[Paper Review] Extra Quarks Decaying to Dark Matter Beyond the Narrow Width Approximation

Hugo Prager, Stefano Moretti+2 more|arXiv (Cornell University)|Jun 13, 2017

Particle physics theoretical and experimental studies8 references3 citations

TL;DR

This paper investigates the impact of finite widths on top-quark partner (XQ) decays to dark matter (DM) at the LHC, showing that large widths significantly alter signal cross-sections and experimental bounds beyond the Narrow Width Approximation (NWA). It demonstrates that including off-shell topologies and width effects increases sensitivity, especially for light DM and couplings to light quarks, enabling better DM spin discrimination and more robust exclusion limits.

ABSTRACT

We explore the effects induced by a finite width in processes of pair production of a heavy top-quark partner and its subsequent decay into a bosonic Dark Matter (DM) candidate -- either scalar or vector -- and a SM up-type quark at the Large Hadron Collider (LHC). We discuss the configurations of masses, widths and couplings where this phenomenology can be important in a simple model with just one such objects. Finally, we emphasise the correct definition of signal and background to be adopted as well as stress the importance of new dedicated experimental searches.

Motivation & Objective

• To assess the validity and limitations of the Narrow Width Approximation (NWA) in interpreting LHC searches for extra quarks decaying to dark matter.
• To identify parameter regions—particularly large XQ widths—where NWA fails and full signal calculations are essential for accurate interpretation.
• To quantify the impact of gauge-invariant topologies (including single XQ production) on signal cross-sections and exclusion bounds.
• To guide future experimental searches by highlighting the importance of dedicated strategies that account for finite widths and spin-dependent effects.
• To enable more sensitive and model-dependent reinterpretation of existing LHC data for XQ–DM phenomenology, especially for light DM and light quark couplings.

Proposed method

• Performs a full partonic-level calculation of signal cross-sections, including all gauge-invariant topologies (e.g., single XQ production) beyond the NWA.
• Uses MadGraph5 and FeynRules to implement a simplified model with a vector-like top-quark partner (T) coupling to scalar or vector DM via a Z2-odd interaction.
• Scans over three free parameters: XQ mass (M_T), DM mass (M_DM), and XQ width (Γ_T), with M_T up to 2500 GeV and Γ_T/M_T from 0% to 40%.
• Simulates events using CTEQ6L1 PDFs, Pythia 8 for parton showering and hadronization, and Delphes 3 for detector effects.
• Recasts existing ATLAS and CMS 13 TeV searches (e.g., ATLAS-1604.07773, ATLAS-1605.03814) using CheckMATE 2 to compare full signal (σ_S) and NWA cross-sections (σ_X).
• Analyzes the ratio (σ_S − σ_X)/σ_X to quantify deviations from NWA and projects exclusion bounds in the (M_T, M_DM) plane for different width ratios.

Experimental results

Research questions

• RQ1 How do finite widths of extra quarks affect the signal cross-section in XQ–DM final states at the LHC?
• RQ2 In what mass and width regimes does the Narrow Width Approximation fail to describe the true signal cross-section?
• RQ3 How do additional gauge-invariant topologies (e.g., single XQ production) alter the interpretation of LHC exclusion bounds?
• RQ4 Can the spin of the dark matter candidate (scalar vs. vector) be distinguished in the large width regime, and how does this depend on XQ couplings?
• RQ5 To what extent do existing LHC searches underestimate exclusion limits when the XQ has a large width, and how can this be corrected?

Key findings

• The ratio (σ_S − σ_X)/σ_X exceeds 100% in regions of large XQ width (Γ_T/M_T ≈ 40%), indicating that NWA significantly underestimates the true signal cross-section.
• Exclusion bounds for XQs decaying to DM are substantially stronger in the large width regime than in the NWA, with limits exceeding 2 TeV for XQ masses when width effects are included.
• For XQ couplings to light quarks (u, c), the distinction between scalar and vector DM becomes possible in the large width regime, unlike in the NWA.
• The shape of exclusion bounds in the (M_T, M_DM) plane changes dramatically with width: regions near mass degeneracy (M_T ≈ M_DM + m_q) become excluded even at high masses.
• The cross-section effect dominates over detector efficiency in shaping the bounds, meaning that width-induced signal enhancements are the primary driver of stronger exclusion limits.
• The NWA leads to less stringent bounds than the full calculation, especially for XQs with large widths, implying that existing reinterpretations may miss significant portions of parameter space.