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

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.