Muon $g-2$ and proton lifetime in SUSY SU(5) GUTs with split superpartners

We consider the interplay of the muon $g-2$ anomaly and the proton decay in the supersymmetry (SUSY) SU(5) grand unified theories (GUTs) with generation-independent scalar soft masses. In these scenarios, we introduce a number of $\mathbf{5}+\overline{\mathbf{5}}$ messenger fields with doublet-triplet splitting in general gauge mediation to transmit SUSY breaking to the visible sector by gauge loops. As a result, squarks and sleptons receive generation-independent soft SUSY breaking masses, which are split already at the messenger scale. Taking into account the perturbative unification of gauge couplings as well as the bounds from electroweak precision and vacuum stability bounds, we showed the parameter space in general gauge mediation to explain the muon $g-2$ anomaly with smuon and sneutrino loops while evading the strong bounds on squarks and gluinos from the Large Hadron Collider. We also obtained the dominant Higgsino contributions to the proton decay mode, $p\to K^{+}\overline{\nu }$, with general generation-independent sparticle masses for squarks and sleptons. Even for split scalar soft masses in our model, however, we found that the bounds from the proton decay are satisfied only if the effective Yukawa couplings of the colored Higgsinos are suppressed further by a factor of order ${10}^{-4}–{10}^{-3}$. We illustrated how such a suppression factor is realized in orbifold GUTs in the extra dimension where the colored Higgsinos in the bulk are not coupled to the matter fields localized at the orbifold fixed points at the leading order.

Figure 1

Soft mass parameters as a function of ${\mathrm{\Lambda }}_G$ in general gauge mediation. We showed $m_{{\tilde{q}}_L}$, $m_{{\tilde{u}}_R}$, $m_{{\tilde{d}}_R}$, which are almost degenerate, with red solid lines, and $m_{{\tilde{l}}_L}$, $m_{{\tilde{e}}_R}$, $M_3$, $M_2$, $M_1$, in blue solid, blue dashed, purple solid, purple dashed, purple dotted lines, respectively. We chose $N_2=10$, $N_3=2$ on the left and $N_2=20$, $N_3=1.5$ on the right.

Figure 2

Feynman diagrams with smuons and sneutrino, contributing to the muon $g-2$.

Figure 3

Parameter space for $N_2$ and $N_3$, explaining the muon $g-2$. We indicated the mass ordering of smuons and the lightest neutralino. We took $\tan \beta =30$, $M_1=M_2/2=400\mathrm{GeV}$ for both plots, and ${\mu }_H=3M_1$ on the left and ${\mu }_H=8M_1$ on the right.

Figure 4

The same for the muon $g-2$ constraints as in Fig. 3, except that we also showed the contours for the lighter smuon mass, $m_{{\tilde{\mu }}_1}=200(250),300,400,500\mathrm{GeV}$ in solid, dashed, dotted, and dot-dashed lines, respectively. We also showed the gray region where $m_{{\tilde{\mu }}_2}<m_{{\tilde{\mu }}_1}$ or $m_{LL}^2<m_{RR}^2$ so the lighter smuon is $\mathrm{SU}(2{)}_L$ doubletlike.

Figure 5

Feynman diagrams with dimension-five operators for proton decay mode, $p\to K^{+}\overline{\nu }$.

Figure 6

Left: proton lifetime in years as a function of the squark mass, $m_{{\tilde{u}}_R}$ in units of GeV. We took $\kappa =1,{10}^{-2}$ in blue solid and dashed lines, respectively. We chose $\tan \beta =30$ in common, ${\mu }_H=1200$, $m_{{\tilde{e}}_R}=250\mathrm{GeV}$ on the left and ${\mu }_H=3200$, $m_{{\tilde{e}}_R}=400\mathrm{GeV}$ on the right.

Figure 7

Parameter space for the scale of general gauge mediation ${\mathrm{\Lambda }}_G$ and the suppression factor for the colored Higgsino Yukawa couplings $\kappa$. The gray region is excluded by the bound on the proton lifetime for $p\to K^{+}\overline{\nu }$. We showed the contours of the slepton mass $m_{{\tilde{e}}_R}=200,500,1000\mathrm{GeV}$ in orange dashed, dotted, and dot-dashed lines, respectively. We took $\tan \beta =30$ in common, and ${\mu }_H=1200\mathrm{GeV}$, $N_2=7$, $N_3=0.4$ on the left and ${\mu }_H=3200\mathrm{GeV}$, $N_2=20$, $N_3=1.5$ on the right.

Figure 8

Parameter space for $N_2$ and $N_3$, explaining the muon $g-2$ and satisfying the bound on the proton lifetime for $p\to K^{+}\overline{\nu }$. We showed the parameter space saturating the bound on the proton lifetime for the suppression factor, $\kappa =6\times {10}^{-4},{10}^{-3},2\times {10}^{-3}$ in dashed, dotted, and dot-dashed lines, respectively. We took $\tan \beta =30$, $M_1=M_2/2=400\mathrm{GeV}$ for both plots, and ${\mu }_H=3M_1$ on the left and ${\mu }_H=8M_1$ on the right. The color codes for yellow and green regions are the same as in Fig. 3 or 4.