Constrained exceptional supersymmetric standard model

We propose and study a constrained version of the exceptional supersymmetric standard model (${\mathrm{E}}_6\mathrm{SSM}$), which we call the ${\mathrm{cE}}_6\mathrm{SSM}$, based on a universal high energy scalar mass $m_0$, trilinear scalar coupling $A_0$ and gaugino mass $M_{1/2}$. We derive the renormalization group (RG) Equations for the ${\mathrm{cE}}_6\mathrm{SSM}$, including the extra $U(1{)}_N$ gauge factor and the low-energy matter content involving three 27 representations of ${\mathrm{E}}_6$. We perform a numerical RG analysis for the ${\mathrm{cE}}_6\mathrm{SSM}$, imposing the usual low-energy experimental constraints and successful electroweak symmetry breaking. Our analysis reveals that the sparticle spectrum of the ${\mathrm{cE}}_6\mathrm{SSM}$ involves a light gluino, two light neutralinos, and a light chargino. Furthermore, although the squarks, sleptons, and $Z^{\prime }$ boson are typically heavy, the exotic quarks and squarks can also be relatively light. We finally specify a set of benchmark points, which correspond to particle spectra, production modes, and decay patterns peculiar to the ${\mathrm{cE}}_6\mathrm{SSM}$, altogether leading to spectacular new physics signals at the Large Hadron Collider.

Figure 1

Two-loop RG flow of gauge couplings within the ${\mathrm{E}}_6\mathrm{SSM}$ for $T_{\mathrm{MSSM}}=T_{\mathrm{ESSM}}=M_t=175\mathrm{GeV}$ (upper lines) and $T_{\mathrm{MSSM}}=250\mathrm{GeV}$, $T_{\mathrm{ESSM}}=1500\mathrm{GeV}$ (lower lines). Here, we fix $\tan \beta =10$ and ${\alpha }_3(M_Z)=0.118$.

Figure 2

${\mathrm{cE}}_6\mathrm{SSM}$ solutions with $\tan \beta =10$, $s=20\mathrm{TeV}$ and ${\kappa }_{1,2,3}=0.25$, ${\lambda }_{1,2}=0.1$ fixed showing the relationship between $\lambda$ and $m_0$ (top), $M_{1/2}$ (bottom left) and $A$ (bottom right). Points in green (light gray) satisfy all experimental constraints from LEP and Tevatron data, while points in black are ruled out.

Figure 3

${\mathrm{cE}}_6\mathrm{SSM}$ solutions with $\tan \beta =10$, $s=5\mathrm{TeV}$ and ${\kappa }_{1,2,3}=0.25$, ${\lambda }_{1,2}=0.1$ fixed showing the relationship between $\lambda$ and $m_0$ (top left and magnified top right) $M_{1/2}$ (bottom left) and $A$ (bottom right). Points in green (light gray) satisfy all experimental constraints from LEP and Tevatron data, while points in black are ruled out.

Figure 4

Physical solutions with $\tan \beta =10$, ${\lambda }_{1,2}=0.1$, $s=\{3,4,5\}\mathrm{TeV}$ fixed and $\lambda \equiv {\lambda }_3$ and $\kappa \equiv {\kappa }_{1,2,3}$ varying, which pass experimental constraints from LEP and Tevatron data. On the left-hand side of each allowed region the chargino mass is less than 100 GeV, while underneath the inert Higgses are less than 100 GeV or becoming tachyonic. The region ruled out immediately to the right of the allowed points is due to $m_h<114\mathrm{GeV}$.

Figure 5

Physical solutions $\tan \beta =10$ (top, left), $\tan \beta =30$ (top, right) and $\tan \beta =3$ (bottom) with ${\lambda }_{1,2}=0.1$, fixed and $\lambda \equiv {\lambda }_3$ and $\kappa \equiv {\kappa }_{1,2,3}$ and $s$ all varying, which pass experimental constraints from LEP and Tevatron data.

Figure 6

The particle mass spectra for ${\mathrm{cE}}_6\mathrm{SSM}$ benchmark point 1, with $\tan \beta =10$, $s=4.0\mathrm{TeV}$, $M_{1/2}=389\mathrm{GeV}$, $m_0=725\mathrm{GeV}$, $A=-1528\mathrm{GeV}$, ${\lambda }_{1,2}(M_X)=2.6$, ${\lambda }_3(M_X)=-2.0$, ${\lambda }_3({\mu }_S)=-0.259$, ${\kappa }_{1,2,3}=2.5$, ${\kappa }_3({\mu }_S)=0.728$.

Figure 7

Benchmark point 2, with $\tan \beta =10$, $s=4.4\mathrm{TeV}$, $M_{1/2}=775\mathrm{GeV}$, $m_0=799\mathrm{GeV}$, $A=919\mathrm{GeV}$, $\lambda (M_X)=-0.3698$, $\lambda ({\mu }_S)=-0.3736$, ${\lambda }_{1,2}(M_X)=0.1$, ${\kappa }_{1,2,3}(M_X)=0.1780$, ${\kappa }_{1,2,3}({\mu }_S)=0.4935$.

Figure 8

Benchmark point 3, with $\tan \beta =10$, $s=3.8\mathrm{TeV}$, $M_{1/2}=390\mathrm{GeV}$, $m_0=998\mathrm{GeV}$, $A=768\mathrm{GeV}$, $\lambda (M_X)=-0.3066$, $\lambda ({\mu }_S)=-0.2845$, ${\lambda }_{1,2}(M_X)=0.1$, ${\kappa }_{1,2,3}(M_X)=0.2463$, ${\kappa }_{1,2,3}({\mu }_S)=0.5935$.

Figure 9

Benchmark point 4, with $\tan \beta =30$, $s=5.0\mathrm{TeV}$, $M_{1/2}=725\mathrm{GeV}$, $m_0=1074\mathrm{GeV}$, $A=1726\mathrm{GeV}$, $\lambda (M_X)=-0.3847$, $\lambda ({\mu }_S)=-0.3788$, ${\lambda }_{1,2}(M_X)=0.1$, ${\kappa }_{1,2,3}(M_X)=0.1579$, ${\kappa }_{1,2,3}({\mu }_S)=0.4559$.

Figure 10

Benchmark point 5, with $\tan \beta =30$, $s=3.4\mathrm{TeV}$, $M_{1/2}=361\mathrm{GeV}$, $m_0=993\mathrm{GeV}$, $A=1121\mathrm{GeV}$, $\lambda (M_X)=-0.33$, $\lambda ({\mu }_S)=-0.32$, ${\lambda }_{1,2}(M_X)=0.1$, ${\kappa }_{1,2,3}(M_X)=0.18$, ${\kappa }_{1,2,3}({\mu }_S)=0.51$.

Figure 11

Benchmark point 6, with $\tan \beta =3$, $s=5.5\mathrm{TeV}$, $M_{1/2}=931\mathrm{GeV}$, $m_0=918\mathrm{GeV}$, $A=751\mathrm{GeV}$, $\lambda (M_X)=-0.434$, $\lambda ({\mu }_S)=-0.375$, ${\lambda }_{1,2}(M_X)=0.1$, ${\kappa }_{1,2,3}(M_X)=0.23$, ${\kappa }_{1,2,3}({\mu }_S)=0.56$.