U(1)' coupling constant at low energies from heterotic orbifolds

Additional Abelian gauge interactions are generic to string compactifications. In heterotic string models, gauge coupling unification of such forces and other gauge interactions is natural due to their common origin. In this letter we study systematically the 1-loop running of the coupling constants in effective vacua emerging from Z8 heterotic orbifold compactifications that provide the matter spectrum of the MSSM plus some vectorlike exotics, restricting to vacua that yield a non-anomalous U(1)' symmetry, gauge coupling unification and the observed values of known gauge couplings. We determine the low-energy value of the U(1)' coupling constant for different scales of supersymmetry breakdown. We find that the U(1)' coupling constant is quite restricted in string models to lie in the range 0.46-0.7 for low-scale supersymmetry or 0.44-0.6 in other cases. We argue that the phenomenology of these string vacua should be further explored to solve some extant issues, such as the stability of the Higgs vacuum.