Yukawa unification predictions for the LHC

Abstract

This paper is divided into two parts. In the first part we analyze the consequences, for the LHC, of gauge and third-family Yukawa coupling unification with a particular set of boundary conditions defined at the grand unification scale. We perform a global ${\ensuremath{\chi}}^{2}$ analysis including the observables ${M}_{W}$, ${M}_{Z}$, ${G}_{F}$, ${\ensuremath{\alpha}}_{\mathrm{em}}^{\ensuremath{-}1}$, ${\ensuremath{\alpha}}_{s}({M}_{Z})$, ${M}_{t}$, ${m}_{b}({m}_{b})$, ${M}_{\ensuremath{\tau}}$, $\mathrm{BR}(B\ensuremath{\rightarrow}{X}_{s}\ensuremath{\gamma})$, $\mathrm{BR}({B}_{s}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})$, and ${M}_{h}$. The fit is performed in the minimal supersymmetric Standard Model in terms of nine grand unification-scale parameters, while $\mathrm{tan}\ensuremath{\beta}$ and $\ensuremath{\mu}$ are fixed at the weak scale. Good fits suggest an upper bound on the gluino mass, ${M}_{\stackrel{\texttildelow{}}{g}}\ensuremath{\lesssim}2\text{ }\text{ }\mathrm{TeV}$. This constraint comes predominantly from fitting the bottom-quark and Higgs masses (assuming a 125 GeV Higgs). Gluinos should be visible at the LHC in the 14 TeV run but they cannot be described by the typical simplified models. This is because the branching ratios for $\stackrel{\texttildelow{}}{g}\ensuremath{\rightarrow}t\overline{t}{\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1,2}^{0}$, $b\overline{b}{\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1,2}^{0}$, $t\overline{b}{\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1,2}^{\ensuremath{-}}$, $b\overline{t}{\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1,2}^{+}$, $g{\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1,2,3,4}^{0}$ are comparable. Top squarks and sbottoms may also be visible. Charginos and neutralinos can be light, with the lightest supersymmetric particle predominantly bino-like. In the second part of the paper we analyze a complete three-family model and discuss the quality of the global ${\ensuremath{\chi}}^{2}$ fits and the differences between the third-family analysis and the full three-family analysis for overlapping observables. We note that the light Higgs in our model couples to matter like the Standard Model Higgs. Any deviation from this would rule out this model.