%% Gives back one-loop beta-functions and anomalous dimensions, %% given combinatorial factors S, a1. function [betags,gamma_phi,gamma_phi2]=betas_gammas_oneloop(d,gs,S,a1) %% Common factors I2=0; for X1=1:2 for X2=1:2 I2=I2+S(X1,X2)*gs(X1)*gs(X2); end end I3=zeros(2,1); for X=1:2 for X1=1:2 for X2=1:2 for X3=1:2 I3(X)=I3(X)+a1(X,X1,X2,X3)*gs(X1)*gs(X2)*gs(X3); end end end end %% Anomalous dimensions and beta functions % gamma_phi gamma_phi=(1/6)*I2; % gamma_phi2 gamma_phi2=I2; % Beta functions eta=gamma_phi; betags=-I3; betags=betags+((-6+d+3*eta)/2)*gs; end