The full two-loop approach to the problem of the light supersymmetric threshold

Summary

The present high values of α₃(M _Z) putSU(5) supergravity (SUGRA) in serious troubles, in the framework of the one-loop approximation to the light supersymmetric threshold. In fact SUGRASU(5) «predicts» the light supersymmetry threshold much belowM _Z. On the other hand SUGRASU(5) is the only reasonable implementation of the celebrated MSSM, the so-called Minimal Supersymmetric extension of the Standard Model: a model with more than twenty parameters, while SUGRASU(5) can be described in terms of only four parameters:m ₀,m _1/2 A, tg β On the other had the one-loop approach is a very rough approximation and it is therefore necessary to work out the full two-loop approximation in order to confirm or not the difficulties of SUGRASU(5). For this reason we have computed the full two-loop detailed light threshold. This has been studied analytically in aSU(3)×SU(2)×U(1) gauge theory. The formulas for α_U,M _U and sin²θ(M _Z) are given, for concreteness, and the hypercharge is normalized according to the assumed SUGRASU(5). It is found that the supersymmetry-breaking scale is increased by a factor of 30 when the two loops are fully taken into account (as compared with the one-loop treatment). This feature allows one to display physically acceptable spectra for values of α₃(M _Z) as high as 0.130 thus allowing SUGRASU(5) to be not in conflict with the present experimental lower bounds on the light supersymmetry threshold.