Spatially nonlocal matrix elements are useful lattice-QCD observables in a variety of contexts, for example in determining hadron structure. To quote credible estimates of the systematic uncertainties in these calculations, one must understand, among other things, the size of the finite-volume effects when such matrix elements are extracted from numerical lattice calculations. In this work, we estimate finite-volume effects for matrix elements of nonlocal operators, composed of two currents displaced in a spatial direction by a distance ξ. We find that the finite-volume corrections depend on the details of the matrix element. If the external state is the lightest degree of freedom in the theory, e.g. the pion in QCD, then the volume corrections scale as e −mπ (L−ξ) , where mπ is the mass of the light state. For heavier external states the usual e −mπ L form is recovered, but with a polynomial prefactor of the form L m /|L − ξ| n that can lead to enhanced volume effects. These observations are potentially relevant to a wide variety of observables being studied using lattice QCD, including parton distribution functions, double-beta-decay and Compton-scattering matrix elements, and long-range weak matrix elements.

The spin-dependent cross sections for semi-inclusive lepton-nucleon scattering are derived in the framework of collinear factorization, including the effects of masses of the target and produced hadron at finite momentum transfer squared Q 2 . At leading order the cross sections factorize into products of parton distribution and fragmentation functions evaluated in terms of new, mass-dependent scaling variables. The size of the hadron mass corrections is estimated at kinematics relevant for future semi-inclusive deepinelastic scattering experiments.

This paper focuses on hadron mass effects in calculations of semi-inclusive kaon production in leptonDeuteron deeply inelastic scattering at HERMES and COMPASS kinematics. In the collinear factorization framework, the corresponding cross section is shown to factorize, at leading order and leading twist, into products of parton distributions and fragmentation functions evaluated in terms of kaon-and nucleon-mass-dependent scaling variables, and to respect gauge invariance. It is found that hadron mass corrections for integrated kaon multiplicities sizeably reduce the apparent large discrepancy between measurements of K þ þ K − multiplicities performed by the two collaborations, and fully reconcile their K þ =K − ratios.