Yukawa unification and sparticle spectroscopy in gauge mediation models

We explore the implications of the $t\text{−}b\text{−}\tau$ (and $b\text{−}\tau$) Yukawa coupling unification condition on the fundamental parameter space and sparticle spectroscopy in the minimal gauge mediated supersymmetry breaking model. We find that this scenario prefers values of the $CP$-odd Higgs mass $m_A\gtrsim 1\mathrm{TeV}$, with all colored sparticle masses above 3 TeV. These predictions will be hard to test at LHC13 but they may be testable at the high-energy LHC (HE-LHC) 33 TeV or a 100 TeV collider. Both the $t\text{−}b\text{−}\tau$ and the $b\text{−}\tau$ Yukawa coupling unification prefer a relatively light gravitino with mass $\lesssim 30\mathrm{eV}$, which makes it a candidate hot dark matter particle. However, it cannot account for more than 15% of the observed dark matter density.

Figure 1

Plots in the $R_{tb\tau }-\mathrm{\Lambda }$, $R_{tb\tau }-M_{\text{mess}}$, $M_{\text{mess}}-\mathrm{\Lambda }$, and $\mu -M_{\text{mess}}$ planes. All points are consistent with REWSB. Green points also satisfy mass bounds and B-physics constraints. Red points are a subset of green and they are compatible with $t\text{−}b\text{−}\tau$ YU. In the top panels regions below the horizontal line are compatible with YU such that $R_{tb\tau }\le 1.1$.

Figure 2

Plots in the $R_{tb\tau }-\tan \beta$ and $R_{b\tau }-\tan \beta$ planes. The color coding is the same as in Fig. 1.

Figure 3

Plots in the $m_h-\tan \beta$ plane for $t\text{−}b\text{−}\tau$ YU (left panel) and $b\text{−}\tau$ YU (right panel). The color coding is the same as in Fig. 1 except the Higgs mass bound is not applied in these panels.

Figure 4

Plots in the $m_{{\tilde{t}}_1}-m_{{\tilde{t}}_2}$, $m_{{\tilde{u}}_L}-m_{\tilde{g}}$, $m_{{\tilde{\tau }}_1}-m_{{\tilde{\tau }}_2}$ and $m_{{\tilde{\chi }}_1^{\pm }}-m_{{\tilde{\chi }}_1^0}$ planes. The color coding is the same as in Fig. 1.

Figure 5

Plots in the $M_{\text{mess}}-m_{\tilde{G}}$, $\mathrm{\Lambda }-m_{\tilde{G}}$, $R_{tb\tau }-m_{\tilde{G}}$ and $R_{b\tau }-m_{\tilde{G}}$ planes. The color coding is the same as in Fig. 1.