Higgs and superparticle mass predictions from the string theory landscape

Abstract

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 mu 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 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 or 2 produce most probabilistically m(h)~125 GeV for negative trilinear terms. For n>=1, there is a pull towards split generations with m(squarks,sleptons)(1,2)~10-30 TeV whilst m(t1)~ 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.