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The fine-tuning price of the early LHC

Alessandro Strumia

TL;DR

The work addresses the naturalness of the weak scale within the CMSSM in light of early LHC data. It employs a Bayesian Monte Carlo scan of the CMSSM parameter space, incorporating the electroweak minimization relation $M_Z^2 \approx 0.7 M_3^2 + 0.2 m_0^2 - 2 \mu^2$ with $M_3 \approx 2.6 M_{1/2}$ and loop corrections, to quantify fine-tuning and the fraction of parameter space that survives LHC and Higgs-mass constraints (approximated by $m_h^{\rm th}>110$ GeV). The main finding is that only about $0.3\%$ of CMSSM survives under these bounds, rising to about $0.9\%$ if the bound on the Higgs mass is circumvented; LHC data thus intensify the little hierarchy problem. The paper discusses possible theoretical directions (e.g., pseudo-Goldstone Higgs, dynamically fixed SUSY scale, anthropic scenarios) and notes that some simple naturalness expectations like a very light gluino are increasingly disfavored, guiding future model-building under experimental pressure.

Abstract

LHC already probed and excluded half of the parameter space of the Constrained Minimal Supersymmetric Standard Model allowed by previous experiments. Only about 0.3% of the CMSSM parameter space survives. This fraction rises to about 0.9% if the bound on the Higgs mass can be circumvented.

The fine-tuning price of the early LHC

TL;DR

The work addresses the naturalness of the weak scale within the CMSSM in light of early LHC data. It employs a Bayesian Monte Carlo scan of the CMSSM parameter space, incorporating the electroweak minimization relation with and loop corrections, to quantify fine-tuning and the fraction of parameter space that survives LHC and Higgs-mass constraints (approximated by GeV). The main finding is that only about of CMSSM survives under these bounds, rising to about if the bound on the Higgs mass is circumvented; LHC data thus intensify the little hierarchy problem. The paper discusses possible theoretical directions (e.g., pseudo-Goldstone Higgs, dynamically fixed SUSY scale, anthropic scenarios) and notes that some simple naturalness expectations like a very light gluino are increasingly disfavored, guiding future model-building under experimental pressure.

Abstract

LHC already probed and excluded half of the parameter space of the Constrained Minimal Supersymmetric Standard Model allowed by previous experiments. Only about 0.3% of the CMSSM parameter space survives. This fraction rises to about 0.9% if the bound on the Higgs mass can be circumvented.

Paper Structure

This paper contains 4 sections, 6 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Naturalness
  3. Conclusions
  4. Acknowledgements

Figures (3)

  • Figure 1: A typical example of the parameter space of the CMSSM model. The green region is allowed (see it in the enlarged box). The dashed line around the boundary of the allowed region is the prediction of the model considered in BS.
  • Figure 2: Left: naturalness scan of the CMSSM. Red points are excluded by LHC, black points have been excluded earlier, green points are allowed. The darker pink region was excluded by LEP and the pink region by early LHC (the red lines show the various bounds from ATLAS and CMS). Right: "naturalness probability distribution" for the gluino mass in the CMSSM. Only its tail was allowed after LEP, and the tail of the tail remains allowed after first LHC data.
  • Figure 3: As in the previous figure \ref{['fig:scan']}a, but assuming that the sparticle mass scale is dynamically determined by minimizing the MSSM potential BS, such that it is naturally heavier than $M_Z$.