Higgs and superparticle mass predictions from the landscape

Predictions for the scale of SUSY breaking from the string landscape go back at least a decade to the work of Denef and Douglas on the statistics of flux vacua. The assumption that an assortment of SUSY breaking $F$ and $D$ terms are present in the hidden sector, and their values are uniformly distributed in the landscape of $D=4$, $N=1$ effective supergravity models, leads to the expectation that the landscape pulls towards large values of soft terms favored by a power law behavior $P\left(m_{soft}\right)\sim m_{soft}^n$. On the other hand, similar to Weinberg's prediction of the cosmological constant, one can assume an anthropic selection of weak scales not too far from the measured value characterized by $m_{W,Z,h}\sim 100$ GeV. Working within a fertile patch of gravity-mediated low energy effective theories where the superpotential $\mu$ term is $\ll m_{3/2}$, as occurs in models such as radiative breaking of Peccei-Quinn symmetry, this biases statistical distributions on the landscape by a cutoff on the parameter ${\Delta }_{EW}$, which measures fine-tuning in the $m_Z$-$\mu$ mass relation. The combined effect of statistical and anthropic pulls turns out to favor low energy phenomenology that is more or less agnostic to UV physics. While a uniform selection $n=0$ of soft terms produces too low a value for $m_h$, taking $n=1$ and $2$ produce most probabilistically $m_h\sim 125$ GeV for negative trilinear terms. For $n\ge 1$, there is a pull towards split generations with $m_{\tilde{q},\tilde{\ell }}(1,2)\sim 10-30$ TeV whilst $m_{{\tilde{t}}_1}\sim 1-2$ TeV. The most probable gluino mass comes in at $\sim 3-4$ TeV — apparently beyond the reach of HL-LHC (although the required quasi-degenerate higgsinos should still be within reach). We comment on consequences for SUSY collider and dark matter searches.