Confronting Vector-Like Quark Models with LHC Searches

This paper introduces VLQBounds, a public Python framework that automates the confrontation of Vector-Like Quark models with LHC exclusion limits by interpolating machine-readable experimental grids to provide rapid, channel-by-channel 95% confidence-level verdicts for various production and decay scenarios.

The Gist

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle-smashing factory. Physicists use it to look for "Vector-Like Quarks" (VLQs)—hypothetical, heavy particles that don't exist in our current understanding of the universe but might be hiding in the debris of these collisions.

The problem is that the LHC experiments (ATLAS and CMS) publish thousands of pages of data, rules, and "exclusion zones" (areas where they say, "We looked here, and we didn't find anything"). For a theorist trying to see if their specific idea about these new particles is still possible, navigating this maze is like trying to find a specific needle in a haystack while wearing blindfolded goggles. Every experiment speaks a slightly different language: some talk about mass, others about mixing angles, and others about how wide the particle's "decay" is.

Enter VLQBounds: The Universal Translator and Detective

This paper introduces VLQBounds, a new computer tool (written in Python) that acts as a universal translator and a detective for these particle physicists. Here is how it works, using simple analogies:

1. The "Universal Translator" (Handling Different Languages)

Imagine you are trying to buy a ticket to a concert, but the ticket booth speaks three different dialects. One booth asks for your height, another asks for your shoe size, and a third asks for your favorite color. If you don't speak those dialects, you can't get in.

In the world of particle physics, experimental results are published in these different "dialects" (mass-mixing, mass-coupling, mass-width).

• What VLQBounds does: It takes your specific theory (e.g., "I have a particle with this mass and this mixing angle") and instantly translates it into the exact language the specific experiment used. It converts your input so it can be directly compared to the experimental data without you having to do the complex math manually.

2. The "Detective's Map" (Interpolation)

The experiments don't test every single possible mass. They test specific points, like checking for a lost key at 1000 meters, 1100 meters, and 1200 meters, but not 1050 meters.

• What VLQBounds does: If you want to check a mass of 1050 meters, the tool uses a smart "connect-the-dots" method (interpolation) to estimate what the experimental limit would be at that exact spot. It draws a smooth map between the tested points so you can check any location on the grid, as long as it's within the area they actually looked.

3. The "Toughest Judge" (Finding the Most Sensitive Search)

Imagine you have a suspect (your particle theory) and a lineup of 50 different detectives (experimental searches). Some detectives are better at finding suspects in the rain; others are better in the snow.

• What VLQBounds does: It doesn't just ask one detective; it runs your theory against all the relevant searches from ATLAS and CMS. It then identifies the one detective who is most likely to catch your suspect. If even that best detective says, "I didn't see it, and I'm very good at looking," then your theory is considered "excluded" (ruled out) at a 95% confidence level.

4. The "Report Card" (Clear Results)

Instead of giving you a confusing wall of numbers, VLQBounds gives you a clear verdict:

• Verdict: "Excluded" or "Not Excluded."
• Evidence: It tells you exactly which experiment (the "detective") made the decision and how close you were to being caught.
• Reproducibility: It keeps a perfect record of how it reached that conclusion, so anyone else can run the same check and get the exact same answer.

What It Can and Cannot Do

• It CAN: Take your idea about a heavy particle, check it against all current public data from the LHC, and tell you if your idea is still alive or if it's been killed by the data. It handles different types of these particles (Top partners, Bottom partners, and exotic ones).
• It CANNOT: It will not guess what happens outside the area the experiments have actually looked at. If the experiments only looked up to 2,000 units of mass, and you ask about 2,500, the tool will politely say, "I don't know, because no one looked there yet." It refuses to make up data.

Why This Matters

Before this tool, checking if a new theory was valid was a slow, manual, and error-prone process. VLQBounds automates this, making it fast and reliable. It allows physicists to quickly scan through thousands of ideas to see which ones are still possible and which ones have been ruled out by the world's most powerful particle collider.

In short, VLQBounds is the tool that helps physicists stop guessing and start knowing which of their ideas about the universe have survived the ultimate test.

Technical Summary

Technical Summary of "VLQBounds: Confronting Vector-Like Quark Models with LHC Searches"

Problem Statement
The search for Vector-Like Quarks (VLQs) is a central component of Beyond the Standard Model (BSM) physics at the Large Hadron Collider (LHC). While ATLAS and CMS have published extensive exclusion limits for VLQs (specifically the top partner $T$, bottom partner $B$, and exotic partners $X$ and $Y$), these results are presented in diverse native formats: upper bounds on cross-sections, exclusion contours in the $(m_Q, \sin \theta_{L/R})$ plane, limits in the $(m_Q, \kappa)$ plane, and bounds in the $(m_Q, \Gamma_Q/m_Q)$ plane under fixed branching ratio assumptions.

