What the Fermilab muon g − 2 experiment tells us about discovering supersymmetry at high luminosity and high energy upgrades to the LHC

Using an artificial neural network, we explore the parameter space of supergravity grand unified models consistent with the combined Fermilab E989 and Brookhaven E821 data on (g − 2)μ. Within an extended mSUGRA model with nonuniversal gaugino masses, the analysis indicates that the region favored by the data is the one generated by gluino-driven radiative breaking of the electroweak symmetry (g SUGRA). This region naturally leads to a split sparticle spectrum with light sleptons and weakinos but heavy squarks, with the stau and the chargino as the lightest charged particles. We show that if the entire deviation from the Standard Model (g − 2)μ arises from supersymmetry, then supersymmetry is discoverable at HL-LHC and HE-LHC via production and decay of sleptons and sneutrinos within the optimal integrated luminosity of HL-LHC and with a smaller integrated luminosity at HE-LHC. The effect of C P phases on the muon anomaly is investigated, and the parameter space of C P phases excluded by the Fermilab constraint is exhibited.