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