Stringent Phenomenological Investigation into Heterotic String Optical Unification

For the weakly coupled heterotic string (WCHS) there is a well-known factorof twenty conflict between the minimum string coupling unification scale, ΛH ∼5×1017 GeV, and the projected MSSM gauge coupling unification scale, ΛU ∼2.5×1016 GeV, assuming an intermediate scale desert (ISD). From a bottom-upapproach, renormalization effects of intermediate scale MSSM-charged exotics(ISME), which are endemic to quasi-realistic string models, can resolve thisissue by pushing the MSSM scale up to the string scale. However, for a genericstring model, this implies that the projected ΛU unification under the ISDassumption is accidental.john [email protected] [email protected] k [email protected]@[email protected] [email protected]@[email protected] [email protected] If the true unification scale is ΛH>∼5.0 × 1017 GeV, is it possible that anillusionary unification at ΛU = 2.5 × 1017 GeV in the ISD scenario is notaccidental? This is an issue recently raised again by Binétruy et al. [1]. If it isnot accidental, then under what conditions would the assumption of ISME in aWCHS model imply an apparent unification at ΛU <ΛH when an ISD is falselyassumed? J. Geidt’s optical unification suggests that ΛU is not accidentaland provides sufficient conditions for the appearance of ΛU . In fact, throughconstrained ISME, optical unification offers a mechanism whereby a genericMSSM scale ΛU <ΛH is guaranteed.A WCHS model was recently constructed that offers the possibility of op-tical unification [20]. Whether optical unification can be realized depends onthe availability of anomaly-cancelling Dand F -flat directions meeting certainphenomenological requirements [21]. This paper reports on the systematic in-vestigation of the optical unification properties of a subset of flat directions ofthis model that are stringently flat. Stringent flat directions can be guaranteedto be F -flat to all finite order (or to at least a given finite order consistentwith electroweak scale supersymmetry breaking) and can be viewed as thelikely roots of more general flat directions. Analysis of the phenomenology ofstringent flat directions gives an indication of the remaining optical unificationphenomenology that must be garnered by flat directions developed from them.This paper is a result of the 2003-2004 NSF REU program at Baylor University.