SU(5) grand unification in pure gravity mediation

We discuss the proton lifetime in pure gravity mediation models with nonuniversal Higgs soft masses. Pure gravity mediation offers a simple framework for studying SU(5) grand unified theories with a split supersymmetrylike spectra. We find that for much of the parameter space gauge coupling unification is quite good leading to rather long lifetimes for the proton. However, for $m_{3/2}\sim 60\mathrm{TeV}$ and $\tan \beta \sim 4$, for which gauge coupling unification is also good, the proton lifetime is short enough that it could be in reach of future experiments.

Figure 1

The $\tan \beta -m_{1,2}$ plane for (a) $m_{3/2}=60\mathrm{TeV}$ and (b) $m_{3/2}=100\mathrm{TeV}$. The Higgs mass is shown by the nearly horizontal thin red contours in 1 GeV intervals. The wino/chargino mass is shown by the thin solid ($\mu >0$) and dashed ($\mu <0$) contours. The thick black contours show the value of the proton lifetime based on the quark Yukawa couplings (solid) and lepton Yukawa couplings (dashed) in units of ${10}^{35}$ years. Lifetime contours for the solid curves are labeled to the left of the contours whereas dashed contours are labeled to the right.

Figure 2

The dependence of the proton lifetime on $\tan \beta$ (left) for fixed $m_{3/2}=60$ and 200 TeV, and on $m_{3/2}$ (right) for fixed $\tan \beta =2$ and 5. Both of the Higgs soft masses have been fixed $m_1=m_2=0$. The dependence of the Higgs mass is also shown with its value given on the right side of each panel. The horizontal line indicates the present experimental bound [46].

Figure 3

The dependence of the GUT-scale mass parameters ($M_{H_C}$ and $M_G$) on $\tan \beta$ (left) for fixed $m_{3/2}=60$ and 200 TeV, and on $m_{3/2}$ (right) for fixed $\tan \beta =2$ and 5. Both of the Higgs soft masses have been fixed $m_1=m_2=0$. The dependence of the Higgs mass is also shown with its value given on the right side of each panel.

Figure 4

(a) The $m_{3/2}$–$m_{1,2}$ plane for $\tan \beta =5$ and (b) the $\mu$–$m_A$ plane for $\tan \beta =5$ and $m_{3/2}=60\mathrm{TeV}$. In both panels, the Higgs mass is shown by thin red dot-dashed contours in 1 GeV intervals. The wino/chargino mass is shown by the thin solid ($\mu >0$) and dashed ($\mu <0$) contours. The thick black contours show the value of the proton lifetime based on the quark Yukawa couplings (solid) and lepton Yukawa couplings (dashed) in units of ${10}^{35}$ years. Lifetime contours for the solid curves are labeled to the left of the contours whereas dashed contours are labeled to the right.

Figure 5

The dependence of the GUT-scale masses ($m_{H_C}$ and $M_G$) on $\mu$ for fixed $\tan \beta =3$ (left) and $\tan \beta =5$ (right) and fixed $m_{3/2}=65,130$, and 260 TeV. Both of the Higgs soft masses have been fixed $m_1=m_2=0$. The extent of the curves is determined by the validity of radiative EWSB.

Figure 6

The dependence of the proton lifetime on $\mu$ for fixed $\tan \beta =3$ (left) and $\tan \beta =5$ (right) and fixed $m_{3/2}=65,130$, and 260 TeV. Both of the Higgs soft masses have been fixed $m_1=m_2=0$. The extent of the curves is determined by the validity of radiative EWSB. The dependence of the Higgs mass is also shown with its value given on the right side of each panel.

Figure 7

One-loop Higgsino-exchanging diagram which gives rise to the dominant contribution to the baryon-number violating four-Fermi operators. The gray dot indicates the dimension-five effective interaction, while the black dot represents the Higgsino mass term.