Higher-orderεterms in Reggeon field theory

Abstract

We calculate the $O\left({\epsilon }^2\right)$ terms of the Wilson expansion of the critical exponents in the Reggeon field theory with a bare linear trajectory and a triple-Regge interaction. We find that the $O\left({\epsilon }^2\right)$ and $O\left(\epsilon \right)$ terms are comparable at $\epsilon =2\mathrm{}$, and we obtain ${\sigma }_{\mathrm{tot}}{\mathrm{}\left(S\right)\mathrm{}}_{S\to \infty }\sim {\left(\ln s\right)}^{0.38}$. We also show that the Gell-Mann-Low function $\beta \mathrm{}\left(g\right)\mathrm{}$ expanded to finite order in both $\epsilon$ and $g$ carries no information about the existence of the Gell-Mann-Low zero at finite $\epsilon$.