Stringent phenomenological investigation into heterotic string optical unification

For the weakly coupled heterotic string (WCHS) there is a well-known factor of 20 conflict between the minimum string coupling unification scale, ΛH∼5x1017 GeV, and the projected minimal supersymmetric standard model (MSSM) gauge coupling unification scale, ΛU∼2.5x1016 GeV, assuming an intermediate scale desert (ISD). From a bottom-up approach, renormalization effects of intermediate scale MSSM-charged exotics (ISME), which are endemic to quasirealistic string models, can resolve this issue by pushing the MSSM scale up to the string scale. However, for a generic string model, this implies that the projected ΛU unification under the ISD assumption is accidental. If the true unification scale is ΛH > or approx. 5.0x1017 GeV, is it possible that an illusionary unification at ΛU=2.5x1017 GeV in the ISD scenario is not accidental? (This is an issue recently raised again by Binetruy et al..) Optical unification suggests that ΛU might not be accidental. Through its ISME constraints, optical unification offers a mechanism whereby a generic MSSM scale ΛU<ΛH is guaranteed. A WCHS model was recently constructed that could yield optical unification, depending on the availability of anomaly-cancelling D- and F-flat directions that meet optical unification ISME requirements. We report the results of a systematic investigation of the optical unification properties of a subset of flat directions of this model that are stringently flat. Stringent flat directions do not require significant fine-tuning and can be easily guaranteed to be F-flat to all finite order (or to at least a given finite order consistent with electroweak scale supersymmetry breaking). They are the likely roots of more complicated (and arguably, more finely tuned) flat directions. To realize optical unification, a flat direction must keep all exotic triplets and doublets massless down to an intermediate mass scale, except for three extra pairs of Higgs which must acquire MSSM (or higher) scale mass. Additionally, six out of seven pairs of exotic hypercharged non-Abelian singlets must acquire MSSM (or higher) scale mass, while the remaining pair remains massless down to the intermediate scale. Our investigation revealed that the best stringent directions could induce MSSM scale or higher mass to at most three of the six pairs of exotic singlets, and to only two out of three pairs of exotic Higgs. Each of these stringent flat directions keeps all of the exotic triplets and remaining exotic doublets massless down to an intermediate scale. Thus, some fine-tuning away from stringent flat directions is necessary, if it is possible for an additional three pairs of exotic hypercharged singlets and one more pair of extra Higgs to become MSSM scale massive. Future research may indicate if such flat directions exist. This paper is a product of the 2003-2004 NSF REU program at Baylor University