Reproducing the $m_{ej}$ resonance in $pp \to \mathrm{LQ} \to ej$ via the LUXlep proton lepton PDF
Domain: physics (high-energy-physics, bsm-phenomenology, leptoquark, lepton-pdf)
Topic: Reproducing scalar leptoquark $m_{ej}$ resonance via LUXlep proton lepton PDF from arXiv:2005.06475
Venue: ARC-Bench Physics 2026
Source paper: arXiv 2005.06475
Headline metric: primary_metric (maximize)

Research briefing:
Reproducing the LHC sensitivity to a scalar leptoquark in the
$pp \to \mathrm{LQ} \to ej$ channel as a benchmark of the agent's
ability to assemble a full Lagrangian -> MC -> shower -> detector ->
analysis pipeline using a non-trivial PDF (LUXlep, with electrons inside
the proton). The Lagrangian
$\mathcal{L} = \lambda_{eu}\,\mathrm{LQ}_{eu}\,e_R^T i\sigma^2 u_R +
\mathrm{h.c.}$ describes an $SU(2)_L$-singlet, color-triplet,
$Q=-1/3$ scalar leptoquark coupling to a right-handed lepton-quark pair.
The diagnostic observable is the reconstructed invariant mass $m_{ej}$
of the leading electron and leading jet, peaked at the input
$M_\mathrm{LQ}=3$ TeV with $\Gamma_\mathrm{LQ}=60$ GeV after Pythia8 +
Delphes ATLAS detector smearing.

A credible study (a) implements the scalar-LQ Lagrangian (FeynRules .fr
+ UFO), (b) generates 100k events at $\sqrt{s}=13$ TeV with the LUXlep
PDF (proton content redefined to include leptons + photon) and
generation cuts $p_T(\ell, j) > 500$ GeV, $|\eta| < 2.5$, (c) applies
the Pythia8 lepton-to-photon workaround (replace initial-state leptons
with photons in the LHE; set Check:event=off; shower; Delphes ATLAS
card with anti-$k_T$ R=0.4 jets; LHCO output), (d) selects events with
exactly one $e$ ($p_T>500$ GeV, $|\eta|<2.5$), one $j$ ($p_T>500$ GeV,
$|\eta|<2.5$), $E_T^\mathrm{miss} < 50$ GeV, lepton veto, jet veto,
(e) histograms $m_{ej}$ in 100 GeV bins from 0 to 5000 GeV weighted by
$\sigma\mathcal{L}/N_\mathrm{gen}$ at $\mathcal{L}=100$ fb$^{-1}$, and
(f) plots on log-y $[10^{-3}, 5\times 10^2]$ events/bin over [1000,
5000] GeV. Research question: *does the agent reproduce the scalar-LQ
resonance peak at $m_{ej} \approx 3$ TeV from Figure 2 of arXiv:2005.06475?*

Hypotheses:
statement: Reconstructed $m_{ej}$ peaks within $\pm 5\%$ of the input $M_\mathrm{LQ}=3000$ GeV after Pythia8+Delphes smearing (i.e., peak in [2850, 3150] GeV)., statement: The generation-level $p_T(\ell, j) > 500$ GeV cut yields $\geq 50\%$ acceptance for the benchmark $M_\mathrm{LQ}=3$ TeV signal., statement: Total event count in the [2.5, 3.5] TeV $m_{ej}$ window at $\mathcal{L} = 100$ fb$^{-1}$ matches the published value within $\pm 30\%$.

Experiment design:
research_question: Does the agent reproduce the $m_{ej}$ invariant-mass distribution for $pp \to \mathrm{LQ} \to ej$ at $\sqrt{s}=13$ TeV with LUXlep PDF and $M_\mathrm{LQ}=3$ TeV (Figure 2 of arXiv:2005.06475)?
conditions: name: lq_3tev_lambda1
description: Scalar LQ at $M_\mathrm{LQ}=3000$ GeV, $\Gamma_\mathrm{LQ}=60$ GeV, $\lambda_{eu}=1$, 100k events at $\sqrt{s}=13$ TeV, LUXlep PDF, $p_T > 500$ GeV gen cuts, Pythia8 + Delphes ATLAS, LHCO output., name: lq_2tev_check
description: Cross-check at $M_\mathrm{LQ}=2000$ GeV with $\lambda_{eu}=1$, same setup; verify that $m_{ej}$ peak shifts to 2 TeV.
baselines: Background-only sanity check: $\lambda_{eu}=0$ (LQ decoupled) should produce zero $m_{ej}$ events above the gen-level cut
metrics: name: peak_position_gev
direction: match_reference
description: Bin-center of the maximum of the reconstructed $m_{ej}$ histogram for the 3 TeV signal., name: acceptance_pt500
direction: match_reference
description: Fraction of generated events with both lepton and jet $p_T > 500$ GeV at $M_\mathrm{LQ}=3$ TeV., name: integrated_yield_in_window
direction: match_reference
description: Sum of weighted events in $m_{ej} \in [2500, 3500]$ GeV at $\mathcal{L}=100$ fb$^{-1}$.
datasets: process_id: pp_to_LQ_to_ej_LUXlep
sqrt_s_TeV: 13
description: Single resonant scalar leptoquark production via lepton-quark fusion using LUXlep proton PDF.
compute_requirements: gpu_required: no
estimated_wall_clock_sec: 3600

