Search for dark matter in a signature with a four-prong large-radius jet in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Technical Summary: Search for Dark Matter in a Signature with a Four-Prong Large-Radius Jet

Problem and Motivation
While the nature of dark matter (DM) remains unknown, extensions to the Standard Model (SM) often predict a "dark sector" containing additional, potentially long-lived particles. This paper investigates a specific nonprompt DM signature where DM candidates are produced in association with initial-state radiation (ISR). The signal model posits a heavy vector or axial-vector mediator ($Y_1$) that couples the SM to a dark sector. This mediator decays into a pair of Dirac fermions ($\chi_2$), which are long-lived and decay nonpromptly into a stable DM particle ($\chi_1$) and a light scalar boson ($Y_0$). The $Y_0$ boson subsequently decays into a pair of SM quarks.

The characteristic signature involves the production of two long-lived $\chi_2$ particles that decay within the detector ("displaced decays"), generating displaced hadronic activity accompanied by significant missing transverse momentum ($p_T^{miss}$) from the two undetected $\chi_1$ particles. Due to the large Lorentz boost of the $Y_1$ system and the small masses of the decay chain particles, the four quarks resulting from the two $Y_0$ decays are expected to be highly collimated. Consequently, the analysis targets events where these four quarks are reconstructed as a single large-radius jet with a four-prong substructure.

Methodology
The analysis utilizes proton-proton collision data collected by the CMS detector at $\sqrt{s} = 13$ TeV during 2016–2018, corresponding to an integrated luminosity of 138 fb$^{-1}$.

• Event Selection: Events are selected requiring at least two large-radius (AK8) jets with transverse momentum $p_T > 200$ GeV and pseudorapidity $|\eta| < 2.5$. The leading AK8 jet must have $p_T > 500$ GeV to ensure high trigger efficiency. A minimum $p_T^{miss}$ of 200 GeV is required to suppress SM backgrounds lacking genuine missing energy. Events containing reconstructed leptons (electrons, muons, or hadronic taus) are rejected.
• Jet Tagging: A Graph Neural Network (GNN) based classifier is employed to identify signal-like jets. The network utilizes an interaction network architecture that constructs a graph from the jet constituents (particles) and secondary vertex information. This approach explicitly models relational information between particles, which is crucial for identifying the nontrivial correlations introduced by displaced topologies. The GNN is trained on simulated signal jets (spanning various mediator masses and lifetimes) and QCD multijet background jets.
• Signal Region (SR) Definition: The SR is defined by selecting events where the leading AK8 jet has an ungroomed PUPPI mass exceeding 40 GeV and a GNN tagger score $s_{GNN} > 0.8$.
• Background Estimation:
  • QCD Multijet: Estimated using a Control Region (CR) with $0.4 < s_{GNN} < 0.8$. Transfer factors (TFs) derived from simulation are used to extrapolate the QCD yield from the CR to the SR.
  • W + Jets: Estimated using a CR containing exactly one lepton and an AK8 jet with $0.4 < s_{GNN} < 0.8$.
  • Z + Jets: Estimated using a CR with $Z(\to \ell\ell) + \text{jets}$ events, utilizing the hadronic recoil vector to emulate the $p_T^{miss}$ distribution of $Z(\to \nu\nu) + \text{jets}$.
  • Subdominant Backgrounds: Top quark production and diboson processes are estimated using Monte Carlo simulation.
• Statistical Analysis: A binned maximum likelihood fit is performed on the $p_T^{miss}$ distribution in the SR. Systematic uncertainties, including those related to jet energy scale/resolution, GNN tagger efficiency (validated via Lund jet plane reweighting), and transfer factor statistical fluctuations, are incorporated as nuisance parameters.

Key Contributions

• First Search in Boosted Displaced Topology: This work presents the first search for a pair of nonprompt DM candidates in a Lorentz-boosted topology characterized by a large-radius jet and large $p_T^{miss}$.
• Application of GNNs to Displaced Jets: The analysis extends the use of GNN-based jet taggers, previously applied to prompt multiprong signatures, to displaced large-radius jets. It validates the use of secondary vertex information within the graph structure to enhance sensitivity to nonprompt decays.
• Comprehensive Background Modeling: The study employs a data-driven approach for the dominant backgrounds (QCD, W+jets, Z+jets) using dedicated control regions and transfer factors, ensuring robustness against simulation uncertainties.

Results
No significant excess of events over the Standard Model expectation is observed in the missing transverse momentum spectrum. Upper limits at 95% confidence level (CL) are set on the signal strength ($\mu = \sigma/\sigma_{theory}$) as functions of the mediator mass ($m_{Y_1}$) and the coupling strength ($g_{\chi_2\chi_1Y_0}$). The observed limits agree with the expected limits within two standard deviations. The analysis excludes specific signal hypotheses corresponding to the tested parameter space, as detailed in the benchmark scenarios (Table 1) and Figure 4.

Significance
The paper claims significance as the inaugural search for this specific experimental signature: a pair of nonprompt dark matter candidates produced in a Lorentz-boosted topology. By successfully reconstructing the decay of light mediators into four quarks as a single large-radius jet and utilizing advanced machine learning techniques to identify displaced substructures, the analysis demonstrates the capability of the CMS detector to probe complex dark sector models involving long-lived particles. The results constrain the parameter space of the simplified model under investigation, specifically excluding regions defined by the tested mediator masses and coupling strengths.