Ific 95/32 Low Energy Yukawa Input Parameters for Yukawa Coupling Unification

GUT and SUSY theories predict some relations among the fermion masses (or more properly among Yukawa couplings) at the unification scale, MGUT ∼ 10(GeV ) . For instance, in SU(5) we have the usual lepton-bottom quarks unification, hb = hτ , hs = hμ, hd = he, or the modified Georgi-Jarlskog relation, hb = hτ , hs = hμ/3, hd = 3he, while for SO(10) typically we get unification of the third family, ht = hb = hτ = hντ . This together with the RGE’s provide us a powerful tool for predicting quark masses at low energies. In the following I will not talk about Unification but rather try to make a short review of the most recent determinations of the quark masses and to do the running to MZ , the mass of the Z boson. Why MZ?, because for model building purposes it is a good idea to have a reference scale, because extensions of the SM appear above MZ and because below MZ the strong coupling constant αs is really strong and then special care has to be taken on the running and the matching in passing a heavy quark threshold. Because of confinement to define what is the mass of a quark is not an easy task. For leptons it is clear that the physical mass is the pole of the propagator but for quarks we need a precise theoretical framework and the masses appear more like coupling constants. Dealing with quark masses we can find the Euclidean mass, ME(p 2 = −M), defined as the mass renormalized at the Euclidean point p = −M, it is gauge dependent but softly dependent on ΛQCD. However, it does not appear in the most recent works. We can talk about the “perturbative” pole mass, M(p = M), perturbative because only order by order in perturbation theory the pole of the propagator is well defined. It is gauge and scheme independent but appears to be ambiguous because of non-perturbative renormalons. Finally m̄(μ), the mass renormalized in the