Renormalization of quark axial current in the chiral potential model

Abstract

Non-conserved composite operators like the quark axial current have divergent matrix elements therefore must be renormalized. We explore how this can be done in quark model calculations where the systematic procedure of dimensional regularization and minimal subtraction is not applicable. We propose a most natural and convenient regularization scheme of cutting the intermediate quark states over which we sum in loop diagram calculations at a certain energy. We show that this scheme works perfectly for the quark axial current and we obtain the quark spin contribution to the proton spin: $Δ_u=0.82$, $Δ_d=-0.43$, $Δ_s=-0.10$, which is in excellent agreement with experiments.