S. Kelley

Probing the desert using gauge coupling unification

Abstract We present analytic one-loop expressions for sin 2 θ w , the unification scale M x , and the coupling at the unification scale α ( M x ), in supersymmetric grand-unified models with arbitrary intermediate scales. We correct these expressions to agree with a two-loop calculation for central values of the inputs. Our general results quickly determine whether a particular model has hope of compatibility with the low energy couplings. We then apply these results to traditional supersymmetric SU (5) and to supersymmetric flipped SU (5) × U (1). These results translate into a narrow bound on a function of the extra intermediate scales. In particular, we conclude that even allowing for the experimental uncertainties in low-energy couplings and effects of supersymmetric and Higgs thresholds, traditional supersymmetric SU (5) grand unification without extra thresholds is about one standard deviation away from the measured value of sin 2 θ w . We also calculate the range of proton decay in minimal flipped SU (5) × U (1) allowing for uncertainties in the low-energy couplings and the effects of supersymmetric and Higgs thresholds. Non-observation of proton decay gives a bound on another function of additional intermediate scales beyond the minimal model.

The price of deriving the standard model from the string

Abstract It is well known that precision LEP data on sin 2 θ w an α 3 are consistent with supersymmetric grand unification at an energy scale almost two orders of magnitude below that calculated in string models. We examine whether one can raise the unification scale, whilst retaining the successful predictions for sin 2 θ w and α 3 by adding to the standard model non-exotic multiplets of particles. We find that one must introduce extra (3,2) representations of SU(3)×SU(2). If there is just one such vector-like (3,2) representation, it must weigh less than abour 10 13 GeV. Moreover, there must be at least one other type of light matter representation. We exhibit a “twisted” version of the flipped SU(5) model derived from the string that can accommodate such light representations.

A detailed comparison of LEP data with the predictions of the minimal supersymmetric SU(5) GUT

Abstract We confront the precise LEP determinations of sin2θw and the strong coupling α3(mz0 with the predictions of the minimal supersymmetric SU(5) GUT. We incorporate O(αemα3) effects in the extraction of sin2θw from LEP data. We incorporate distinct thresholds for the supersymmetric partners of the different species of Standard Model particles, parameterized in terms of a scalar mass m0 and a gaugino mass m 1 2 that are assumed to be universal at the GUT scale. We also allow for uncertainties in the top, higgs and higgsino masses. We use the full two-loop renormalization group equations including top, bottom and tau Yukawa couplings. We show that GUT threshold effects are small because proton stability prevents triplet Higgs particles from weighing much less than 1016 GeV. Using 1−σ errors for the experimental inputs and plausible ranges for unknown supersymmetric model parameters, in particular an upper bound of 300 GeV on the higgs mixing parameter μ, we find that either 3.0×10 12 TeV >m 1 2 >21 TeV or m 1 2 GeV , with the intermediate range allowed at the 2 − σ level. An upper bound of μ=500 GeV excludes m 1 2 from 80 GeV to 5 TeV at 1 − σ, and an upper bound of μ=1 TeV excludes m 1 2 from 110 GeV to 620 GeV at 1 − σ. It is not possible at present to fix the supersymmetry breaking scale with any precision.

A new string-inspired standard model (SISM)

Abstract The unification of gauge couplings in string models is predicted to occur at scales (∼10 16 GeV) which are in disagreement with those obtained, using presice LEP data, in supersymmetric models with minimal matter content (∼10 16 GeV). We present a string-inspired extension of the standard model with one pair of extra vector-like Q and D c representations which allows string unification for D c masses in the few TeV region or less, predicts a light ( unique minimal choice in this class of extra vector models, it can be embedded most economically in a flipped SU (5) structure, and may be derivable from string.

No scale supergravity confronts experiment

We present a numerical study of the complete parameter space of the minimal supersymmetric unified model when the seed of supersymmetry breaking is a universal gaugino mass (m12), as is the case in typical no-scale supergravity models. After imposing all consistency and experimental constraints on the model, we obtain a rather range of the allowed values of m12: 100≲m12≲300 (400) GeV for μ>0 (μ<0). This scenario predicts all supersymmetric particle masses to be below 1 TeV, with all the sleptons below 290 GeV. In fact, the choice of just three parameters, namely mt, tan β, and m12, completely determines all masses and couplings in the model, and hence makes it a highly predictive and testable scenario.

