Chiral Lagrangian with confinement from the QCD Lagrangian

Abstract

An effective Lagrangian for the light quark in the field of a static source is derived systematically using the exact field correlator expansion. The lowest Gaussian term is bosonized using nonlocal colorless bosonic fields and a general structure of effective chiral Lagrangian is obtained containing all set of fields. The new and crucial result is that the condensation of scalar isoscalar field which is a usual onset of chiral symmetry breaking and is constant in space-time, assumes here the form of the confining string and contributes to the confining potential, while the rest bosonic fields describe mesons with the q\bar q quark structure and pseudoscalars play the role of Nambu-Goldstone fields. Using derivative expansion the effective chiral Lagrangian is deduced containing both confinement and chiral effects for heavy-light mesons. The pseudovector quark coupling constant is computed to be exactly unity in the local limit,in agreement with earlier large N_c arguments.