INSTRUCTIONS FOR THE MATHEMATICA PACKAGE zetaalsu5.m BY W. MARTENS: This mathematica package contains the two-loop decoupling coefficients for alpha_1/2/3 for matching the Georgi-Glashow SU(5) model to the Standard Model. The main functions are: zetaAlU1, izetaAlU1, zetaAlSU2, izetaAlSU2, zetaAlSU3, izetaAlSU3. The arguments are: alpha4pi = alpha(mu)/(4*pi) the unique gauge coupling in the GUT in MSbar at the scale mu alpha14pi = alpha_1(mu)/(4*pi) the U(1) gauge coupling in the SM in MSbar at the scale mu alpha24pi = alpha_2(mu)/(4*pi) the SU(2) gauge coupling in the SM in MSbar at the scale mu alpha34pi = alpha_3(mu)/(4*pi) the SU(3) gauge coupling in the SM in MSbar at the scale mu yt = the top Yukawa coupling in the GUT (for zetaAl...) or the SM (for izetaAl...) in MSbar yb = the (unified) bottom-tau Yukawa coupling in the GUT (for zetaAl...) or the SM (for izetaAl...) in MSbar Mx = the on-shell mass of the heavy gauge boson living in (3,2bar,-5/6) + (3bar,2,5/6) of 24 MHc = the on-shell mass of the colored Higgs triplet (3,1,-1/3) in 5_H Msig = the on-shell mass of the color oktet Higgs (8,1,0) in 24_H M24 = the on-shell mass of the singlet Higgs (1,1,0) in 24_H mu = the decoupling scale Loops = the number of loops of the RGE analysis, i.e. Loops=3 gives the two-loop decoupling coefficient, Loops=2 gives the one-loop decoupling coefficient The description of their arguments can also be obtained by e.g. the command ?zetaAlU1 Important Note: We perform a one-step decoupling here. Hence, be careful when choosing the mass spectrum. Too far separated masses can lead to power-enhanced contributions and spoil the perturbative expansion (check whether the two-loop contribution is smaller than the one-loop contribution). Usually up to two orders of magnitude separation is still safe. For more details, please have a look at the paper: "Towards a Two-Loop Matching of Gauge Couplings in Grand Unified Theories " W. Martens Or contact me: martens@particle.uni-karlsruhe.de