The sigma term and the quark number operator in QCD

Abstract

We discuss the relationship of the forward matrix element of the operator $\bar\psi\psi$, related to the so-called sigma term, to the quark number. We show that in the naive quark model in the canonical formalism these quantities coincide in the limit of small average quark momenta. In the QCD parton model defined through light-front quantization this result is preserved at leading perturbative order but it receives radiative corrections. We analyze the theoretical and phenomenological consequences of this result, which provides a bridge between a current algebra quantity, the sigma term, and a deep-inelastic quantity, the parton number.