Parton distributions from nonlocal chiral SU(3) effective theory. I. Splitting functions

TL;DR

This paper develops a nonlocal covariant chiral effective theory to compute proton splitting functions, incorporating meson loop corrections and gauge invariance, providing detailed insights into parton distributions with both local and nonlocal effects.

Contribution

It introduces a novel nonlocal formulation for meson loop corrections to nucleon parton distributions, including gauge links and off-shell effects, advancing the theoretical modeling of parton structure.

Findings

Computed full set of proton splitting functions including on-shell and off-shell contributions.

Demonstrated the impact of nonlocal effects and finite size on splitting function shapes.

Provided numerical examples using a dipole regulator to illustrate the functions.

Abstract

We present a new formulation of pseudoscalar meson loop corrections to nucleon parton distributions within a nonlocal covariant chiral effective field theory, including contributions from SU(3) octet and decuplet baryons. The nonlocal Lagrangian, constrained by requirements of local gauge invariance and Lorentz-invariant ultraviolet regularization, generates additional interactions associated with gauge links. We use these to compute the full set of proton $\to$ meson + baryon splitting functions, which in general contain on-shell and off-shell contributions, in addition to $\delta$-function terms at zero momentum, along with nonlocal contributions associated with the finite size of the proton. We illustrate the shapes of the various local and nonlocal functions numerically using a simple example of a dipole regulator.