# Higgs and superparticle mass predictions from the landscape

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## 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 *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 \( {m}_{\tilde{q},\tilde{\ell}}\left(1,2\right)\sim 10-30 \) TeV whilst \( {m}_{{\tilde{t}}_1}\sim 1-2\ \mathrm{T}\mathrm{e}\mathrm{V} \)^{.} 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.

## Keywords

Supersymmetry Phenomenology Strings and branes phenomenology## Notes

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