The ${\hat{I}}^2$-function for Yukawa theory at large $N_f$

Abstract

We compute the ${\hat{I}}^2$-function for a massless Yukawa theory in a closed form at the order $\mathcal{O}(1/N_f)$ in the spirit of the expansion in a large number of flavours $N_f$. We find an analytic expression with a finite radius of convergence, and the first singularity occurs at the coupling value $K=5$.

15 pages, 2 figures. v3 error in the computation of the n-loop scalar self-energy corrected. The first singularity occurs at $K=5$, qualitatively the analysis is unchanged