Reproducing $U_1$ vector-leptoquark $\sqrt{|g_c^* g_b|}$ vs $M_{U_1}$ exclusion from ATLAS+CMS $pp \to \tau\nu$
Domain: physics (high-energy-physics, bsm-phenomenology, leptoquark, flavor-anomaly, statistical-recast)
Topic: Reproducing $U_1$ vector leptoquark exclusion from combined ATLAS+CMS $pp \to \tau\nu$ recast from arXiv:1811.07920
Venue: ARC-Bench Physics 2026
Source paper: arXiv 1811.07920
Headline metric: primary_metric (maximize)

Research briefing:
Reproducing the LHC sensitivity to a $U_1$ vector leptoquark from the
$pp \to \tau\nu$ channel via $bc \to U_1 \to \tau\nu$ exchange,
combining ATLAS + CMS searches in a binned profile-likelihood, as a
benchmark of the agent's ability to (i) generate LQ events with
bottom-quark and charm-quark initial-state partons, (ii) run two
parallel detector-card simulations (Delphes ATLAS card vs CMS card),
(iii) recast experimental data into a profile-likelihood fit. The
Lagrangian couples $U_1$ to $(\bar c \gamma^\mu P_L \nu_\tau)$ and
$(\bar b \gamma^\mu P_L \tau)$ with couplings $g_c, g_b$, and the
diagnostic figure is the 2$\sigma$ exclusion contour in the
$(\sqrt{|g_c^* g_b|}, M_{U_1})$ plane along with the LH and RH
$R_{D^{(*)}}$ flavor-anomaly bands.

A credible study (a) implements the $U_1$ Lagrangian (FeynRules .fr +
UFO), (b) runs MadGraph + Pythia8 + Delphes for $M_{U_1} \in \{750,
1000, 1250, 1500, 2000, 2500, 3000, 4000, 5000\}$ GeV with both ATLAS
and CMS cards (LHCO output), (c) applies the published ATLAS and CMS
$\tau$-channel selections (lepton veto, hadronic-$\tau$ requirement,
$E_T^\mathrm{miss}$ cut, $m_T$ cut), (d) builds a binned signal
template that scales as $g^4$ and runs the per-bin profile likelihood
with nuisance parameters $\theta_i$, (e) combines ATLAS + CMS, finds
the 2$\sigma$ exclusion via $-2\Delta\ln\mathcal{L} = 4$, and (f)
overlays the analytic LH band $g_\mathrm{LH}(M) = (M/v)\sqrt{2 V_{cb}\,
\epsilon_L}$ with $\epsilon_L = 0.11 \pm 0.02$ and the analogous RH band.
Research question: *does the agent reproduce the $(\sqrt{|g_c^* g_b|},
M_{U_1})$ exclusion contour and the $R_{D^{(*)}}$ overlay bands of
Figure 3 of arXiv:1811.07920?*

Hypotheses:
statement: The combined ATLAS+CMS 2$\sigma$ exclusion at $M_{U_1} = 1$ TeV gives $\sqrt{|g_c^* g_b|} \in [0.3, 1.5]$, matching the published value within 30%., statement: The reconstructed exclusion contour intersects the LH $R_{D^{(*)}}$ band ($\epsilon_L = 0.11$) at an excluded mass $M_{U_1}^* \in [1.0, 2.5]$ TeV., statement: Selection efficiency on signal events is $\geq 5\%$ at $M_{U_1}=1$ TeV in both ATLAS and CMS analyses (gauge of pipeline working end-to-end through Delphes).

