Study of Dynamical Chiral Symmetry Breaking in (2+1) Dimensional Abelian Higgs Model

In this paper, we study the dynamical mass generation in the Abelian Higgs model in 2 + 1 dimensions. Instead of adopting the approximations in [Jiang H et al., J. Phys. A 41 2008 255402.], we numerically solve the coupled Dyson-Schwinger Equations (DSEs) for the fermion and gauge boson propagators using a specific truncation for the fermion-photon vertex ansatz and compare our results with the corresponding ones in the above mentioned paper. It is found that the results quoted in the above paper remain qualitatively unaffected by refining the truncation scheme of the DSEs, although there exist large quantitative differences between the results presented in the above paper and ours. In addition, our numerical results show that the critical number of fermion flavor N-c decreases steeply with the the gauge boson mass m(a) (or the ratio of the Higgs mass m(h) to the gauge boson mass m(a), r = m(h)/m(a)) increasing. It is thus easier to generate a finite fermion mass by the mechanism of DCSB for a small ratio r for a given m(a).