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 ( m soft ) ∼ 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 ∼ 100 GeV. Working within a fertile patch of gravity-mediated low energy effective theories where the superpotential μ term is ≪ 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 Δ EW , which measures fine-tuning in the m Z - μ 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 ∼ 125 GeV for negative trilinear terms. For n ≥ 1, there is a pull towards split generations with m_q̃,ℓ̃(1,2)∼ 10-30 TeV whilst m_t̃_1∼ 1-2 TeV . The most probable gluino mass comes in at ∼ 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.