Making ends meet: String unification and low-energy data.

A long-standing problem in string phenomenology has been the fact that the string unification scale disagrees with the GUT scale obtained by extrapolating low-energy data within the framework of the minimal supersymmetric standard model (MSSM). In this paper we examine several effects that may modify the minimal string predictions and thereby bring string-scale unification into agreement with low-energy data. These include heavy string threshold corrections, non-standard hypercharge normalizations, light SUSY thresholds, intermediate gauge structure, and thresholds arising from extra matter beyond the MSSM. We explicitly evaluate these contributions within a variety of realistic free-fermionic string models, including the flipped SU(5), SO(6)×SO(4), and various SU(3)×SU(2)×U(1) models, and find that most of these sources do not substantially alter the minimal string predictions. Indeed, we find that the only way to reconcile string unification with low-energy data is through certain types of extra matter. Remarkably, however, many of the realistic string models contain precisely this required matter in their low-energy spectra. ∗ E-mail address: [email protected] † E-mail address: [email protected] Heterotic string theories have a number of properties which make them the leading candidates for a unified theory of the fundamental particles and interactions. Not only do they provide a first-quantized description of gravity, for example, but they also incorporate N = 1 supersymmetric gauge theories as their low-energy limits. This is an important feature, for such supersymmetric gauge theories are natural extensions of the Standard Model which are in agreement with all low-energy experimental data. Moreover, one such theory in particular, namely the minimal supersymmetric Standard Model (MSSM), provides a successful scenario for gauge coupling unification, with a predicted unification scaleMMSSM ≈ 2×10 16 GeV. String theories, by contrast, predict gauge coupling unification at a somewhat larger unification scale, typically Mstring ≈ gstring × 5 × 10 17 GeV where gstring ≈ 0.8 at unification. This discrepancy between these two unification scales implies that string theory naively predicts incorrect values for the electroweak and strong couplings sin θW and αstrong at the Z scale. Resolving this discrepancy and “making the two ends meet” is therefore one of the major problems confronting string phenomenology. There are many possible effects which may account for this discrepancy and alter the running of the gauge couplings between the high and low energy scales. First, there are the so-called “heavy string threshold corrections” which represent the contributions from the massive Planck-scale string states that are otherwise neglected in an analysis of the purely low-energy (i.e., massless) string spectrum. Second, there are potential corrections due to the fact that in string theory, the normalization of the U(1) hypercharge need not take the standard value that it has in various field-theoretic GUT models. Third, if supersymmetry is ultimately broken at the TeV-scale, the required SUSY-breaking terms will lead to additional light SUSY thresholds. Fourth, in various GUT scenarios, there can be corrections due to the presence of non-trivial gauge structure at intermediate scales. Finally, there may also be contributions from additional exotic states beyond those predicted by the MSSM. While such states are not expected in standard field-theoretic GUT scenarios, we shall see that they appear naturally in certain self-consistent string models. Many of these effects have been discussed previously, each in an abstract setting and in isolation. However, within the tight constraints of a given realistic string model, the mechanisms giving rise to three generations and the MSSM gauge group may prove inconsistent with, for example, large threshold corrections or extra nonMSSM matter. Moreover, the increased complexity of the known realistic string models may substantially alter previous expectations based on simplified or idealized scenarios. It is therefore important to rigorously calculate all of these effects simultaneously, within the context of a wide variety of actual realistic string models, in order to determine which path to unification (if any) such models actually take. In this paper, we shall present the results of the first such systematic evaluation. A more complete discussion of our analysis and results will be presented in Ref. [1]. Surprisingly, we find that most of these effects in these models cannot resolve the discrepancy between string unification and low-energy data. In particular, they do