Meson masses in large Nf QCD from the Bethe-Salpeter equation -: art. no. 076001

We solve the homogeneous Bethe-Salpeter (HBS) equation for the scalar, pseudoscalar, vector, and axial-vector bound states of quarks and antiquarks in large N-f QCD with the improved ladder approximation in the Landau gauge. The quark mass function in the HBS equation is obtained from the Schwinger-Dyson (SD) equation in the same approximation for consistency with the chiral symmetry. Amazingly, because of the fact that the two-loop running coupling of large N-f QCD is explicitly written in terms of an analytic function, large N-f QCD turns out to be the first example in which the SD equation can be solved in the complex plane and hence the HBS equation directly in the time-like region. We find that approaching the chiral phase transition point from the broken phase, the scalar, vector, and axial-vector meson masses vanish to zero with the same scaling behavior, all degenerate with the massless pseudoscalar meson. This may suggest a new type of manifestation of the chiral symmetry restoration in large N-f QCD.