Mesonic fluctuations in a nonlocal Nambu-Jona-Lasinio model

Abstract

The effects of meson fluctuations are studied in a nonlocal generalization of the Nambu-Jona-Lasinio model, by including terms of next-to-leading order (NLO) in 1/N_c. In the model with only scalar and pseudoscalar interactions NLO contributions to the quark condensate are found to be very small. This is a result of cancellation between virtual mesons and Fock terms, which occurs for the parameter sets of most interest. In the quark self-energy, similar cancellations arise in the tadpole diagrams, although not in other NLO pieces which contribute at the \sim 25% level. The effects on pion properties are also found to be small. NLO contributions from real $\pi\pi$ intermediate states increase the sigma meson mass by $\sim 30%$. In an extended model with vector and axial interactions, there are indications that NLO effects could be larger.