Aspects of radiative electroweak breaking in supergravity models

Abstract We discuss several aspects of state-of-the-art calculations of radiative electroweak symmetry breaking in supergravity models. These models have a five-dimensional parameter space in contrast with the 21-dimensional one of the MSSM. We examine the Higgs one-loop effective potential V 1 = V 0 + ΔV , in particular how its renormalization-scale ( Q ) independence is affected by the approximation used to calculate ΔV and by the presence of a Higgs-field-independent term which makes V 1 (0) ≠ 0. We show that the latter must be subtracted out to achieve Q -independence. We also discuss our own approach to the exploration of the five-dimensional parameter space and the fine-tuning constraints within this approach. We apply our methods to the determination of the allowed region in parameter space of two models which we argue to be the prototypes for conventional (SSM) and string (SISM) unified models. To this end we impose the electroweak breaking constraint by minimizing the one-loop effective potential and study the shifts in μ and B relative to the values obtained using the tree-level potential. These shifts are most significant for small values of μ and B , and induce corresponding shifts on the lightest μ-and/or B -independent particle masses, i.e., those of the lightest stau, neutralino, chargino, and Higgs boson states. Finally, we discuss the predictions for the squark, slepton, and one-loop corrected Higgs boson masses.

Constraints From Gauge Coupling Unification On The Scale Of Supersymmetry Breaking

We reanalyze precision LEP data and coupling constant unification in the minimal supersymmetric SU(5) model including the evolution of the gaugino masses. We derive general bounds on the primordial gaugino supersymmetry-breaking mass-scale m 1/2 in terms of the various input parameters. The model cannot accommodate m1/2 < 1TeV for values of �3(mZ) < 0.115, even for extreme 1 � values of the other inputs. We emphasize the sensitivity of this type of calculations to the various input parameters.

A new mechanism for lepton-flavor violation τ → μγ in the flipped string

Abstract We explore a new mechanism for lepton-flavor violation which is manifest in the flipped SU(5) string model, and may be a generic feature of string-derived models. this mechanism generates off-diagonal slepton masses from otherwise flavor diagonal Yukawa matrices when heavy vector-like leptons decouple at a high-mass scale. As an example of lepton-flavor violation, we present an order of magnitude prediction for the branching ratio BR( τ → μγ ) in the flipped string. The result depends crucially on the details of the extra vector-like fermion decoupling, and on the assumed nature and scale of supersymmetry breaking. For natural choices of the parameters we obtain a large BR( τ → μγ ), which we show to be well within the reach of present and future experimental searches.

The extra vector abeyance (EVA) mechanism as the origin of the KM matrix

Abstract We examine a general mechanism whereby an extra vector-like quark of mass M eva generates realistic quark mixing angles from otherwise flavor diagonal quark Yukawa matrices. For scales above M eva the vector-like quark is manifest, while the Yukawa matrices are diagonal, i.e., the KM matrix is held in abeyance. Conversely, for scales below M eva the vector-like quark is in an abeyant state, while the KM matrix is manifest. This mechanism is naturally realized in many superstring models. In fact, knowledge of the Yukawa matrices at the string scale, together with suitable renormalization group scaling, unambigously determines the quark mass ratios and the KM angles at low energies. Conversely, these low-energy observables may be used to determine asyet-unknown parameters in the string model. We explicitly apply the EVA mechanism to a toy model inspired by the structure of the flipped SU (5) string model, to illustrate how this mechanism may be used to predict some of the KM angles. We also outline the procedure to be followed in a realistic calculation in the flipped SU (5) string model.

Higgs boson masses in no-scale supergravity

Abstract We explore the Higgs sector of the minimal supersymmetric “no-scale” unified model with the inclusion of radiative corrections which modify the usual tree-level Higgs mass relations. In the process, we rederive the complete allowed parameter space of the model using the one-loop effective potential. Our results can be compared with previous, generic analyses, where restrictive assumptions regarding low-energy supersymmetry breaking and squark mixing terms have been made. We find that in this class of models the lightest Higgs boson is always the lightest CP -even mass eigenstate (h), with m h ⪆M w for a large portion of the allowed parameters space, and m h max ≈ 115 GeV an absolute upper bound. For low values of m 1 2 (e.g., m 1 2 ⪅ 150 GeV ), the heavier Higgses (A, H, H + ) lie mostly in the intermediate mass region ( M w −2 M z ), and become increasingly heavier and degenerated as m 1 2 grows. Depending on the sign of μ, we obtained an upper bound on m 1 2 which leads to absolute upper bounds on all Higgs masses. Finally, we discuss the relevant Higgs decay signatures at LEP and hadron colliders which may reveal their existence.