations may be also worth exploring in view of the results of Ref. [35] although this would correspond to the resummation of baryon selfenergy insertions of higher order. For this purpose it would be relevant to have more information about the ∆ pole position for the different lattice ensembles.…”

“…Indeed, in a combined fit to both elastic and inelastic πN scattering data d 16 has been recently extracted, albeit with a large uncertainty [26]. Baryon ChPT (BChPT) has been used to calculate the axial charge within the heavy-baryon [27][28][29][30][31] and relativistic [22,23,30,[32][33][34][35] ChPT approaches both without and with the ∆(1232) as an explicit degree of freedom. In the relativistic framework, both infrared and extended-on-mass-shell (EOMS) regularization methods have been applied.…”

“…In the relativistic framework, both infrared and extended-on-mass-shell (EOMS) regularization methods have been applied. Some of these studies also address the nucleon axial form factor at low four-momentum transfers squared [32][33][34][35]. The M π dependence of g A has been specifically investigated in Refs.…”