Requirements:
type: artifact
description: A canonical results.json file exists at the workspace root with at least the keys: primary_metric (number), metric_key (string), metrics (object with numeric keys), hypotheses (object with h1/h2/h3 entries each carrying a `supported` boolean), summary (non-empty string)., type: numeric
description: results.json metrics MUST contain at least 3 numeric (non-null, finite) values directly relevant to the headline physics observable named in the experiment_design.metrics list above — these are the numbers the paper will report in its Results section., type: discussion
description: results.json hypotheses.h1/h2/h3 each MUST have an explicit `supported` boolean AND a `details` string ≥ 40 characters quoting the numerical evidence (specific values + their source artifact) used to reach the verdict., type: artifact
description: At least one publication-quality figure file (PDF or PNG, ≥150 DPI for raster) exists under figures/ or output/figures/ with axes labeled in physical units (GeV / pb / fb / dimensionless) and a legend if multiple series are plotted.  The figure must directly support a hypothesis verdict., type: artifact
description: The BSM Lagrangian is implemented either as a FeynRules .fr file (models/*.fr) with a matching UFO directory (models/*_UFO/ containing at least particles.py, parameters.py, couplings.py, vertices.py), OR as analytic Python code that explicitly computes the cross sections from the Lagrangian terms.  A pure SM baseline with no BSM piece is NOT sufficient., type: numeric
description: results.json metrics MUST report the reconstructed m_ej peak position (after Pythia8+Delphes smearing) in the interval [2850, 3150] GeV (input M_LQ=3 TeV ±5%)., type: discussion
description: The summary or structured_results section provides a one-paragraph mechanistic interpretation of WHY the headline observable comes out the way it does (which interference / propagator structure / cut effect drives the result).  Nice-to-have, not blocking proceed., type: discussion
description: results.json or a sibling reproducibility section names: (a) the MadGraph5_aMC@NLO version, (b) the PDF set used (if applicable), (c) at least one explicit random seed.  Required for full reproducibility but not for scientific correctness.

