Light-flavor sea-quark distributions in the nucleon in the SU(3) chiral quark soliton model. II. Theoretical formalism

The path integral formulation is given to obtain quark and antiquark distribution functions in the nucleon within the flavor SU(3) version of the chiral quark soliton model. The basic model action is a straightforward generalization of the corresponding SU(2) one, except for one distinguishable feature, i.e., the presence of the SU(3) symmetry breaking term arising from the sizably large mass difference $\Delta m_s$ between the strange and nonstrange quarks. We treat this SU(3) symmetry breaking effect by relying upon the first-order perturbation theory in the mass parameter $\Delta m_s.$ We also address the problem of the ordering ambiguity of the relevant collective space operators, which arises in the evaluation of the parton distribution functions at the subleading order of the ${1/N}_c$ expansion.