Experiment design:
research_question: Does the agent reproduce the 2$\sigma$ exclusion contour for the $U_1$ vector leptoquark in the $(\sqrt{|g_c^* g_b|}, M_{U_1})$ plane from combined ATLAS+CMS $pp \to \tau\nu$ recast (Figure 3 of arXiv:1811.07920)?
conditions: name: atlas_recast
description: Mass scan $M_{U_1} \in \{750, 1000, 1250, 1500, 2000, 2500, 3000, 4000, 5000\}$ GeV at $\sqrt{s}=13$ TeV, 10k events each, Pythia8 shower, Delphes ATLAS card, LHCO output. Selection: lepton veto, hadronic-$\tau$ $p_T > 80$ GeV, $|\eta_\tau| < 2.3$, $E_T^\mathrm{miss} > 150$ GeV, $m_T > 250$ GeV., name: cms_recast
description: Same mass scan with Delphes CMS card; selection: lepton veto, $\tau$ $p_T>80$ GeV, $|\eta|<2.1$, $E_T^\mathrm{miss}>200$ GeV, $0.7 < p_T^\tau / E_T^\mathrm{miss} < 1.3$, $\Delta\phi(\tau, E_T^\mathrm{miss}) > 2.4$, $m_T > 320$ GeV.
baselines: Published ATLAS background table (22 bins, 250-3200 GeV log-spaced) and CMS background table (3 bins) act as the SM-only null hypothesis
metrics: name: exclusion_coupling_at_1tev
direction: match_reference
description: $\sqrt{|g_c^* g_b|}$ at the 2$\sigma$ exclusion boundary at $M_{U_1}=1$ TeV from combined fit., name: selection_efficiency
direction: match_reference
description: Fraction of generated signal events passing the ATLAS or CMS selection at $M_{U_1}=1$ TeV., name: rdstar_band_intersection_tev
direction: match_reference
description: Mass at which the LH $R_{D^{(*)}}$ band crosses the exclusion contour.
datasets: process_id: pp_to_taunu_via_U1
sqrt_s_TeV: 13
description: $pp \to \tau\nu$ via $bc \to U_1$ exchange. Two detector simulations (Delphes ATLAS, Delphes CMS).
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 2σ combined ATLAS+CMS √(g_c* g_b) exclusion band at M_U1=1 TeV; the band lower edge must be in [0.21, 0.39] and the upper edge in [1.05, 1.95] (published [0.3, 1.5] ±30%)., 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 $U_1$ vector-leptoquark recast of LHC $pp \to \tau\nu$ (ATLAS+CMS). 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): $U_1$ vector LQ in $(\mathbf{3},\mathbf{1},2/3)$ rep coupling to $(\bar c\gamma^\mu P_L\nu_\tau)$ and $(\bar b\gamma^\mu P_L\tau)$ with couplings $g_c, g_b$.
task_category: Code Development
finegrained_task_category: Method Implementation, requirements: MadGraph generate-process card or analytic process module matches the paper's process string: $pp \to \tau\nu$ via $bc \to U_1 \to \tau\nu$ exchange at $\sqrt{s}=13$ TeV, mass scan.
task_category: Code Development
finegrained_task_category: Method Implementation, requirements: PDF set and generation-level cuts match the paper exactly: Standard 13 TeV proton PDF; 9 mass points $\{750,\ldots,5000\}$ GeV with $b$ and $c$ parton initial states; 10k events per (mass, detector); Pythia8 shower; Delphes ATLAS card and Delphes CMS card runs in parallel; 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 — Combined ATLAS+CMS 2$\sigma$ exclusion at $M_{U_1}=1$ TeV gives $\sqrt{|g_c^* g_b|} \in [0.3, 1.5]$.
task_category: Result Analysis
finegrained_task_category: Logging, Analysis & Presentation, requirements: Quantitative test of H2 — Reconstructed exclusion contour intersects the LH $R_{D^{(*)}}$ band ($\epsilon_L=0.11$) at excluded mass $M_{U_1}^* \in [1.0, 2.5]$ TeV. Use the same graded relative-error scale as H1.
task_category: Result Analysis
finegrained_task_category: Logging, Analysis & Presentation, requirements: Quantitative test of H3 — Selection efficiency $\geq 5\%$ on signal at $M_{U_1}=1$ TeV in both ATLAS and CMS recasts. 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: Exclusion contour in $(\sqrt{|g_c^* g_b|}, M_{U_1})$ plane, 4:3 aspect, x in TeV $[0.8, 5.0]$, y $[0, 4.0]$, with LH band (blue dashed + light-blue band) and RH band (red dashed + light-red band).
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