$t \bar{t}$ production as a window to invisible new physics

Technical Summary: $t\bar{t}$ Production as a Window to Invisible New Physics

Problem and Motivation
Despite numerous theoretical proposals for Dark Matter (DM), no experimental observation has been confirmed. A primary goal of current searches is to develop methods to detect or exclude DM candidates, particularly those interacting with the Standard Model (SM) via a mediator particle. Recent observations by the ATLAS and CMS collaborations of an enhancement in the $t\bar{t}$ production cross-section near threshold have renewed interest in Beyond-the-Standard-Model (BSM) scenarios involving pseudoscalar mediators coupled to top quarks. While SM dynamics may explain a significant portion of this enhancement, room remains for additional contributions. This study addresses the need to probe the sensitivity to invisible DM mediators produced in association with a $t\bar{t}$ pair at the Large Hadron Collider (LHC), specifically extending previous work on scalar mediators to include spin-1 mediators (vector and axial-vector).

Methodology
The authors employ a phenomenological approach using the simplified DM model DMsimp, which includes spin-0 ($Y_0$) and spin-1 ($Y_1$) mediators interacting with a dark sector of Dirac fermions. The analysis focuses on the process $pp \to t\bar{t}Y$, where $Y$ is an invisible mediator with a fixed mass of $m_Y = 5$ GeV.

• Event Generation: Signal samples for $pp \to t\bar{t}Y_0$ (spin-0) and $pp \to t\bar{t}Y_1$ (spin-1) were generated using MadGraph5_aMC@NLO at $\sqrt{s} = 13$ TeV. Spin-0 signals were generated at Leading Order (LO), while spin-1 signals were generated at Next-to-Leading Order (NLO) in QCD to ensure accuracy at low mediator masses. The analysis considers only the dileptonic decay channel of the $t\bar{t}$ system ($t\bar{t} \to b\ell^+\nu_\ell \bar{b}\ell^-\bar{\nu}_\ell$).
• Simulation and Reconstruction: Events were processed through parton showering (PYTHIA) and a fast detector simulation (Delphes) with ATLAS parameters. A key methodological feature is the kinematic reconstruction of the $t\bar{t}$ system without explicitly reconstructing the invisible mediator. This involves:
  1. Assigning jets to $b$-quarks using a Boosted Decision Tree with Gradient boosting (BDTG) trained on parton-level distributions (e.g., $\Delta R$, $\Delta \phi$, $\Delta \theta$ between leptons and $b$-jets) to distinguish correct from wrong pairings.
  2. Solving a system of kinematic equations based on $W$ and top mass constraints and missing transverse energy ($E_T^{miss}$) to reconstruct neutrino momenta.
• Observables: The study utilizes two CP-sensitive angular observables to discriminate between hypotheses:
  1. $\Delta \phi_{\ell^+\ell^-}$: The azimuthal angle difference between the charged leptons.
  2. $b_4$: Defined as $p_z^t \cdot p_z^{\bar{t}} / (|\vec{p}_t| \cdot |\vec{p}_{\bar{t}}|)$, representing the product of the polar cosines of the top and anti-top quarks in the laboratory frame.
• Statistical Analysis: Confidence Level (CL) exclusion limits were calculated for various scenarios comparing SM backgrounds against signal hypotheses involving pure or mixed spin-0 and spin-1 mediators.

Key Contributions

1. Extension to Spin-1 Mediators: The work extends previous analyses of scalar mediators to include spin-1 mediators ($Y_1$) with both vector ($g_V$) and axial-vector ($g_A$) couplings to top quarks.
2. Kinematic Reconstruction Efficiency: The authors demonstrate that full kinematic reconstruction of the $t\bar{t}$ system remains effective even in the presence of a light spin-1 mediator. While reconstruction efficiency drops slightly compared to the spin-0 case (68% for vector, 48% for axial-vector at $m_Y=5$ GeV), a significant fraction of events survives, suggesting standard $t\bar{t}$ analyses are sensitive to such invisible particles.
3. Perturbative Unitarity Constraints: The paper explicitly addresses the constraints imposed by perturbative unitarity on axial-vector couplings. It highlights that for light mediators, the axial-vector cross-section scales as $1/m_Y^2$ due to the non-conservation of the axial current, requiring a correlation between the coupling $g_A$ and the mediator mass to remain within perturbative bounds.
4. Discrimination Power: The study quantifies the ability of angular observables to distinguish between different spin and CP hypotheses (scalar, pseudoscalar, vector, axial-vector).

Results

• Exclusion Limits: For an integrated luminosity of $3000 \text{ fb}^{-1}$ (HL-LHC), the analysis sets stringent exclusion limits on the couplings $g_V/g_V^{SM}$ and $g_A/g_A^{SM}$. The limits on axial-vector couplings are significantly stronger than those for vector couplings due to the larger cross-section.
• Observable Sensitivity:
  • The $b_4$ observable is identified as the most sensitive probe for distinguishing the parity (P) nature of spin-1 mediators (distinguishing vector from axial-vector) and for excluding scalar components in the presence of a vector mediator.
  • The $\Delta \phi_{\ell^+\ell^-}$ observable proves more effective for distinguishing pseudoscalar components from vector mediators, as the $b_4$ distributions for vector and pseudoscalar cases are too similar.
• Scenario Analysis:
  • Scenario 1 (SM Null): The analysis can exclude the presence of spin-1 mediators with couplings significantly below the benchmark values.
  • Scenarios 2 & 3 (Discovery Null): Assuming a discovery of a pure vector or axial-vector mediator, the study shows that angular observables can effectively constrain the presence of mixed states (e.g., vector + scalar, vector + pseudoscalar). However, distinguishing a pure vector mediator from a pseudoscalar one remains challenging at lower luminosities ($200 \text{ fb}^{-1}$), particularly if the vector coupling is small.
• Higgs Constraints: An appendix derives a bound on the vector coupling $g_V$ from the Higgs invisible decay width ($h \to Y_1 Y_1$) via a top-quark loop. The resulting bound ($|g_V| \lesssim 1.04$) is found to be weaker than the exclusion limits derived from the $t\bar{t}$ analysis at high luminosity.

Significance and Claims
The paper claims that $t\bar{t}$ final states at the LHC serve as a powerful framework not only for searching for invisible particles but also for characterizing their fundamental properties (spin and parity) in the event of a discovery. The authors emphasize that:

• Kinematic reconstruction techniques used for standard $t\bar{t}$ analyses are robust enough to retain sensitivity to events containing light invisible mediators.
• CP-sensitive angular observables provide necessary discrimination power to differentiate between vector, axial-vector, scalar, and pseudoscalar scenarios.
• While high luminosity (HL-LHC) significantly improves the ability to distinguish between hypotheses, certain regions of parameter space (e.g., distinguishing pure vector from pseudoscalar at low couplings) remain unconstrained, implying that invisible particles could exist in $t\bar{t}$ events without producing clearly distinguishable signatures in this specific channel alone.
• The results highlight the complementarity of $t\bar{t}$ searches with other probes, such as Higgs invisible width measurements, for constraining top-philic dark sectors.