Mass dependent α_s evolution and the light gluino existence

Abstract

There is an intriguing discrepancy between$\bar \alpha _S (M_z )$ values measured directly at the CERNZ ₀-factory and low-energy (at few GeV) measurements transformed toQ=M _z0 by a massless QCD$\bar \alpha _S (Q)$ evolution relation. There exists and attempt to reconcile this discrepancy by introducing a light gluino≈g in the MSSM. We study in detail the influence of heavy thresholds on$\bar \alpha _S (Q)$ evolution. First, we construct the “exact” explicit solution to the mass-dependent two-loop RG equation for the running$\bar \alpha _S (Q)$. This solution describes heavy thresholds smoothly. Second, we use this solution to recalculate a new$\bar \alpha _S (M_z )$ values corresponding to “low-energy” input data. Our analysis demonstrates that usingmass-dependent RG procedure generally produces corrections of two types: Asymptotic correction due to effective shift of threshold position; Local threshold correction only for the case when input experiment lies in the close vicinity of heavy particle threshold:Q _expt ≈-M _h . Both effects result in the effective shift of the$\bar \alpha _S (M_z )$ values of the order of 10⁻³. However, the second one could be enhanced when the gluino mass is close to a heavy quark mass. For such a case the sum effect could be important for the discussion of the light gluino existence as it further changes the≈g mass.