Unification of Gauge Couplings

It is now well known that the (properly normalized) observed gauge couplings do not unify when extrapolated to a large scale using the standard model predictions for the running, but they do within experimental uncertainties if they run according to the MSSM [21]. Since the electroweak couplings and are known precisely, it is useful to use them as inputs to predict the more uncertain [22]. Using present data, one predicts , where the first uncertainty is from the input couplings and the second is an estimate of the theoretical uncertainties from the low energy (supersymmetry) and superheavy (grand unification) thresholds, and from possible nonrenormalizble operators (NRO). As discussed in Section 2, this is in good agreement with the experimental values determined from the Z lineshape and from the LEP jet event analysis, but is high compared with some low energy detrminations of . In contrast, the non-supersymmetric standard model prediction is , well below the experimental values.

Thus, the observed couplings are consistent to first approximation with simple supersymmetric grand unification and the associated concept of a grand desert between the TeV and GUT scales. However:

• Threshold corrections associated with the supersymmetric particles are and are usually positive assuming universal soft supersymmetry breaking terms [27], and supersymmetric contributions to the electroweak radiative corrections generally lead to larger [27]. Thus, low-scale threshold effects are not likely by themselves to lower the predicted much below . The experimental value of is not a settled issue, but if the lower values (e.g., 0.110-0.115) suggested by some determinations are correct, one would have to invoke large but not unreasonable GUT or string threshold effects, NRO, or intermediate scale matter to maintain consistency.
• The MSSM couplings unify at a scale GeV. This is far enough below the Planck scale GeV that it may be consistent to consider grand unification of the strong and electroweak couplings without gravity. Nevertheless, it is tempting to bring gravity into the game. For example, one expects that in superstring compactifications the couplings will unify around the string scale GeV, which is one order of magnitude above . It is possible that the string compactification first produces a grand unified theory in four dimensions, which then breaks at the lower scale . However, it is difficult to find models in which this occurs and for which the necessary Higgs multiplets to break the GUT symmetry are present. Alternatively, the string compactification may lead directly to the standard model group, in which case one must invoke string threshold effects, intermediate scale matter, or higher Kac-Moody levels to explain the discrepancy of scales.
• Much attention has been focussed on the deviation of from and on the predicted . However, the actual unification predictions are for and . The former is consistent with the string scale to within 10% and the latter is accurate to within 15%as well. Given the enormous number of perturbations on the predictions that can occur in string and GUT models one should view the predictions as a major success for the general idea of GUT or string unification.
• Most types of new physics at the TeV scale would have very large (order 1) effects on the gauge unification prediction. Unless the success is just an accident, and barring cancellations between large effects, this severely restricts the possibilities for new physics beyond the MSSM at the TeV scale. Essentially the only possibilities are extended gauge groups which commute with the standard model group, such as additional factors associated with heavy bosons, complete ordinary or mirror additional families, new exotic families which correspond to complete GUT multiplets, and standard model singlets.