Isovector axial form factors of the nucleon in two-flavor lattice QCD

Abstract

We present a lattice calculation of the nucleon isovector axial and induced pseudoscalar form factors on the CLS ensembles using [Formula: see text] dynamical flavors of nonperturbatively [Formula: see text]-improved Wilson fermions and an [Formula: see text]-improved axial current together with the pseudoscalar density. Excited-state effects in the extraction of the form factors are treated using a variety of methods, with a detailed discussion of their respective merits. The chiral and continuum extrapolation of the results is performed both using formulae inspired by Heavy Baryon Chiral Perturbation Theory (HBChPT) and a global approach to the form factors based on a chiral effective field theory (EFT) including axial vector mesons. Our results indicate that careful treatment of excited-state effects is important in order to obtain reliable results for the axial form factors of the nucleon, and that the main remaining error stems from the systematic uncertainties of the chiral extrapolation. As final results, we quote [Formula: see text], [Formula: see text], and [Formula: see text] for the axial charge, axial charge radius and induced pseudoscalar charge, respectively, where the first error is statistical and the second is systematic.

Nucleon isovector charges and twist-2 matrix elements with Nf=2+1 dynamical Wilson quarks

“…Finally, we remark that from a theoretical point of view these simultaneous fits also supersede earlier attempts using a fixed gap as used in Ref. [9] with statistically much less precise data.…”

“…(27) represents our final fit model, which has already been applied in a previous analysis of lattice data with N f = 2 dynamical quark flavors in Ref. [9]. In principle, it is possible to fit the model in Eq.…”

“…Still, from a theoretical point of view it is desirable to apply such fits without additional assumptions, in contrast to Ref. [9], where the gap was fixed to ∆ 0 = 2M π on each ensemble. Therefore, we choose a more sophisticated approach, fitting the model in Eq.…”

“…g u−d A = 1.2724 (23) [1], as it can be measured from the β-decay of a neutron into a proton, hence providing a crucial test for lattice QCD. This has led to considerable interest in computing the axial charge on the lattice [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Recently, g u−d A has been included in the FLAG review (Ref.…”

Lattice QCD Inputs for nuclear double beta decay

“…The potentials V (a,b) 6,7 require the hadronic and nuclear realization of isovector quark bilinears of the formūΓd (Γ ∈ {1, γ 5 , γ µ , γ µ γ 5 , σ µν }), which also appear in the analysis of single beta decay of nuclei in the SM and beyond. The LQCD input needed here is the single-nucleon charges [93][94][95][96][97] as well as LECs associated with two-body currents [98][99][100]. In Sections 2.1.2 and 2.1.3, only V are discussed in detail, since at the leading order (LO), these potentials involve genuinely non-factorizable contributions with new LECs that cannot be extracted from data and whose first-principles determination requires input from LQCD.…”