Analytic structure of scalar composites in the symmetric phase of the gauged Nambu-Jona-Lasinio model

The gauged Nambu-Jona-Lasinio model in the quenched-ladder approximation has non-trivial dynamics near a critical scaling region (critical curve) separating a chiral symmetric and a dynamically chiral symmetry broken phase. Scalar and pseudoscalar composites corresponding to the four-fermion interaction become relevant degrees of freedom at short distances, which is reflected in the appearance of a large anomalous dimension of the four-fermion operators. A method is introduced for solving the Schwinger-Dyson equation for the Yukawa vertex in specific kinematic regimes. This allows one to derive an analytic expression for the scalar propagator, which is valid along the entire critical curve. The mass and width of the scalar composites in the critical scaling region are reexamined and the conformal phase transition at the critical gauge coupling is discussed.