Solution of the coupled β functions of the Standard Model and its minimal supersymmetric extension

Abstract

The Standard Model contains three coupling constants α1, α2 and α3 associated to the intern symmetry groups. However, even such constants are named like that, in fact they are not, they are energy dependent functions. The functional form of the evolution satisfies a set of coupled differential equations the coupled β functions. In general these β functions are highly coupled, from this arises the necessity of using numerical methods for the solution of the problem, because it is not possible to obtain it analytically. In this work it is used the adaptive Runge-Kutta method for a set of ordinary differential equations. The physical motivation of this work arise from the fact that the coupling constants α1, α2 and α3 are associated to the electromagnetic interaction, the weak interaction and the strong interaction, respectively. In the Standard Model, the solutions for α1 and α2 intersect in a point, which can be interpreted as a unification of two fundamental interactions exists. Nevertheless, using the minimal supersymmetric extension of the Standard Model, the three coupling constants intersect in a region, reaching what is known as the Grand Unification.