Abstract
We look for the minimal particle content which is necessary to add to the standard model in order to have a complete unification of gauge couplings and gravity at the weakly coupled heterotic string scale. Using the current precision electroweak data, we find that the presence of a vector-like fermion at an intermediate scale and a non-standard hypercharge normalization are in general sufficient to achieve this goal at two-loop level. If one requires the extra matter scale to be below the TeV scale, then it is found that the addition of three vector-like fermion doublets with a mass around 700 GeV yields a perfect string-scale unification, provided that the affine levels are kY=13/3, k2=1 and k3=2, as in the SU(5)⊗SU(5) string-GUT. Furthermore, if supersymmetry is broken at the unification scale, the Higgs mass is predicted in the range 125–170 GeV, depending on the precise values of the top quark mass and tanβ parameter.
Highlights
Superstring theory has emerged as the most promising candidate for a quantum theory of all known interactions
In view of the above considerations and in the light of the current precision electroweak data, in this letter we study the problem of gauge coupling unification within string theory, with the aim to look for the minimal particle content which is necessary to add to the standard model (SM) in order to achieve unification at the weakly coupled heterotic string scale
For a weakly coupled heterotic string, the unification scale is expected around 5 ×1017 GeV, which is too high to be achieved in the SM or MSSM, even with a non-canonical normalization of the hypercharge
Summary
Superstring theory has emerged as the most promising candidate for a quantum theory of all known interactions. It is remarkable that, in the nonsupersymmetric SM, the one-loop g2 and g3 gauge couplings already unify at a scale ΛSM ≈ 1017 GeV, which is close to the unification scale predicted by the string theory In this case, gauge coupling unification could be achieved for a hypercharge normalization kY ≈ 13/10 [8]. We show that the addition of vector-like fermions with an intermediate mass scale leads to such a unification, provided that the hypercharge affine level is non-canonical, i.e. kY = 5/3 The existence of such matter states is in general expected in realistic string theories. This normalization is consistent with an SU(5) ⊗ SU(5) or SO(10) ⊗ SO(10) string-GUT compactification [13,14]
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