The $$(q\bar q) - pion$$ and its decay constant in a chiral potential modeland its decay constant in a chiral potential model

Abstract

Pion mass and its decay constant have been studied in a chiral symmetric potential model of independent quarks. The non-perturbative multi-gluon interaction which is responsible for quark confinement in a hadron is phenomenologically represented here by an effective potentialU(r) = 1/2(1 +γ 0)(ar 2 +V 0). The residual interactions due to quark-pion coupling arising out of the chiral symmetry preservation and that due to quark-gluon coupling arising out of single-gluon exchange are treated as low order perturbations. The centre of mass correction is also taken into account appropriately. This leads to the $$(q\bar q) - pion$$ mass in consistency with that of the PCAC-pion and the pion decay constant in reasonable agreement with experiment.