Sparticle spectroscopy and neutralino dark matter for Yukawa and gauge-Yukawa unified models

This dissertation examines third generation (t-b-tau) Yukawa and gauge-Yukawa coupling unification in supersymmetric SU(4) c x SU(2)L x SU(2)RGUT. We assume a framework of gravity mediated supersymmetry breaking so the 4-2-2 structure dictates the form of the soft supersymmetry breaking parameters at M GUT. We study the spectroscopic implications of Yukawa and gauge-Yukawa unification that may be testable at the Large Hadron Collider. We also discuss the prospects of a Yukawa or gauge-Yukawa unified 4-2-2 model yielding solutions that are observable in direct and indirect dark matter detection experiments.;We demonstrate the importance of finite corrections to the bottom quark Yukawa coupling for the question of Yukawa unification. We also show that Yukawa coupling unification in 4-2-2 is compatible with neutralino dark matter. If we restrict ourselves to the case of same sign gaugino soft mass terms, the resulting Yukawa unified model predicts a very characteristic sparticle spectrum with gluino as the next to lightest supersymmetric particle (NLSP) and heavy (multi-TeV) squarks and sleptons. By considering gaugino mass soft terms with a relative sign, we are able to realize Yukawa coupling unification with the universal soft supersymmetry breaking scalar mass parameter m 0 ≥ 400 GeV as opposed to m0 ≥ 8 TeV for same sign gauginos. We have demonstrated the existence of a variety of coannihilation scenarios involving gluino, wino and stau, in addition to the light Higgs, Z and A resonance solutions and the bino-Higgsino mixed dark matter solution. The 4-2-2 model with opposite sign gauginos also has relatively 'light' (m0 ∼ 43 GeV) neutralinos compatible with Yukawa unification and neutralino dark matter. We may also satisfy the Delta (g-2)mu constraint along with all the other experimental bounds for the case of opposite sign gauginos which is not possible for same sign gauginos.;We show that gauge-Yukawa coupling unification is sensitive to the top quark mass mt. Varying mt within 1sigma of its current central value yields a variety of gauge-Yukawa unification as well as WMAP compatible neutralino dark matter solutions. They include mixed bino-Higgsino dark matter, stau and gluino coannihilation scenarios, and the A-resonance solution.;We investigate mixed bino-Higgsino dark matter as the best scenario in the MSSM to be observed at direct and indirect dark matter search experiments. If the observed relic density is saturated by the bino-Higgsino dark matter, it fixes the amount of allowable bino-Higgsino mixing and provides predictions for other observables which can be tested at the Large Hadron Collider (LHC). We study the correlation between the cross sections and the branching ratio of Bs→ mu + mu -. Finally, we show the bino-Higgsino mixing solutions that are compatible with Yukawa and gauge-Yukawa unification and may soon be detected at direct and indirect dark matter surveys.