No-scale supersymmetric standard model

Anomaly mediation and dimensional transmutation

Weak interaction gauge symmetry breaking can be generated by radiative corrections in a spontaneously broken supergravity theory, provided the top quark is heavy enough. In one class of such theories the weak Higgs vacuum expectation values are determined by dimensional transmutation a la Coleman‐Weinberg, and may be considerably larger than the magnitudes of susy breaking mass parameters. In this scenario mt≥65 GeV, the supersymmetric partners of known particles may have masses ≪mW, the mass of the lighter neutral scalar Higgs boson is determined by radiative corrections, and there is some variant of a light pseudoscalar axion. In contrast to conventional Coleman‐Weinberg models, the weak phase transition is second order and there is no likelihood of excess entropy production.

I discuss the constraints on supersymmetric grand unified theories (SSGUT's) imposed by requiring that such theories be compatible with the presently observed baryon asymmetry of the Universe. I concentrate on those SSGUT's in which the scale of supersymmetry breaking is small compared to the scale at which the baryon asymmetry is generated. If one neglects the supersymmetry breaking, most models of this kind have, at zero temperature, degenerate vacuums which include the gauge-symmetric ground state. In general, it is very hard to obtain a realistic scenario for the phase transitions of these models in the early Universe (i.e., at large temperatures). One of thereasons for this difficulty is due to the following theorem: In SSGUT models with a simple unifying gauge group, one cannot have a situation in which the gauge symmetry decreases as the temperature is raised (in a regime where the coupling constant is small). I argue that if supersymmetry is relevant in grand unified models, it is probably broken at a fairly high scale---above the scale of baryon-number generation.

Two-loop radiative corrections to the mass of the lightest Higgs boson in supersymmetric standard models

The relation between the Hubble constant and the scale of supersymmetry breaking isinvestigated in models of inflation dominated by a string modulus. Usually in this kind ofmodel the gravitino mass is of the same order of magnitude as the Hubble constant, whichis not desirable from the phenomenological point of view. It is shown that slow-roll saddlepoint inflation may be compatible with a low scale of supersymmetry breaking only if somecorrections to the lowest-order Kähler potential are taken into account. However,choosing an appropriate Kähler potential is not enough. There are also conditionsfor the superpotential and, for example, the popular racetrack superpotentialturns out to be not suitable. A model is proposed in which slow-roll inflation anda light gravitino are compatible. It is based on a superpotential with a triplegaugino condensation and the Kähler potential with the leading string corrections.The problem of fine-tuning and experimental constraints are discussed for thatmodel.

We consider “super no-scale models” in the framework of the heterotic string, where the N=4,2,1→0 spontaneous breaking of supersymmetry is induced by geometrical fluxes realizing a stringy Scherk–Schwarz perturbative mechanism. Classically, these backgrounds are characterized by a boson/fermion degeneracy at the massless level, even if supersymmetry is broken. At the 1-loop level, the vacuum energy is exponentially suppressed, provided the supersymmetry breaking scale is small, m3/2≪Mstring. We show that the “super no-scale string models” under consideration are free of Hagedorn-like tachyonic singularities, even when the supersymmetry breaking scale is large, m3/2≃Mstring. The vacuum energy decreases monotonically and converges exponentially to zero, when m3/2 varies from Mstring to 0. We also show that all Wilson lines associated to asymptotically free gauge symmetries are dynamically stabilized by the 1-loop effective potential, while those corresponding to non-asymptotically free gauge groups lead to instabilities and condense. The Wilson lines of the conformal gauge symmetries remain massless. When stable, the stringy super no-scale models admit low energy effective actions, where decoupling gravity yields theories in flat spacetime, with softly broken supersymmetry.

In locally supersymmetric grand unified models we show a rather model-independent upper bound 3·1011 GeV for the scale of supersymmetry breaking, which is derived by consideringSU2×U1 breaking at electroweak mass scale. This bound necessarily implies the existence of new particles (superpartners) below 104 GeV.

Cosmological and astrophysical bounds on the scale of supersymmetry breaking

MSSM‐like string models from the compactification of the heterotic string on toroidal orbifolds (of the kind ) have distinct phenomenological properties, like the spectrum of vector‐like exotics, the scale of supersymmetry breaking, and the existence of non‐Abelian flavor symmetries. We show that these characteristics depend crucially on the choice of the underlying orbifold point group P. In detail, we use boosted decision trees to predict P from phenomenological properties of MSSM‐like orbifold models. As this works astonishingly well, we can utilize machine learning to predict the orbifold origin of the MSSM.

