[Paper Review] Indications of the CMSSM Mass Scale from Precision Electroweak Data

John Ellis, S. Heinemeyer+2 more|ArXiv.org|Apr 21, 2006

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper re-evaluates constraints on the CMSSM mass scale using precision electroweak data, including updated top quark mass and LEP Higgs bounds. It finds persistent indications for a low supersymmetry scale, with preferred $ m_{1/2} \sim 300\text{--}600\,\text{GeV} $, strongly supported by $ (g-2)_\mu $, and robust under updated $ m_t $ and $ M_h $ constraints.

ABSTRACT

We discuss the sensitivities of present-day electroweak precision data to the possible scale of supersymmetry within the constrained minimal supersymmetric extension of the Standard Model (CMSSM). Our analysis is based on M_W, sin^2 theta_eff, (g-2)_mu, BR(b -> s gamma), and the lightest MSSM Higgs boson mass, M_h. We display the impact of the recent reduction in m_t from 178.0 +- 4.3 GeV to 172.7 +- 2.9 GeV on the interpretation of the precision observables. We show the currently preferred values of the CMSSM mass scale m_{1/2} based on a global chi^2 fit, assuming that the lightest supersymmetric particle (LSP) is a neutralino, and fixing m_0 so as to obtain the cold dark matter density allowed by WMAP and other cosmological data for specific values of A_0, tan beta and mu > 0. The recent reduction in m_t reinforces previous indications for relatively light soft supersymmetry-breaking masses, offering good prospects for the LHC and the ILC, and in some cases also for the Tevatron. Finally, we discuss the sensitivity of the global chi^2 function to possible future evolution in the experimental central value of m_t and its error.

Motivation & Objective

• To reassess the preferred scale of supersymmetry breaking in the CMSSM using updated precision electroweak data.
• To evaluate the impact of the revised top quark mass ($ m_t = 172.7 \pm 2.9\,\text{GeV} $) on CMSSM parameter constraints.
• To incorporate improved treatment of the LEP direct Higgs search bound on $ M_h $ in the global $ \chi^2 $ analysis.
• To assess the robustness of the preferred $ m_{1/2} $ range against future changes in $ m_t $'s central value and uncertainty.
• To determine the prospects for discovering supersymmetric particles at the LHC, ILC, and Tevatron based on current data.

Proposed method

• Performs a global $ \chi^2 $ fit to precision electroweak observables: $ M_W $, $ \sin^2\theta_{\text{eff}} $, $ (g-2)_\mu $, $ \text{BR}(b \to s\gamma) $, and $ M_h $.
• Fixes $ m_0 $ to satisfy the WMAP cold dark matter density constraint $ 0.094 < \Omega_{\text{CDM}}h^2 < 0.129 $, with $ \mu > 0 $, $ \tan\beta $, and $ A_0 $ as parameters.
• Uses the constrained minimal supersymmetric standard model (CMSSM) framework with universal soft-breaking masses at the GUT scale.
• Applies theoretical predictions for loop-induced processes and Higgs masses within the MSSM, including radiative corrections.
• Evaluates the sensitivity of the $ \chi^2 $ function to variations in $ m_t $'s central value and experimental error $ \delta m_t $, keeping other observables fixed.
• Computes 90% confidence level upper limits on $ m_{1/2} $ and tracks the minimum $ \chi^2 $ as a function of $ m_t $ and $ \delta m_t $.

Experimental results

Research questions

• RQ1 How does the updated $ m_t = 172.7 \pm 2.9\,\text{GeV} $ affect the preferred $ m_{1/2} $ range in the CMSSM?
• RQ2 To what extent does the LEP bound on the lightest MSSM Higgs boson mass $ M_h $ influence the global $ \chi^2 $ fit and the preferred $ m_{1/2} $ values?
• RQ3 Is the preference for low $ m_{1/2} $ values robust against changes in the central value and uncertainty of $ m_t $?
• RQ4 What are the implications of the current data for the discovery potential of supersymmetric particles at the LHC, ILC, and Tevatron?
• RQ5 How sensitive is the global $ \chi^2 $ function to future experimental updates of $ m_t $?

Key findings

• The updated $ m_t = 172.7 \pm 2.9\,\text{GeV} $ reinforces the previous preference for low soft-breaking masses in the CMSSM, with $ m_{1/2} \sim 300\text{--}600\,\text{GeV} $.
• The minimum $ \chi^2 $ value increases noticeably for $ m_t < 170\,\text{GeV} $, but remains nearly unchanged for $ m_t $ in the range $ 170\text{--}180\,\text{GeV} $.
• The 90% confidence level upper limit on $ m_{1/2} $ varies by less than 10% for $ m_t \gtrsim 170\,\text{GeV} $, indicating robustness against $ m_t $ uncertainty.
• The preference for low $ m_{1/2} $ is primarily driven by $ (g-2)_\mu $, with additional support from $ M_W $ and $ \sin^2\theta_{\text{eff}} $.
• The preferred $ m_{1/2} $ range corresponds to gluinos and other sparticles being light enough for discovery at the LHC and the ILC.
• Future measurements of $ M_W $ and $ m_t $ at the Tevatron are expected to be particularly important for further constraining the CMSSM parameter space.