Study the Curci–Ferrari model with matter fields

Investigate the Curci–Ferrari model of massive Yang–Mills fields when matter (e.g., quark) fields are included, determining how the presence of matter affects the model’s dynamics and symmetry structure within the spontaneously broken BRST and anti‑BRST effective framework.

Background

The paper derives the Curci–Ferrari model as the elementary-field sector of a BRST- and anti‑BRST‑invariant effective Lagrangian after spontaneous symmetry breaking, where effective gluon and ghost masses arise from nonzero vacuum expectation values of composite Fujikawa fields.

Throughout the work, the quark (matter) sector is omitted for simplicity. The authors explicitly note that incorporating matter fields is a remaining task, indicating an open avenue to explore how quark dynamics integrate into the Curci–Ferrari framework obtained from spontaneous BRST breaking.