Constraints from gauge coupling unification on the scale of supersymmetry breaking

We argue that fields responsible for inflation and supersymmetry breaking are connected by gravitational couplings. In view of the recent progress in studying supersymmetry breaking in a metastable vacuum, we have shown that in models of supersymmetric hybrid inflation, where R-symmetry plays an important role, the scale of supersymmetry breaking is generated dynamically at the end of inflation and turns out to be consistent with gravity mediation.

Recently, a simple prescription to embed the global Peccei-Quinn (PQ) symmetry into a gauged U(1) symmetry has been proposed. There, explicit breaking of the global PQ symmetry expected in quantum gravity are highly suppressed due to the gauged PQ symmetry. In this paper, we apply the gauged PQ mechanism to models where the global PQ symmetry and supersymmetry (SUSY) are simultaneously broken at around mathcal{O}left(1{0}^{11-12}right) GeV. Such scenario is motivated by an intriguing coincidence between the supersymmetry breaking scale which explains the observed Higgs boson mass by the gravity mediated sfermion masses, and the PQ breaking scale which evades all the astrophysical and the cosmological constraints. As a concrete example, we construct a model which consists of a simultaneous supersymmetry/PQ symmetry breaking sector based on SU(2) dynamics and an additional PQ symmetry breaking sector based on SU(N) dynamics. We also show that new vector-like particles are predicted in the TeV range in the minimum model, which can be tested by the LHC experiments.

In supersymmetric models with minimal particle content and without large left-right squarks mixing, the conventional knowledge is that the Higgs Boson mass around 125 GeV leads to top squark masses O(10) TeV, far beyond the reach of colliders. Here, we pointed out that this conclusion is subject to several theoretical uncertainties. We find that electroweak symmetry breaking and evaluation of Higgs mass at a scale far away from the true electroweak symmetry breaking scale introduce a large uncertainty in Higgs mass calculation. We show that the electroweak symmetry breaking at the scale near the true vacuum expectation value of Higgs field can increase the Higgs Boson mass about 4–5 GeV and can lower the bounds on squarks and slepton masses to 1 TeV. Here we pointed out that the Higgs mass even with inclusion of radiative corrections can vary with electroweak symmetry breaking scale. We calculate it at two loop level and show that it varies substantially. We argue that Higgs mass like other coupling parameters can vary with energy scale and the Higgs potential with all orders loop corrections is scale invariant. This uncertainty to the Higgs mass calculation due to electroweak symmetry breaking around the supersymmetry breaking scale, normally taken as mt˜Lmt˜R, to minimize the 1-loop radiative corrections can be removed if one considers all significant radiative contributions to make Higgs potential renormalization group evolution scale invariant and evaluates electroweak symmetry breaking at the scale near the electroweak symmetry breaking scale. A large parameter space becomes allowed when one considers electroweak symmetry breaking at its true scale not only for producing correct values of the Higgs masses, but also for providing successful breaking of this symmetry in more parameter spaces.

In the minimal supersymmetric model (MSSM), the Higgs self-interactions are related to the SU L (2) × U Y (1) gauge couplings. These relations impose an upper limit on the mass of the lightest Higgs boson of the model. When one-loop radiative corrections to this limit are included, one finds that the corrections are large and grow logarithmically with the supersymmetry breaking scale. Renormalization group techniques are employed in order to sum the leading log radiative corrections to all orders, and the result is that m h o — m Z converges to an infrared fixed point. However, due to the m t 4 behavior of the dominant term, the radiative corrections can still lift the upper bound on the lightest Higgs mass above the reach of LEP-200. The radiatively corrected upper bound for m h o as a function of mt is presented.

In supergravity models with low supersymmetry breaking scale the gravitinos can be superlight, with mass in the 10{sup -6} eV to few keV range. In such a case, gravitino emission provides a new cooling mechanism for protoneutron stars and therefore can provide constraints on the mass of a superlight gravitino. This happens because the coupling to matter of superlight gravitinos is dominated by its goldstino component, whose coupling to matter of superlight gravitinos is dominated by its goldstino component, whose coupling to matter is inversely proportional to the scale of supersymmetry breaking and increases as the gravitino mass decreases. Present observations therefore provide lower limits on the gravitino mass. Using the recently revised goldstino couplings, we find that the two dominant processes in supernova cooling are e{sup +} e{sup -} {yields} GG and {gamma}+e{sup -} {yields} e{sup -} GG. They lead to a lower limit on the supersymmetry breaking scale {Lambda}{sub s} from 160 to 500 GeV for core temperatures 30 to 60 MeV and electron chemical potentials 200 to 300 MeV. The corresponding lower limits on the gravitino mass are .6 - 6 x 10{sup -6} eV.