Stringent phenomenological investigation into heterotic string optical unification

Abstract

For the weakly coupled heterotic string (WCHS) there is a well-known factor of twenty conflict between the minimum string coupling unification scale, Λ H ∼ 5 × 10 17 GeV, and the projected MSSM gauge coupling unification scale, Λ U ∼ 2.5×10 16 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 quasi-realistic 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 Λ U unification under the ISD assumption is accidental. * john perkins@baylor.edu † ben dundee@baylor.edu ‡ richard k obousy@baylor.edu § hattst@wwc.edu ¶ ekasper@physics.tamu.edu m robinson@baylor.edu * * cwsloan@edisto.cofc.edu † † zkrs18@imail.etsu.edu ‡ ‡ gerald cleaver@baylor.edu If the true unification scale is Λ H > ∼5.0 × 10 17 GeV, is it possible that an illusionary unification at Λ U = 2.5 × 10 17 GeV in the ISD scenario is not accidental? This is an issue recently raised again by Binétruy et al. [1]. If it is not accidental, then under what conditions would the assumption of ISME in a WCHS model imply an apparent unification at Λ U < Λ H when an ISD is falsely assumed? J. Geidt's optical unification suggests that Λ U is not accidental and provides sufficient conditions for the appearance of Λ U . In fact, through constrained ISME, optical unification offers a mechanism whereby a generic MSSM scale Λ U < Λ H is guaranteed.A WCHS model was recently constructed that offers the possibility of optical unification [20]. Whether optical unification can be realized depends on the availability of anomaly-cancelling D-and F -flat directions meeting certain phenomenological requirements [21]. This paper reports on the systematic investigation of the optical unification properties of a subset of flat directions of this model that are stringently flat. Stringent flat directions can be guaranteed to be F -flat to all finite order (or to at least a given finite order consistent with electroweak scale supersymmetry breaking) and can be viewed as the likely roots of more general flat directions. Analysis of the phenomenology of stringent flat directions gives an indication of the remaining optical unification phenomenology 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. 1 Review of Optical UnificationThe lower limit to string coupling unification in a weakly coupled heterotic string (WCHS) was shown by Kaplunovsky in 1992 to be around Λ H ∼ 5 × 10 17 GeV [2]. In contrast, under the scenario of an intermediate scale desert (ISD), the runnings of the SU(3) C ×SU(2) L ×U(1) Y ([321]) couplings in the Minimal Supersymmetric Standard Model (MSSM) predict a unification scale Λ U ∼ 2.5 × 10 16 GeV [3]. The issue of this factor-of-twenty difference was raised again in the third of the Twenty-Five Questions for String Theorists by Binétruy et al. ...

On Geometrical Interpretation of Non-Abelian Flat Direction Constraints

“…The necessity of non-stringent F -flatness was also shown for free fermionic flipped SU(5) models [34] and for possible heterotic string realization of optical unification [35,36,33]. Related classificiation of flipped SU(5) finite-order directions, F -flat to at least 17 th order (as required for viable observablesector SUSY-beaking) is thus underway.…”

“…In Table 1B of [15], four of our flat directions are lifted to all order by the vanishing of terms with more than two non-Abelian fields. As a second example, flatness of the phenomenologically preferred directions of [33] was lifted from 11 th order to beyond 17 th via an SU(3) triplet/anti-triplet generalization of the SU(2) self-cancellation example presented in section 3.2 herein.…”

Quasirealistic heterotic-string models with vanishing one-loop cosmological constant and perturbatively broken supersymmetry?

“…This basis of gauge-invariants can always be formed with particular attributes: (1) each basis element term contains at most one unVEVed field (since to threaten F -flatness, a gauge-invariant term, necessarily without anomalous charge, can contain no more than one unVEVed field); (2) there is at most one basis term for each unVEVed field in the model; and (3) when an unVEVed field appears in a basis term, it appears only to the first power. The SVD process generated a possibly threading basis of superpotential terms for several models (see for example [5,6,9,17,29,30,31]). …”

“…If none survive, then F -flatness is proven to all finite order. This technique has been used to prove F -flatness to all finite order for various directions in several models [5,6,9,17,29,30,31]. Alternately, if any terms do survive, the lowest order is determined at which stringent F -flatness is broken.…”