Impact of recent measurement of $(g-2)_\mu$, LHC search for supersymmetry, and LZ experiment on Minimal Supersymmetric Standard Model

Abstract

Motivated by the recent measurement of muon anomalous magnetic moment at Fermilab, the rapid progress of the LHC search for supersymmetry, and the significantly improved sensitivities of dark matter direct detection experiments, we studied their impacts on the Minimal Supersymmetric Standard Model (MSSM). We conclude that higgsino mass should be larger than about $500~{\rm GeV}$ for $M_1 < 0 $ and $630~{\rm GeV}$ for $M_1 > 100~{\rm GeV}$, where $M_1$ denotes the bino mass. These improved bounds imply a tuning of ${\cal{O}}(1\%)$ to predict the $Z$-boson mass and simultaneously worsen the naturalness of the $Z$- and $h$-mediated resonant annihilations to achieve the measured dark matter density. We also conclude that the LHC restrictions have set lower bounds on the sparticle mass spectra: $ m_{\tilde{\chi}_1^0} \gtrsim 210~{\rm GeV}$, $m_{\tilde{\chi}_2^0}, m_{\tilde{\chi}_1^\pm} \gtrsim 235~{\rm GeV}$, $m_{\tilde{\chi}_3^0} \gtrsim 515~{\rm GeV}$, $m_{\tilde{\chi}_4^0} \gtrsim 525~{\rm GeV}$, $m_{\tilde{\chi}_2^\pm} \gtrsim 530~{\rm GeV}$, $m_{\tilde{\nu}_\mu} \gtrsim 235~{\rm GeV}$, $ m_{\tilde{\mu}_1} \gtrsim 215~{\rm GeV}$, and $m_{\tilde{\mu}_2} \gtrsim 250~{\rm GeV}$, where $\tilde{\chi}_{2}^0$ and $\tilde{\chi}_1^\pm$ are wino-dominated when they are lighter than about $500~{\rm GeV}$. These bounds are far beyond the reach of the LEP experiments in searching for supersymmetry and have not been acquired before. In addition, we illuminate how some parameter spaces of the MSSM have been tested at the LHC and provide five scenarios in which the theory coincides with the LHC restrictions. Once the muon g-2 anomaly is confirmed to originate from supersymmetry, this research may serve as a guide to explore the characteristics of the MSSM in future experiments.