Scoring rubric:
requirements: A credible HEP collider study reproducing the published reference figure for Scalar leptoquark resonance $m_{ej}$ via LUXlep proton lepton PDF. The agent must (a) implement the BSM Lagrangian, (b) generate Monte Carlo events for the specified process with appropriate PDFs and generation cuts, (c) run the necessary detector / shower simulation if required, (d) reconstruct the diagnostic kinematic distribution, and (e) compare against the published reference figure with quantitative residuals tied to H1, H2, H3.
judging_note: Physics topics are scored on whether the agent (i) assembles a working HEP MC pipeline AND (ii) reproduces the published numbers within stated tolerance. Partial credit is allowed; the agent may use analytic shortcuts in place of MadGraph for cases where it is overkill, as long as the answer matches the published reference within the per-leaf tolerance. Quantitative result leaves are scored on a graded scale: 100% if relative error < 3%, 67% if < 10%, 33% if < 30%, 0% otherwise.
sub_tasks: requirements: Code-development bucket: BSM model + process card + PDF/cuts + full pipeline are wired correctly.
sub_tasks: requirements: BSM Lagrangian implemented (FeynRules .fr file + UFO output, or equivalent analytic Python module): Scalar LQ in $SU(2)_L$ singlet, color triplet, $Q=-1/3$; $\mathcal{L} = \lambda_{eu}\,\mathrm{LQ}_{eu}\,e_R^T i\sigma^2 u_R + \mathrm{h.c.}$; $M_\mathrm{LQ}=3$ TeV, $\Gamma=60$ GeV, $\lambda_{eu}=1$.
task_category: Code Development
finegrained_task_category: Method Implementation, requirements: MadGraph generate-process card or analytic process module matches the paper's process string: $pp \to \mathrm{LQ} \to ej$ resonant single LQ production at $\sqrt{s}=13$ TeV.
task_category: Code Development
finegrained_task_category: Method Implementation, requirements: PDF set and generation-level cuts match the paper exactly: LUXlep PDF (proton content includes electrons and photon); generation cuts $p_T(\ell, j) > 500$ GeV, $|\eta|<2.5$; Pythia8 with lepton-to-photon LHE workaround (Check:event=off); Delphes ATLAS card with anti-$k_T$ R=0.4 jets; LHCO output.
task_category: Code Development
finegrained_task_category: Experimental Setup, requirements: Full HEP chain wired together (model -> events -> [shower -> detector] -> reconstruction -> analysis -> figure). For analytic shortcuts the chain may be simpler but must still terminate in the diagnostic figure.
task_category: Code Development
finegrained_task_category: Method Implementation, requirements: Execution-validity bucket: MC sample passes nevents threshold, physics-validity gates clear, MC stats are sufficient.
sub_tasks: requirements: MC sample(s) generated successfully with at least the requested number of events per cell (or a documented partial count if compute-limited), with no fatal MadGraph or downstream errors.
task_category: Code Execution
finegrained_task_category: Evaluation, Metrics & Benchmarking, requirements: Physics-validity gate: no negative cross sections; gauge invariance / unitarity sanity checks pass; mass spectrum and decay widths printed by MadGraph match the input parameter card; no obviously unphysical kinematics in the generated events.
task_category: Code Execution
finegrained_task_category: Evaluation, Metrics & Benchmarking, requirements: MC statistics are sufficient: relative MC error in the signal region is < 10% OR at least 3 random seeds are run with std reported across them.
task_category: Code Execution
finegrained_task_category: Evaluation, Metrics & Benchmarking, requirements: Results bucket: quantitative comparison of three hypothesis-driven observables to the published figure, plus a reproduced figure artifact and a per-hypothesis writeup.
sub_tasks: requirements: Quantitative test of H1 — Reconstructed $m_{ej}$ peaks within $\pm 5\%$ of input $M_\mathrm{LQ}=3000$ GeV (peak in $[2850, 3150]$ GeV).
task_category: Result Analysis
finegrained_task_category: Logging, Analysis & Presentation, requirements: Quantitative test of H2 — Generation-level $p_T > 500$ GeV cut yields $\geq 50\%$ acceptance on the 3 TeV signal. Use the same graded relative-error scale as H1.
task_category: Result Analysis
finegrained_task_category: Logging, Analysis & Presentation, requirements: Quantitative test of H3 — Total weighted yield in $m_{ej} \in [2500, 3500]$ GeV at $\mathcal{L}=100$ fb$^{-1}$ within $\pm 30\%$ of published value. Use the same graded relative-error scale as H1.
task_category: Result Analysis
finegrained_task_category: Logging, Analysis & Presentation, requirements: A reproduced figure exists in artifacts (PDF or PNG) with axes, units, ranges, and legend matching the published reference: Reconstructed $m_{ej}$ histogram, 100 GeV bins from 0 to 5000 GeV, weighted by $\sigma\mathcal{L}/N_\mathrm{gen}$, log-y $[10^{-3}, 5\times 10^2]$ events/bin, 1:1 aspect, title 'LHC, $\sqrt{s}=13$ TeV'.
task_category: Result Analysis
finegrained_task_category: Logging, Analysis & Presentation, requirements: Writeup discusses the outcome of each hypothesis (supported / refuted / inconclusive) tied to numeric residuals, identifies the dominant systematic uncertainty (PDF set, scale variation, k-factor, Delphes card, statistical MC error), and states explicitly any analytic shortcuts taken in place of full MC.
task_category: Result Analysis
finegrained_task_category: Logging, Analysis & Presentation, requirements: Reproducibility bucket (new for physics topics; absent in T-rubrics): the artifacts contain everything needed to rerun the analysis from scratch.
sub_tasks: requirements: UFO model directory (or analytic model Python module) is checked into the artifacts and is loadable by MadGraph (or directly importable for analytic models).
task_category: Code Development
finegrained_task_category: Reproducibility, requirements: MadGraph run_card / param_card, Pythia8 settings, Delphes card, and MadAnalysis5 (or equivalent analysis) cards are saved alongside the run with explicit parameter values per cell.
task_category: Code Development
finegrained_task_category: Reproducibility, requirements: RNG seeds are documented; rerunning the run from saved seeds should give matching central values within the reported MC error. For analytic shortcuts, the seed requirement is replaced by an explicit list of input numerical parameters.
task_category: Code Development
finegrained_task_category: Reproducibility