Pion momentum distributions in the nucleon in chiral effective theory

Abstract

We compute the light-cone momentum distributions of pions in the nucleon in chiral effective theory using both pseudovector and pseudoscalar pion-nucleon couplings. For the pseudovector coupling we identify $\ensuremath{\delta}$-function contributions associated with end-point singularities arising from the pion-nucleon rainbow diagrams, as well as from pion bubble and tadpole diagrams which are not present in the pseudoscalar model. Gauge invariance is demonstrated, to all orders in the pion mass, with the inclusion of Kroll-Ruderman couplings involving operator insertions at the $\ensuremath{\pi}NN$ vertex. The results pave the way for phenomenological applications of pion cloud models that are manifestly consistent with the chiral symmetry properties of QCD.