Chiral perturbation theory and the first moments of the generalized parton distributions in a nucleon

Abstract

We discuss the first moments of the parity-even Generalized Parton Distributions (GPDs) in a nucleon, corresponding to six (generalized) vector form factors. We evaluate these fundamental properties of baryon structure at low energies, utilizing the methods of covariant Chiral Perturbation Theory in the baryon sector (BChPT). Our analysis is performed at leading-one-loop order in BChPT, predicting both the momentum and the quark-mass dependence for the three (generalized) isovector and (generalized) isoscalar form factors, which are currently under investigation in lattice QCD analyses of baryon structure. We also study the limit of vanishing four-momentum transfer where the GPD-moments reduce to the well known moments of Parton Distribution Functions (PDFs). For the isovector moment x u−d our BChPT calculation predicts a new mechanism for chiral curvature, connecting the high values for this moment typically found in lattice QCD studies for large quark masses with the smaller value known from phenomenology. Likewise, we analyze the quark-mass dependence of the isoscalar moments in the forward limit and extract the contribution of quarks to the total spin of the nucleon. We close with a first glance at the momentum dependence of the isoscalar C-form factor of the nucleon.

Moments of generalized parton distributions and quark angular momentum of the nucleon

“…We perform 2-parameter fits with a s 20 , c 9 for the isoscalar and a v 20 , c 8 for the isovector channel at a scale of λ = 1GeV and fixed the other values following ref. [9]. A strong m π dependence is observed especially for the isovector channel, but the extrapolated values in both channels overshoot beyond the phenomenological values estimated using the CTEQ6 parton distribution functions.…”

“…However, the empirical dipole fit for the generalized form factors has no solid justification from a theoretical point of view. Therefore we count on the covariant baryon chiral perturbation [9] to extract the forward values of B 20 as well as the chiral extrapolation of A 20 and B 20 .…”

Nucleon and pion distribution functions in the valence region

“…04 Q " -Quenched-QCD study described in (Göckeler et al, 2005), with renormalization scale, Q 0 , fixed via nonperturbative renormalization and linear chiral extrapolation (error is statistical combined with estimates of systematic errors arising from renormalization, operator choice, and continuum and chiral extrapolations); "Lat. 08" -Analysis reported in (Hägler et al, 2008), with renormalization scale, Q 0 , fixed via nonperturbatively-improved one-loop renormalization and extrapolation via covariant baryon chiral perturbation theory (Dorati et al, 2008) portant, and were attentive in estimating systematic errors arising from from nonperturbative renormalization, operator choice, and continuum and linear chiral extrapolations.…”

“…It was argued that finitevolume errors are negligible with respect to statistical errors, whilst errors associated with nonzero lattice spacing (a = 0.124 fm) were not discussed. In order to quote a result at the physical pion mass, covariant baryon chiral perturbation theory was employed (Dorati et al, 2008). As anticipated in (Detmold et al, 2001), an extrapolation nonlinear in m 2 π can have an enormous impact: in this instance, a 25% reduction in the value of the moment.…”

Spin structure of the nucleon (theory)

“…This work was done in collaboration with M. Dorati from Pavia and T. Hemmert from Munich, and was later published by the Munich group in Ref. [10]. In that paper, the first moments of the parity-even Generalized Parton Distributions (GPDs) in a nucleon, corresponding to six (generalized) vector form factors, were calculated.…”