Quasifixed points from scalar sequestering and the little hierarchy problem in supersymmetry

In supersymmetric models with scalar sequestering, superconformal strong dynamics in the hidden sector suppresses the low-energy couplings of mass dimension 2, compared to the squares of the dimension-1 parameters. Taking into account restrictions on the anomalous dimensions in superconformal theories, I point out that the interplay between the hidden and visible sector renormalizations gives rise to quasifixed point running for the supersymmetric Standard Model squared mass parameters, rather than driving them to 0. The extent to which this dynamics can ameliorate the little hierarchy problem in supersymmetry is studied. Models of this type in which the gaugino masses do not unify are arguably more natural, and are certainly more likely to be accessible, eventually, to the Large Hadron Collider.

Figure 1

The assumed hierarchies of scales involved in the communication of supersymmetry breaking from the hidden sector (where supersymmetry is spontaneously broken) to the visible sector (which contains the MSSM particles).

Figure 2

Renormalization group running of the Higgs mass parameters $(m_{H_u}^2+{\mu }^2{)}^{1/2}$, $(m_{H_d}^2+{\mu }^2{)}^{1/2}$, and $B=b/\mu$, as a function of the RG scale $Q$, for a model with $M_1=M_2=M_3=4500\mathrm{GeV}$ at $M_{\mathrm{GUT}}$, and $\mathrm{\Gamma }=0.3$ and $\mathrm{\Lambda }={10}^{11}\mathrm{GeV}$. Each line is the RG trajectory for a different boundary condition of the common scalar squared mass $m_0^2=b$ at the GUT scale, showing the approach to the quasifixed point behavior at low RG scales.

Figure 3

RG running of the squark and slepton mass parameters $m_{{\tilde{u}}_R}$ (left panel) and $m_{{\tilde{e}}_R}$ (right panel) for a model with $M_1=M_2=M_3=4500\mathrm{GeV}$ at $M_{\mathrm{GUT}}$, and $\mathrm{\Gamma }=0.3$ and $\mathrm{\Lambda }={10}^{11}\mathrm{GeV}$. Each line is the RG trajectory for a different boundary condition of the common scalar mass at the GUT scale, showing the approach to the quasifixed point behavior. The running gluino and bino masses $M_3$ and $M_1$ are also shown for comparison.

Figure 4

The spectrum of physical masses of the gluino, squarks, sleptons, electroweakinos, and the heavier Higgs bosons, for a model line with varying GUT-scale input parameter $m_{1/2}$, with calculated $M_h$ between 123 (lower edge of $m_{1/2}$) and 127 GeV (higher edge). The scalar trilinear coupling parameter $A_0$ and the Higgsino mass parameter $\mu$ are determined by requiring electroweak symmetry breaking with $m_Z=91\mathrm{GeV}$ and $\tan \beta =15$. In the left panel, the common scalar mass is $m_0=m_{1/2}$, and the LSP is a slepton. In the right panel, $m_0=2.5m_{1/2}$, and the LSP is a binolike neutralino. In both cases, $b=m_{1/2}^2$ is imposed at the GUT scale. The solid lines are, from top to bottom, the gluino, Higgsino, wino, and bino. The long-dashed lines are squarks, the short-dashed lines are sleptons, and the dot-dashed lines are the pseudoscalar Higgs boson $A^0$ and the nearly degenerate charged and heavy neutral Higgs scalar bosons $H^0$, $H^{\pm }$.

Figure 5

Results obtained by solving the electroweak symmetry-breaking conditions $m_Z=91\mathrm{GeV}$ and $\tan \beta =15$, for models with fixed GUT-scale parameters $M_1=M_2=4\mathrm{TeV}$, $m_0=3\mathrm{TeV}$, and $b={(2\mathrm{TeV})}^2$, as a function of varying $M_3$. The left panel shows the solutions for the GUT-scale parameters $A_0$ and $\mu (M_{\mathrm{GUT}})$. The right panel shows the resulting top-squark mixing parameter $X_t/M_{\mathrm{SUSY}}$ at $Q=M_{\mathrm{SUSY}}$, where $X_t=a_t/y_t-\mu /\tan \beta$ and $M_{\mathrm{SUSY}}=\sqrt{m_{{\tilde{t}}_1}{m}_{{\tilde{t}}_2}}$. The dots are the special case of gaugino mass unification.

Figure 6

Renormalization group running of the Higgs mass parameters $(m_{H_u}^2+{\mu }^2{)}^{1/2}$, $(m_{H_d}^2+{\mu }^2{)}^{1/2}$, and $B=b/\mu$, for a model with nonuniversal gaugino masses $M_1=2000\mathrm{GeV}$, $M_2=4000\mathrm{GeV}$, and $M_3=1200\mathrm{GeV}$ at the GUT scale. Each line is the RG trajectory for a different boundary condition of the common scalar squared mass $m_0^2=b$ at the GUT scale, showing the approach to the quasifixed point behavior at low RG scales.

Figure 7

RG running of the squark and slepton mass parameters $m_{{\tilde{u}}_R}$ (left panel) and $m_{{\tilde{e}}_R}$ (right panel) for a model with nonuniversal gaugino masses $M_1=2000\mathrm{GeV}$, $M_2=4000\mathrm{GeV}$, and $M_3=1200\mathrm{GeV}$ at the GUT scale. Each line is the RG trajectory for a different boundary condition of the common scalar mass at the GUT scale, showing the approach to the quasifixed point behavior. The running gluino and bino masses $M_3$ and $M_1$ are also shown for comparison.

Figure 8

The spectrum of physical masses of the gluino, squarks, sleptons, electroweakinos, and the heavier Higgs scalar bosons, for a model line with fixed GUT-scale input parameters $M_3=1200\mathrm{GeV}$, $M_2=4000\mathrm{GeV}$, $M_1=2000\mathrm{GeV}$, and $b=(2000\mathrm{GeV}{)}^2$, as a function of $m_0$. The scalar trilinear coupling parameter $A_0$ and the Higgsino mass parameter $\mu$ are determined by requiring electroweak symmetry breaking with $m_Z=91\mathrm{GeV}$ and $\tan \beta =15$. The lightest neutral Higgs boson mass is close to 125 GeV, due to large top-squark mixing.