Reproducing $\sigma(pp \to Z' \to \mu^+\mu^-)$ vs $M_{Z'}$ for SSM and E6-$\psi$ scenarios at $\sqrt{s}=13$ TeV
Domain: physics (high-energy-physics, bsm-phenomenology, z-prime)
Topic: Reproducing SSM and $E_6$-$\psi$ Z' dimuon cross sections at 13 TeV LHC from arXiv:2103.02708
Venue: ARC-Bench Physics 2026
Source paper: arXiv 2103.02708
Headline metric: primary_metric (maximize)

Research briefing:
Reproducing the dimuon production cross section $\sigma(pp \to Z' \to
\mu^+\mu^-)$ as a function of $M_{Z'}$ for two canonical $Z'$ benchmarks
- the Sequential Standard Model (SSM) where the $Z'$ inherits SM
electroweak couplings, and the $E_6$-derived $Z'_\psi$ with universal
coupling $g_\psi = 0.0942$. The general Lagrangian
$\mathcal{L}_{NP} \supset -Z'_\mu \sum_f \bar f \gamma^\mu (g_{Lf} P_L
+ g_{Rf} P_R) f$ has 7 free chiral couplings $g_{Lu}, g_{Ru}, g_{Ld},
g_{Rd}, g_{Le}, g_{Re}, g_{Lv}$, fixed differently in each benchmark.
The diagnostic observable is the dimuon production cross section
scanned over $M_{Z'} \in \{200, 400, 600, \ldots, 5500\}$ GeV at
$\sqrt{s}=13$ TeV.

A credible study (a) implements the general $Z'$ model (FeynRules + UFO)
with the 7 couplings as inputs, (b) sets up two parameter cards
encoding the SSM and $E_6$-$\psi$ coupling tables, (c) scans 14 mass
points per benchmark with auto-computed $\Gamma_{Z'}$ (two-body decays
only), (d) extracts the cross section per (mass, scenario) cell, and
(e) plots two curves (SSM = green dotted, $Z'_\psi$ = blue solid) on
log-y over $M_{Z'} \in [200, 5500]$ GeV, $\sigma \in [5\times 10^{-6},
5\times 10^{-1}]$ pb. Research question: *does the agent reproduce the
cross-section curves and the well-known SSM $\gtrsim Z'_\psi$ ordering
in dilepton production from Figure 4 of arXiv:2103.02708?*

Hypotheses:
statement: $\sigma_\mathrm{SSM}(M_{Z'}=2\,\mathrm{TeV}) > \sigma_\psi(M_{Z'}=2\,\mathrm{TeV})$ by a factor in $[3, 30]$ at $\sqrt{s}=13$ TeV (SSM has larger couplings)., statement: $\sigma_\mathrm{SSM}(M_{Z'}=1\,\mathrm{TeV})$ falls within $\pm 30\%$ of the published reference value., statement: The SSM cross section drops by $\geq 4$ orders of magnitude between $M_{Z'}=200$ GeV and $M_{Z'}=5500$ GeV (PDF + propagator suppression).

Experiment design:
research_question: Does the agent reproduce $\sigma(pp \to Z' \to \mu^+\mu^-)$ vs $M_{Z'}$ for the SSM ($Z'_\mathrm{SSM}$) and $E_6$-derived $Z'_\psi$ benchmarks at the 13 TeV LHC (Figure 4 of arXiv:2103.02708)?
conditions: name: ssm_mass_scan
description: $Z'_\mathrm{SSM}$ with electroweak couplings $g_{Lu} = (e/s_W c_W)(1/2 - 2 s_W^2/3)$, etc. (SM-like). Scan $M_{Z'} \in \{200, 400, 600, 800, 1000, 1500, 2000, 2500, 3000, 3500, 4000, 4500, 5000, 5500\}$ GeV at $\sqrt{s}=13$ TeV., name: e6psi_mass_scan
description: $Z'_\psi$ from $E_6$ with universal coupling $g_\psi = 0.0942$ for all SM fermions. Same mass scan.
baselines: Internal cross-check: SSM/E6-$\psi$ ratio should be approximately mass-independent (set by the ratio of squared couplings) far from mass thresholds
metrics: name: cross_section_pb
direction: match_reference
description: $\sigma(pp \to Z' \to \mu^+\mu^-)$ in pb at each (mass, benchmark) cell., name: ssm_to_e6_ratio_at_2tev
direction: match_reference
description: $\sigma_\mathrm{SSM}/\sigma_\psi$ at $M_{Z'}=2$ TeV., name: mass_dropoff_factor_ssm
direction: match_reference
description: $\sigma_\mathrm{SSM}(M=200)/\sigma_\mathrm{SSM}(M=5500)$.
datasets: process_id: pp_to_Zprime_to_mumu_general
sqrt_s_TeV: 13
description: $pp \to Z' \to \mu^+\mu^-$ in the general 7-coupling $Z'$ model. Two benchmark coupling tables: SSM and $E_6$-$\psi$.
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 ratio σ_SSM/σ_ψ at M_Z'=2 TeV, √s=13 TeV, and that ratio MUST be in [3, 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 General $Z'$: SSM vs $E_6$-$\psi$ dimuon cross section vs mass at LHC. 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): General $Z'$ with 7 chiral couplings $g_{Lu/Ru/Ld/Rd/Le/Re/Lv}$; SSM tabulated values vs $E_6$-$\psi$ universal $g_\psi=0.0942$.
task_category: Code Development
finegrained_task_category: Method Implementation, requirements: MadGraph generate-process card or analytic process module matches the paper's process string: $pp \to Z' \to \mu^+\mu^-$ at $\sqrt{s}=13$ TeV, mass scan over 14 points $\{200,\ldots,5500\}$ GeV.
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; widths auto-computed (two-body decays only); 14 mass points x 2 benchmarks = 28 runs.
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 — $\sigma_\mathrm{SSM}(2\,\mathrm{TeV}) / \sigma_\psi(2\,\mathrm{TeV})$ in $[3, 30]$.
task_category: Result Analysis
finegrained_task_category: Logging, Analysis & Presentation, requirements: Quantitative test of H2 — $\sigma_\mathrm{SSM}(M_{Z'}=1\,\mathrm{TeV})$ 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: Quantitative test of H3 — $\sigma_\mathrm{SSM}$ drops $\geq 4$ orders of magnitude from $M=200$ GeV to $M=5500$ GeV. 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: Two curves on log-y $\sigma \in [5\times 10^{-6}, 5\times 10^{-1}]$ pb vs $M_{Z'}\in[200,5500]$ GeV linear: $Z'_\mathrm{SSM}$ green dotted, $Z'_\psi$ blue solid.
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