Howard Baer

Simple SUSY GUT models based on the gauge group SO(10) require t-b-\tau Yukawa coupling unification, in addition to gauge coupling and matter unification. The Yukawa coupling unification places strong constraints on the expected superparticle mass spectrum, with scalar masses \sim 10 TeV while gaugino masses are quite light. A problem generic to all supergravity models comes from overproduction of gravitinos in the early universe: if gravitinos are unstable, then their late decays may destroy the predictions of Big Bang nucleosynthesis. We present a Yukawa-unified SO(10) SUSY GUT scenario which avoids the gravitino problem, gives rise to the correct matter-antimatter asymmetry via non-thermal leptogenesis, and is consistent with the WMAP-measured abundance of cold dark matter due to the presence of an axino LSP. To maintain a consistent cosmology for Yukawa-unified SUSY models, we require a re-heat temperature T_R\sim 10^6-10^7 GeV, an axino mass around \sim 0.1-10 MeV, and a PQ breaking scale f_a\sim 10^{12} GeV.

We present brief synopses of supersymmetric models where either the neutralino composition or its mass is adjusted so that thermal relic neutralinos from the Big Bang saturate the measured abundance of cold dark matter in the universe. We first review minimal supergravity (mSUGRA), and then examine its various one-parameter extensions where we relax the assumed universality of the soft supersymmetry breaking parameters. Our goal is to correlate relic-density-allowed parameter choices with expected phenomena in direct, indirect and collider dark matter search experiments. For every non-universal model, we first provide plots to facilitate the selection of ``dark-matter allowed'' parameter space points, and then present salient features of each model with respect to searches at Tevatron, LHC and ILC and also direct and indirect dark matter searches. We present benchmark scenarios that allow one to compare and contrast the non-universal models with one another and with the paradigm mSUGRA framework. We show that many implications about sparticle properties and collider signals drawn from the analysis of the relic density constraint within mSUGRA do not carry over to simple one-parameter extensions of the mSUGRA framework. We find that in many relic-density-consistent models, there is one (or more) detectable edge in the invariant mass distribution of same-flavour, opposite sign dileptons in SUSY cascade decay events at the LHC. Finally, we scan the parameter space of these various models, requiring consistency with the LEP2 constraint on the chargino mass, and with the observed relic density, and examine prospects for direct and indirect dark matter detection. We find that in a large number of cases the mechanism that causes the early universe neutralino annihilation rate to be large (so as to produce the measured relic density) also enhances the direct detection rate, and often also the rates for indirect detection of neutralino dark matter.

Simple supersymmetric grand unified models based on the gauge group SO(10) require --in addition to gauge and matter unification-- the unification of t-b-\tau Yukawa couplings. Yukawa unification, however, only occurs for very special values of the soft SUSY breaking parameters. We perform a search using a Markov Chain Monte Carlo (MCMC) technique to investigate model parameters and sparticle mass spectra which occur in Yukawa-unified SUSY models, where we also require the relic density of neutralino dark matter to saturate the WMAP-measured abundance. We find the spectrum is characterizd by three mass scales: first/second generation scalars in the multi-TeV range, third generation scalars in the TeV range, and gauginos in the \sim 100 GeV range. Most solutions give far too high a relic abundance of neutralino dark matter. The dark matter discrepancy can be rectified by 1. allowing for neutralino decay to axino plus photon, 2. imposing gaugino mass non-universality or 3. imposing generational non-universality. In addition, the MCMC approach finds 4. a compromise solution where scalar masses are not too heavy, and where neutralino annihilation occurs via the light Higgs h resonance. By imposing weak scale Higgs soft term boundary conditions, we are also able to generate 5. low \mu, m_A solutions with neutralino annihilation via a light A resonance, though these solutions seem to be excluded by CDF/D0 measurements of the B_s\to \mu^+\mu^- branching fraction. Based on the dual requirements of Yukawa coupling unification and dark matter relic density, we predict new physics signals at the LHC from pair production of 350--450 GeV gluinos. The events are characterized by very high b-jet multiplicity and a dilepton mass edge around mz2-mz1 \sim 50-75 GeV.

The observation of the Egret experiment of an excess of diffuse gamma rays with energies above E_\gamma =1 GeV has previously been interpreted in the context of the minimal supergravity model (mSUGRA) as coming from neutralino annihilation into mainly b-quarks in the galactic halo, with neutralino mass in the vicinity of 50-70 GeV. We observe that in order to obtain the correct relic abundance of neutralinos in accord with WMAP measurements, the corresponding neutralino-proton direct detection (DD) rates should be in excess of recent limits from the Xenon-10 collaboration. While it does not appear possible to satisfy the Egret, WMAP and Xenon-10 constraints simultaneously within the mSUGRA model, we find that it is easily possible in models with non-universal Higgs soft masses (NUHM). In either case, gluino pair production from m(gluino)\sim 400-500 GeV should occur at large rates at the CERN LHC, and a gluino pair production signal should be visible with just 0.1 fb^{-1} of integrated luminosity. The NUHM interpretation predicts a rather light spectrum of heavy Higgs bosons with m_A\sim 140-200 GeV over the whole parameter space which would interpret Egret data. Spin-independent DD rates are predicted to be just above 10^{-8} pb, within range of the next round of direct dark matter detection experiments.

Traditional searches for SUSY at hadron colliders rely heavily on the presence of large missing transverse energy (ME_T) to reject background compared to signal. On the other hand, initial searches for new physics at the LHC may not be able to rely on ME_T due to a variety of detector calibration issues. We show that much of SUSY parameter space is accessible to discovery even {\it without} using ME_T, and with rather low integrated luminosities 0.1-1 fb^{-1}. A key role is played by isolated lepton multiplicity which arises from gluino and squark cascade decays. Requiring \ge 3 isolated leptons plus jets yields a high rate of background rejection compared to signal. We find an LHC reach in m(gluino) of about 700-750 GeV for just 0.1 fb^{-1} of integrated luminosity by requiring events with \ge 4 jets plus \ge 3 isolated leptons but {\it without} using ME_T. If a large enough event sample is assembled, then kinematic reconstruction of sparticle mass properties should be possible just as in the case where large ME_T is required. SUSY without ME_T can also be seen in opposite-sign/same flavor {\it dilepton plus jets} events when a characteristic invariant mass edge stands out against background.

We observe that in SUSY models with non-universal GUT scale gaugino mass parameters, raising the GUT scale SU(2) gaugino mass |M_2| from its unified value results in a smaller value of -m_{H_u}^2 at the weak scale. By the electroweak symmetry breaking conditions, this implies a reduced value of \mu^2 {\it vis \`a vis} models with gaugino mass unification. The lightest neutralino can then be mixed Higgsino dark matter with a relic density in agreement with the measured abundance of cold dark matter (DM). We explore the phenomenology of this high |M_2| DM model. The spectrum is characterized by a very large wino mass and a concomitantly large splitting between left- and right- sfermion masses. In addition, the lighter chargino and three light neutralinos are relatively light with substantial higgsino components. The higgsino content of the LSP implies large rates for direct detection of neutralino dark matter, and enhanced rates for its indirect detection relative to mSUGRA. We find that experiments at the LHC should be able to discover SUSY over the portion of parameter space where m_{\tg} \alt 2350-2750 ~GeV, depending on the squark mass, while a 1 TeV electron-positron collider has a reach comparable to that of the LHC. The dilepton mass spectrum in multi-jet + \ell^+\ell^- + \eslt events at the LHC will likely show more than one mass edge, while its shape should provide indirect evidence for the large higgsino content of the decaying neutralinos.