String landscape guide to soft SUSY breaking terms

We examine several issues pertaining to statistical predictivity of the string theory landscape for weak scale supersymmetry (SUSY). We work within a predictive landscape wherein superrenormalizable terms scan while renormalizable terms do not. We require stringy naturalness wherein the likelihood of values for observables is proportional to their frequency within a fertile patch of landscape including the minimal supersymmetric standard model as low energy effective theory with a pocket-universe value for the weak scale nearby to its measured value in our universe. In the string theory landscape, it is reasonable that the soft terms enjoy a statistical power-law draw to large values, subject to the existence of atoms as we know them (atomic principle). We argue that gaugino masses, scalar masses, and trilinear soft terms should each scan independently. In addition, the various scalars should scan independently of each other unless protected by some symmetry. The expected nonuniversality of scalar masses—once regarded as an undesirable feature—emerges as an asset within the context of the string landscape picture. In models such as heterotic compactifications on Calabi-Yau manifolds, where the tree-level gauge kinetic function depends only on the dilaton, gaugino masses may scale mildly, while scalar masses and A terms, which depend on all the moduli, may scale much more strongly leading to a landscape solution to the SUSY flavor and $CP$ problems in spite of nondiagonal Kähler metrics. We present numerical results for Higgs and sparticle mass predictions from the landscape within the generalized mirage mediation SUSY model and discuss resulting consequences for LHC SUSY and weakly interacting massive particles dark matter searches.

Figure 1

The $m_0^{MM}$ vs $m_{1/2}^{MM}$ plane of the ${\mathrm{GMM}}^{\prime }$ model for a value of $n_{1/2}=1$ for all frames but with (a) $n_0=1$, (b) $n_0=2$, (c) $n_0=3$, and (d) $n_0=4$. For all frames, we take $m_{3/2}=20\mathrm{TeV}$, $\mu =200\mathrm{GeV}$, $m_A=2\mathrm{TeV}$, $\tan \beta =10$, and $a_3=1.6\sqrt{c_m}$. We require $m_Z^{\mathrm{PU}}<4m_Z^{\mathrm{OU}}$.

Figure 2

Probability distribution $dP/d{m}_h$ vs $m_h$ for $n_{1/2}=1$ and $n_0=1$, 2, 3, and 4 for scans of the ${\mathrm{GMM}}^{\prime }$ model for $m_{3/2}=20\mathrm{TeV}$, $\mu =200\mathrm{GeV}$, $m_A=2\mathrm{TeV}$, $\tan \beta =10$, and $a_3=1.6\sqrt{c_m}$. We require $m_Z^{\mathrm{PU}}<4m_Z^{\mathrm{OU}}$.

Figure 3

Probability distribution for mass of light Higgs boson $m_h$ for $n_{1/2}=1$ with $n_0=1$ (blue line) and $n_0=2$ (red line) from statistical scans over the ${\mathrm{GMM}}^{\prime }$ model with $m_{3/2}=20\mathrm{TeV}$.

Figure 4

Upper panels: Distributions in $m_{\tilde{g}}$ (left) and $m_{{\tilde{t}}_1}$ (right). Lower panels: Distributions in $m_{{\tilde{t}}_2}$ (left) and $m_A$ (right). Here, $n_{1/2}=1$ but $n_0=1$ (blue lines) and $n_0=2$ (red lines) are from statistical scans over the ${\mathrm{nGMM}}^{\prime }$ model with $m_{3/2}=20\mathrm{TeV}$.

Figure 5

Probability distribution $dP/d{m}_{{\tilde{u}}_L}$ vs $m_{{\tilde{u}}_L}$ from general scan for $n_{1/2}=1$ but for $n_0=1$ and 2.