Chiral symmetry breaking in the colour dielectric model

Abstract

Approximating the long-distance gluon dynamics ofSU(3)colour by colour-dielectric block-spin variables, we obtain an effective QCD theory of a scalar colour-dielectric field and a massive colour-bleached gluon field coupled to light quarks. The massive vector field produces a strong attraction betweenq\(\bar q\) pairs, which leads toq\(\bar q\) condensation when the colour-dielectric field becomes small. We calculate\(\left\langle {\bar \psi \psi } \right\rangle\) and the pion decay constantf n as a function of the dielectric field expectation value, by evaluating the fermion determinant in a derivative expansion, and integrating out the bosonic variables. We find that the effective quark-gluon coupling,α s eff , including quark effects, is large on the surface of bags, where\(\left\langle {\bar \psi \psi } \right\rangle\) ±0, but decreases inside hadronic bags, where |\(\left\langle {\bar \psi \psi } \right\rangle\)| is decreasing.