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

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.

💡 Research Summary

This paper investigates the possibility of detecting a torsion field and a spin‑2 dark neutral gauge boson (denoted A′) within a simplified Einstein‑Cartan (EC) gravity framework using simulated data for the High‑Luminosity Large Hadron Collider (HL‑LHC) operating at √s = 14 TeV with an integrated luminosity of 3000 fb⁻¹. The authors focus on the angular distribution of high‑mass dimuon pairs, specifically the cosine of the Collins‑Soper (CS) polar angle, cos θ_CS, which is designed to reduce distortions from the transverse momenta of the incoming partons and to provide a clean observable for forward‑backward asymmetry studies.

In the Standard Model (SM), dimuon production at high invariant mass is dominated by the Drell‑Yan (DY) process, which exhibits a pronounced forward‑backward asymmetry (A_FB). New physics scenarios, such as those involving a torsion field coupled axially to fermions, predict different shapes for the cos θ_CS distribution. In the EC model considered, a heavy torsion field (mass M_TS) mediates quark‑antiquark annihilation into a pair of dark matter fermions (χ) with mass M_χ = 500 GeV. The χ particles can subsequently produce a dark gauge boson A′ (mass M_A′) which decays into a muon pair, yielding the experimental signature μ⁺μ⁻ + missing transverse energy (E_T^miss). The torsion‑fermion axial coupling is fixed at g_η = 0.125, while the A′‑χ coupling is set to g_D = 1.0, following recommendations from the LHC Dark Matter Working Group.

Signal events are generated with MadGraph5_aMC@NLO (v3.5.0) at next‑to‑leading order (NLO), showered with Pythia 8, and passed through a fast detector simulation of the CMS experiment using Delphes, configured for HL‑LHC conditions. The SM backgrounds (DY, tt̄, tW, WW, ZZ, WZ, and QCD‑jet fakes) are simulated with the same tool chain and normalized to their NLO cross sections. All samples are scaled to 3000 fb⁻¹.

Event selection proceeds in two stages. The pre‑selection requires two opposite‑sign muons with p_T > 30 GeV, |η| < 2.5, and isolation criteria, as well as a dimuon invariant mass above 60 GeV. For the signal region, the dimuon mass is constrained to a window around the hypothesized A′ mass (±40 GeV). Additional “tight” cuts exploit the kinematic correlation between the dimuon system and the missing transverse energy: (i) Δϕ(μμ, E_T^miss) > 2.5 rad, (ii) |E_T^{μμ} − E_T^miss|/E_T^{μμ} < 0.4, (iii) a minimum azimuthal separation between the muons and the missing momentum, and (iv) a veto on extra jets (N_jets < 1) to suppress tt̄ and diboson contributions.

After these selections, the authors examine the normalized cos θ_CS distribution for events with reconstructed dimuon masses in the 460–540 GeV window, which corresponds to an A′ mass of 500 GeV in the benchmark scenario. The SM DY distribution shows the expected asymmetric shape, while the EC signal yields a symmetric distribution peaked at cos θ_CS ≈ 0, characteristic of a spin‑2 resonance. The signal shape is well described by the functional form par