Renormalization Group Study of Chern-Simons Field Coupled to Scalar Matter in a Modified BPHZ Subtraction Scheme

We apply a soft version of the BPHZ subtraction scheme to the computation of two-loop corrections from an Abelian Chern-Simons field coupled to (massive) scalar matter with a $\lambda ({\mathrm{\Phi }}^{\mathrm{†}}\mathrm{\Phi }{)}^2$ and $\nu ({\mathrm{\Phi }}^{\mathrm{†}}\mathrm{\Phi }{)}^3$ self-interactions. The two-loop renormalization group functions are calculated. We compare our results with those in the literature.