Distribution of supersymmetry mu parameter and Peccei-Quinn scale f_a from the landscape

TL;DR

This paper explores how different solutions to the SUSY mu problem influence the distribution of the mu parameter and Peccei-Quinn scale in the string landscape, affecting predictions for sparticle masses and axion physics.

Contribution

It derives the expected landscape distributions for the mu parameter and PQ scale under two solutions to the SUSY mu problem, incorporating anthropic selection effects.

Findings

Predicted Higgs mass peak at 125 GeV with heavy sparticles beyond LHC reach.

The mu parameter distribution depends on the solution to the mu problem, affecting phenomenological predictions.

The PQ scale is constrained to around 10^{11} GeV in the GSPQ model due to anthropic considerations.

Abstract

A scan of soft SUSY breaking parameters within the string theory landscape with the MSSM assumed as the low energy effective field theory -- using a power-law draw to large soft terms coupled with an anthropic selection of a derived weak scale to be within a factor four of our measured value -- predicts a peak probability of m_h~125 GeV with sparticles masses typically beyond the reach of LHC Run 2. Such multiverse simulations usually assume a fixed value of the SUSY conserving superpotential mu parameter to be within the assumed anthropic range, mu<~ 350 GeV. However, depending on the assumed solution to the SUSY mu problem, the expected mu term distribution can actually be derived. In this paper, we examine two solutions to the SUSY mu problem. The first is the gravity-safe-Peccei-Quinn (GSPQ) model based on an assumed Z_{24}^R discrete R-symmetry which allows a gravity-safe accidental, approximate Peccei-Quinn global symmetry to emerge which also solves the strong CP problem. The second case is the Giudice-Masiero solution wherein the mu term effectively acts as a soft term and has a linear draw to large values. For the first case, we also present the expected landscape distribution for the PQ scale f_a; in this case, weak scale anthropics limits its range to the cosmological sweet zone of around f_a~ 10^{11} GeV.