Reproducing $pp \to \mu^\pm N$ cross section vs heavy-Majorana-neutrino mass at $\sqrt{s} = 7, 8, 14$ TeV
Domain: physics (high-energy-physics, bsm-phenomenology, neutrino-physics)
Topic: Reproducing heavy Majorana neutrino production $pp \to \mu^\pm N$ at LHC 7/8/14 TeV from arXiv:1308.2209
Venue: ARC-Bench Physics 2026
Source paper: arXiv 1308.2209
Headline metric: primary_metric (maximize)

Research briefing:
Reproducing the LHC sensitivity to a single heavy Majorana neutrino $N$
in the muon channel as a benchmark of the agent's ability to assemble a
hadron-collider Lagrangian -> MC -> analysis pipeline. The BSM extension
adds a right-handed singlet $N$ mixing with $\nu_\mu$ via the
dimensionless real parameter $V_{\mu N}$, so the relevant interaction is
$\mathcal{L}_N \supset -(g_2/\sqrt{2})\,V_{\mu N}\,(\bar\mu\gamma^\mu P_L
N)\,W^-_\mu + (\text{NC term}) + \text{h.c.}$ The diagnostic observable
is the $W^*$-mediated cross section $\sigma(pp \to \mu^\pm N)$ scanned
over $m_N \in \{100, 200, \ldots, 1000\}$ GeV with $|V_{\mu N}|=1$, at
three LHC energies $\sqrt{s} \in \{7, 8, 14\}$ TeV with the CTEQ6L PDF.

A credible study (a) implements the heavy-Majorana-neutrino Lagrangian
(FeynRules .fr or analytic UFO modification), (b) sets up MadGraph runs
for the 30 (mass, energy) cells with the CTEQ6L PDF, (c) extracts the
cross section per cell, and (d) plots three side-by-side panels of
$\sigma(m_N)$ on a log-y axis over $[100,1000]$ GeV vs $[0.1, 4\times
10^4]$ fb. Research question: *does the agent reproduce the steep
PDF-driven fall-off of $\sigma(pp \to \mu^\pm N)$ with $m_N$ and the
correct ordering between $\sqrt{s}=7$, 8, and 14 TeV predicted by
arXiv:1308.2209 Fig. 3?*

Hypotheses:
statement: At $m_N = 200$ GeV and $\sqrt{s}=14$ TeV, $\sigma(pp \to \mu^\pm N)$ falls within $\pm 30\%$ of the published reference value., statement: Cross-section ordering $\sigma(14\,\mathrm{TeV}) > \sigma(8\,\mathrm{TeV}) > \sigma(7\,\mathrm{TeV})$ holds at every mass point, with the 14/7 ratio at $m_N = 500$ GeV in $[5, 30]$., statement: $\sigma(m_N)$ falls by at least 2 orders of magnitude between $m_N = 100$ GeV and $m_N = 1000$ GeV at every LHC energy.

Experiment design:
research_question: Does the agent reproduce the cross-section curves for $pp \to \mu^\pm N$ as a function of the heavy-Majorana-neutrino mass at the 7, 8, and 14 TeV LHC, matching Figure 3 of arXiv:1308.2209?
conditions: name: lhc_7tev
description: $pp$ collisions at $\sqrt{s}=7$ TeV with CTEQ6L PDF, mass scan $m_N \in \{100, 200, 300, 400, 500, 600, 700, 800, 900, 1000\}$ GeV, $|V_{\mu N}|=1$., name: lhc_8tev
description: Same setup at $\sqrt{s}=8$ TeV (LHC Run 1 final dataset energy)., name: lhc_14tev
description: Same setup at $\sqrt{s}=14$ TeV (HL-LHC design).
baselines: Charged-current SM $pp \to \mu \nu_\mu$ (W production) cross check at the same energies
metrics: name: cross_section_fb
direction: match_reference
description: Total $\sigma(pp \to \mu^\pm N)$ in fb at each (mass, energy) cell., name: energy_ratio_14_to_7
direction: match_reference
description: $\sigma(14\,\mathrm{TeV})/\sigma(7\,\mathrm{TeV})$ at $m_N = 500$ GeV., name: mass_dropoff_factor
direction: match_reference
description: $\sigma(m_N=100)/\sigma(m_N=1000)$ at each $\sqrt{s}$.
datasets: process_id: pp_to_muN_via_Wstar
sqrt_s_TeV: 14
description: $pp \to \mu^\pm N$ via $W^*$ at the LHC (CTEQ6L PDF). Three sub-samples for $\sqrt{s} \in \{7,8,14\}$ TeV.
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 a numeric `sigma_pp_to_muN_at_mN200_14TeV_fb` (or equivalent) within ±30% of the published reference value at m_N=200 GeV, √s=14 TeV., 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 Heavy Majorana neutrino $pp \to \mu^\pm N$ at LHC 7/8/14 TeV. 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): BSM single right-handed Majorana neutrino $N$ mixing with the muon flavor: $\mathcal{L}_N \supset -(g_2/\sqrt 2) V_{\mu N} (\bar\mu \gamma^\mu P_L N) W^-_\mu - (g_2/2 c_W) V_{\mu N} (\bar\nu_\mu \gamma^\mu P_L N) Z_\mu + \mathrm{h.c.}$ at $|V_{\mu N}| = 1$.
task_category: Code Development
finegrained_task_category: Method Implementation, requirements: MadGraph generate-process card or analytic process module matches the paper's process string: $pp \to \mu^\pm N$ via $W^*$ at the LHC, mass scan $m_N \in \{100,\ldots,1000\}$ GeV at three energies.
task_category: Code Development
finegrained_task_category: Method Implementation, requirements: PDF set and generation-level cuts match the paper exactly: CTEQ6L PDF for all $\sqrt{s}$ values; 30 (mass, energy) cells (10 masses x 3 energies).
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 — $\sigma(pp \to \mu^\pm N)$ at $m_N=200$ GeV, $\sqrt{s}=14$ TeV agrees with reference within $\pm 30\%$.
task_category: Result Analysis
finegrained_task_category: Logging, Analysis & Presentation, requirements: Quantitative test of H2 — Energy ordering $\sigma(14) > \sigma(8) > \sigma(7)$ TeV holds at every mass; 14/7 ratio at $m_N=500$ GeV in $[5, 30]$. Use the same graded relative-error scale as H1.
task_category: Result Analysis
finegrained_task_category: Logging, Analysis & Presentation, requirements: Quantitative test of H3 — $\sigma(m_N)$ falls $\geq 2$ orders of magnitude from $m_N=100$ to $m_N=1000$ GeV at every $\sqrt{s}$. 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: Three-panel figure (one per $\sqrt{s}$), 1:1 aspect, x-axis $m_N \in [100,1000]$ GeV linear, y-axis $\sigma \in [0.1, 4\times10^4]$ fb log.
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