The diversity of these representations, combined with the complexity of VLQ phenomenology (including singlet, doublet, and triplet representations with varying mixing patterns), makes it difficult to test arbitrary VLQ scenarios coherently and automatically. Existing general-purpose reinterpretation tools (e.g., MadAnalysis 5, CheckMATE) are not specifically organized around the native parameterizations used in VLQ publications, while dedicated tools like XQCAT are limited to specific production modes and on-shell decay assumptions. There is a lack of a lightweight, data-driven framework capable of mapping user-defined VLQ parameters directly onto the native experimental limits for both pair and single production.

Methodology
The authors introduce VLQBounds, a public Python framework designed to confront VLQ scenarios with public ATLAS and CMS exclusion limits. The methodology relies on a data-driven approach where experimental limits and theoretical cross-sections are stored as machine-readable JSON files.

1. Theoretical Framework: The code supports standard VLQ representations (singlets, doublets, triplets) mixing dominantly with the third SM generation. It handles the conversion between different parameterizations:

   • Mass and mixing angles ($m_Q, s_{L/R}$).
   • Mass and effective coupling ($m_Q, \kappa$).
   • Mass and relative width ($m_Q, \Gamma_Q/m_Q$).
   • The framework utilizes established relations (Table 1 in the paper) to translate between mixing angles and the effective coupling $\kappa$ used in experimental publications.

2. Experimental Inputs: The framework incorporates a curated collection of ATLAS and CMS searches covering pair production ($pp \to Q\bar{Q}$) and single production ($pp \to Qq$). These inputs include metadata on center-of-mass energy, luminosity, decay topologies, and lepton multiplicities.

3. Interpolation and Decision Logic:

   • Interpolation: Since experimental limits are published at discrete points, VLQBounds performs shape-preserving or linear interpolation within the published kinematic domain. Crucially, the code does not extrapolate beyond the available grid; points outside the domain are flagged.
   • Comparison: For a given model point, the framework calculates the theoretical cross-section ($\sigma_{\text{theo}}$) and compares it against observed ($\sigma_{\text{obs}}$) and expected ($\sigma_{\text{exp}}$) limits.
   • Selection: It computes sensitivity ratios $r = \sigma_{\text{theo}} / \sigma_{\text{limit}}$ for all relevant channels. The most sensitive channel is selected by maximizing the expected ratio $r_{\text{exp}}$.
   • Verdict: A 95% Confidence Level (CL) exclusion is returned if the observed ratio of the selected channel satisfies $r_{\text{obs}} \geq 1$.

4. Software Architecture: The package is modular, separating model definitions, physics utilities, experimental data access, and inference logic. It provides a unified public API (facade) for setting parameters and running scans, as well as internal tools for generating validation plots directly from the data files.

Key Contributions

• Dedicated Framework: VLQBounds is the first public tool specifically designed to interpret VLQ limits in their native parameter spaces ($m_Q, s_{L/R}$, $m_Q, \kappa$, $m_Q, \Gamma_Q/m_Q$), bridging the gap between general recasting tools and specific VLQ phenomenology.
• Comprehensive Coverage: It supports all four canonical VLQ states ($T, B, X, Y$) across singlet, doublet, and triplet representations, handling both pair and single production mechanisms.
• Reproducibility: The framework ensures reproducibility by generating validation plots and scan outputs directly from the same internal machine-readable data files used for the exclusion logic, avoiding hard-coded numerical arrays in user scripts.
• Modular Design: The code is structured to allow future extensions to new collider searches and non-minimal decay patterns (e.g., 2HDM+VLQ scenarios).

Results
The paper validates the framework through several examples:

• Validation: The authors demonstrate that VLQBounds can reproduce published exclusion contours. Figure 3 shows the reconstruction of CMS mass-width limits for a singlet $T$, and Figure 4 shows the reconstruction of ATLAS mass-coupling limits. The tool successfully interpolates within the published data to reproduce the observed and expected boundaries.
• Benchmark Scans: Figure 5 presents exclusion contours for six representative scenarios (T Singlet, T Doublet, B Singlet, B Doublet, X Doublet, Y Doublet) in the $(m_Q, \Gamma_Q/m_Q)$ plane.
  • The results illustrate the expected phenomenology: at small relative widths, exclusions are dominated by QCD pair-production searches, resulting in near-vertical mass thresholds.
  • As the width (and effective coupling) increases, single-production channels become dominant, extending sensitivity to higher masses.
  • The tool correctly identifies the transition between pair and single production dominance based on the specific representation and mixing parameters.

Significance and Claims
The authors position VLQBounds as a "dedicated and lightweight layer" for the direct use of public VLQ searches. Its significance lies in its ability to automate the confrontation of theoretical VLQ models with experimental data without requiring detector-level reanalysis.

The paper claims the tool is suitable for:

1. Fast phenomenological scans over large parameter spaces.
2. Validation of public limits.
3. Reproducible reinterpretation workflows.

The implementation is described as "deliberately conservative," strictly adhering to published kinematic coverage without extrapolation. The authors note that while the current version covers a broad set of public limits, the architecture is designed to accommodate future extensions, specifically mentioning the potential for a 2HDM+VLQ framework to handle exotic decay channels (e.g., $T \to Ht$, $B \to Hb$) and future projections for Run-3 and the High-Luminosity LHC. The tool is released as open-source software to facilitate community adoption and further development.