We analyze gauge coupling unification in the context of heterotic strings on anisotropic orbifolds. This construction is very much analogous to effective five-dimensional orbifold grand unified theory field theories. Our analysis assumes three fundamental scales: the string scale M S , a compactification scale M C , and a mass scale for some of the vectorlike exotics M EX ; the other exotics are assumed to get mass at M S . In the particular models analyzed, we show that gauge coupling unification is not possible with M EX ¼ M C , and in fact we require M EX ( M C $ 3 Â 10 16 GeV. We find that about 10% of the parameter space has a proton lifetime (from dimension six gauge exchange) 10 33 yr & ðp ! 0 e þ Þ & 10 36 yr. The other 80% of the parameter space gives proton lifetimes below Super-Kamiokande bounds. The next generation of proton decay experiments should be sensitive to the remaining parameter space.
In this paper, we discuss the issues of supersymmetry breaking and moduli stabilization within the context of E 8 E 8 heterotic orbifold constructions and, in particular, we focus on the class of ''minilandscape'' models. In the supersymmetric limit, these models admit an effective low-energy field theory with a spectrum of states and dimensionless gauge and Yukawa couplings very much like that of the minimal supersymmetric standard model. These theories contain a non-Abelian hidden gauge sector which generates a nonperturbative superpotential leading to supersymmetry breaking and moduli stabilization. We demonstrate this effect in a simple model which contains many of the features of the more general construction. In addition, we argue that once supersymmetry is broken in a restricted sector of the theory, then all moduli are stabilized by supergravity effects. Finally, we obtain the low-energy superparticle spectrum resulting from this simple model.
Since differences in wavelength calibration between instruments are arguably a primary source of error encountered in the transfer of calibration models from one instrument to another in near-infrared (NIR) spectroscopy, a readily available, convenient, inexpensive secondary wavelength calibration standard for the NIR spectral region is needed. This paper describes the advantages of trichloromethane as a wavelength standard for the calibration of dispersive NIR spectrometers used in the transmission mode. The spectrum of trichloromethane, taken with a Fourier transform NIR spectrometer whose wavenumber scale was calibrated with the ro-vibrational lines of ethyne as determined by the National Institute of Standards and Technology (NIST), is presented. The wavelengths of four strong, sharp, well-resolved bands of trichloromethane were determined with the calibrated Fourier transform NIR spectrometer and were found to be 1152.13 ± 0.01 nm (3v1), 1410.21 ± 0.01 nm (2v1 + v4), 1691.9 ± 0.7 nm (2v1), and 1861.22 ± 0.01 nm (v1 + 2v4). These bands were then used to calibrate the wavelength scale of a commercial 0.25 m monochromator equipped with a 300 line mm−1 grating. The calibration revealed that, while the wavelength scale of the monochromator was linear, there was a systematic error of about + 12 nm in the NIR region.
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. ...
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