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 $(g-2{)}_{\mu }$. 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 ($\tilde{g}\mathrm{SUGRA}$). 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 $(g-2{)}_{\mu }$ 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 $CP$ phases on the muon anomaly is investigated, and the parameter space of $CP$ phases excluded by the Fermilab constraint is exhibited.

Figure 1

$\mathrm{\Delta }{a}_{\mu }^{\mathrm{SUSY}}$ arising from the SUGRA parameter space using an ANN. The points satisfy the Higgs boson mass, the dark matter relic density, and limits from dark matter direct detection experiments and the LHC. One sigma error corridor on $\mathrm{\Delta }{a}_{\mu }$ experimental result from Brookhaven (red dashed lines) and from the combined Fermilab and Brookhaven result (blue dashed lines) are also displayed.

Figure 2

A scatter plot of $\mathrm{\Delta }{a}_{\mu }$ versus the chargino mass as a result of a scan of the SUGRA parameter space using an artificial neural network. The points satisfy the Higgs boson mass, the dark matter relic density, and limits from dark matter direct detection experiments and the LHC.

Figure 3

The same scatter plots as in Figs. 1 (top panel) and 2 but with the LHC constraints relaxed. We note that the dips in the model points in the smuon mass range near 600 GeV and in the chargino mass range near 800 GeV that appeared in Figs. 1 (top panel) and 2 are now populated.

Figure 4

A scatter plot in the lightest neutralino mass-right-handed smuon mass plane. The color axis denotes the ratio $m_2/m_1$. Notice that the larger $m_2/m_1$ is the lighter ${\tilde{\mu }}_{\mathrm{R}}$ becomes.

Figure 5

Exhibition of the light sparticle spectrum in $\tilde{g}\mathrm{SUGRA}$ models constrained by $\mathrm{\Delta }{a}_{\mu }^{\mathrm{FB}}$. The top panel is for the case of chargino NLSP and bottom panel is for the stau NLSP. The plots are drawn using PySLHA [50].

Figure 6

Spin-independent proton-neutralino cross section ${\sigma }_{\mathrm{SI}}$ as a function of the neutrino mass constrained by $\mathrm{\Delta }{a}_{\mu }^{\mathrm{FB}}$. Here $R=\mathrm{\Omega }{h}^2/(\mathrm{\Omega }{h}^2{)}_{\text{Planck}}$ where $(\mathrm{\Omega }{h}^2{)}_{\text{Planck}}\sim 0.12$.

Figure 7

A two-dimensional plot in the number of ISR jets ($N_{\mathrm{ISR}}$) versus non-ISR jets ($N_{\text{jet}}$).

Figure 8

A sample of the discriminating variables using by the DNN for training and testing. The distributions are in the normalized number of events scaled by a specific integrated luminosity to show the discriminating power of each variable.

Figure 9

Distributions in the DNN response for the signal (dashed histogram) and background (colored histograms) events pertaining to benchmark (a) at 14 TeV (top panel) and 27 TeV (bottom panel) for the signal region $\mathrm{SR}\text{−}2\ell 2\mathrm{j}$ in the slepton pair production channel. The bottom pad of each panel shows the significance as defined by Eq. (8) as a function of the cut on the “DNN response” variable. The binning for the significance distribution is finer to clearly show the rise and fall of the significance.

Figure 10

Distributions in the DNN response for the signal (dashed histogram) and background (colored histograms) events pertaining to benchmark (d) at 14 TeV (top panel) and 27 TeV (bottom panel) for the signal region $\mathrm{SR}\text{−}2\ell 1\mathrm{j}$ in the slepton associated production channel. The bottom pad of each panel shows the significance as defined by Eq. (8) as a function of the cut on the “DNN response” variable. The binning for the significance distribution is finer to clearly show the rise and fall of the significance.

Figure 11

The integrated luminosities needed for discovery of SUSY at HL-LHC and HE-LHC assuming that $\mathrm{\Delta }{a}_{\mu }^{\mathrm{FB}}$ arises from SUSY loops. The signal regions and production modes shown are the ones giving the highest sensitivity for discovery. Also shown are the integrated luminosities after including the “YR18” uncertainties on the signal and background.

Figure 12

Top and middle panels: Exclusion plots in the $CP$ phases ${\xi }_1$ and ${\xi }_2$ arising from the $\mathrm{\Delta }{a}_{\mu }^{\mathrm{FB}}$ constraint. The contours correspond to $\mathrm{\Delta }{a}_{\mu }\times {10}^9$ consistent with the combined experimental result on $g-2$. Bottom panel: Variation of $a_{\mu }^{\mathrm{SUSY}}$ with the phase ${\xi }_2$. In all plots, ${\alpha }_{A_0}=0.2\mathrm{rad}$. The masses of the light particles in the loops are in this order $(\tilde{\mu },{\tilde{\chi }}_1^{\pm },{\tilde{\chi }}_1^0)$: (400,392,1,391.7) GeV for the top panel and (445,301.6,301.4) GeV for the middle panel and shown in the legend for the bottom panel. The star in the top and middle panels indicate illustrative tiny regions of the cancellation mechanism [73], where one can simultaneously obtain a muon $g-2$ and the electron EDM consistent with experiment, $|d_e|<1.1\times {10}^{-29}e\mathrm{cm}$.