Probing torsion field with Einstein-Cartan gravity at the HL-LHC: an angular distribution case study

TL;DR

This work investigates the angular distribution of high-mass dimuon pairs at the HL-LHC within a simplified Einstein-Cartan gravity model that includes a torsion field and a dark neutral gauge boson $A′$ coupled to dark matter. The analysis exploits the Collins-Soper frame observable $\cos\theta_{CS}$ to distinguish a spin-2–like signal from Standard Model backgrounds, using privately generated HL-LHC simulations at $\sqrt{s}=14$ TeV and $\mathcal{L}=3000\,\mathrm{fb}^{-1}$. Signal and background samples are produced with MG5_aMC@NLO, Pythia 8, and DELPHES, with a tight set of event selections that leverage the $\mu^+\mu^-+E_T^{miss}$ signature and angular variables. The results yield projected 5$\sigma$ discovery claims for certain $(M_{A′}, M_{TS})$ combinations and provide 95% CL upper limits on $\sigma\times\mathrm{BR}(A′\to μμ)$, along with mass exclusions for the torsion field, thereby highlighting the discriminating power of angular observables in probing torsion- and dark-sector physics at the HL-LHC.

Abstract

This analysis utilizes simulated data privately generated based on the High Luminosity Large Hadron Collider (HL-LHC) configuration to investigate the angular distribution of high-mass dimuon pairs produced during the foreseen proton-proton collisions at a center-of-mass energy of 14 TeV. The study focuses on the cos$θ_{CS}$ variable, which is defined in the Collins-Soper frame. In the Standard Model, the production of high-mass dimuon pairs is primarily governed by the Drell-Yan process, which demonstrates a significant forward-backward asymmetry. However, scenarios beyond the Standard Model suggest different shapes for the cos$θ_{CS}$ distribution. By observing excess events not predicted by the Standard Model, the angular distribution can help differentiate among these alternative models. Furthermore, we used a simplified Einstein-Cartan gravity model to analyze the simulated data. This analysis established upper limits at the 95\% confidence level regarding the masses of various particles within the model, including a spin-2 dark neutral gauge boson and the torsion field.

Figures (8)

• Figure 1: Feynman diagram for the simplified model based on Einstein-Cartan gravity; for the production of dark gauge boson (A$^{\prime}$) in association to dark matter ($\chi$) pair R1.
• Figure 2: Normalized distributions of cos$\theta_{CS}$ for one resonant model based on Einstein-Cartan gravity generated with a mass of $A^{\prime}$ equal to 200 GeV and Drell-Yan events at $\sqrt{s} = 14$ TeV. All events must pass the pre-selection listed in table \ref{['table:selection2']} and have a reconstructed invariant mass in the 160 - 240 GeV range. All histograms are normalized to unity to highlight qualitative features.
• Figure 3: Distributions of cos$\theta_{CS}$ are illustrated, for events passing pre-selection listed in table \ref{['table:selection2']}, for the standard model expectations (histograms) for several dimuon mass windows: 160 $< M_{\mu^+\mu^-} <$ 240 GeV \ref{['bin1']}, 260 $< M_{\mu^+\mu^-} <$ 340 GeV \ref{['bin2']}, 360 $< M_{\mu^+\mu^-} <$ 440 GeV \ref{['bin3']}, 460 $< M_{\mu^+\mu^-} <$ 540 GeV \ref{['bin4']}, and 560 $< M_{\mu^+\mu^-} <$ 640 GeV \ref{['bin5']}. The signal presentation of the model corresponding to the Einstein-Cartan gravity with the value of $M_{A^{\prime}}$ runs from 200 to 600 GeV is superimposed.
• Figure 4: Distributions of $\Delta\phi_{\mu^{+}\mu^{-},\vec{E}_{T}^{\text{miss}}}$\ref{['deltaphi']}, $|E_{T}^{\mu^{+}\mu^{-}} - E_{T}^{\text{miss}}|/E_{T}^{\mu^{+}\mu^{-}}$\ref{['ptdiff']}, $\text{cos}(\text{angle}_{3D})$\ref{['3Dangle']}, and the number of jets \ref{['Njets']} for the signal presentations of the model corresponding to the Einstein-Cartan gravity with $M_{A^{\prime}} =$ 200 and 500 GeV and SM backgrounds, for dimuon events with each muon passing the pre-selection summarized in table \ref{['table:selection2']}.
• Figure 5: Distributions of the N-1 efficiencies plotted against the transverse momentum of the leading reconstructed muon ($p^{\mu}_{T}$) for the 4 analysis cuts. Illustrated for the signal in the EC gravity scenario with $M_{TS} = 2000$ GeV, $M_{A'} = 200$ GeV, and coupling constants $\texttt{g}_{\eta} = 0.125$ and $\texttt{g}_{D} = 1.0$ and for the SM backgrounds.