Reproducing $\sigma(pp \to Z')$ vs $g_1'$ slices for kinetic-mixing B-L Z' at $\sqrt{s}=13$ TeV
Domain: physics (high-energy-physics, bsm-phenomenology, z-prime)
Topic: Reproducing $\sigma(pp \to Z')$ vs $g_1'$ slices for kinetic-mixing B-L Z' at 13 TeV from arXiv:1605.02910
Venue: ARC-Bench Physics 2026
Source paper: arXiv 1605.02910
Headline metric: primary_metric (maximize)

Research briefing:
Reproducing the $\sqrt{s}=13$ TeV LHC production cross section
$\sigma(pp \to Z')$ as a function of $g_1'$ along three constant-
$\tilde g$ slices, for the same kinetic-mixing B-L $Z'$ model as P03.
The cross section is exactly quadratic in the couplings,
$\sigma(g_1', \tilde g) = A g_1'^2 + B g_1' \tilde g + C \tilde g^2$,
so 3 MadGraph runs per mass point determine $(A,B,C)$ on the entire
$(g_1', \tilde g)$ plane. The diagnostic figure has two panels
(Panel A: $M_{Z'}=2$ TeV with $\tilde g\in\{0, -0.05, -0.10\}$;
Panel B: $M_{Z'}=3$ TeV with $\tilde g\in\{0, -0.30, -0.60\}$).

A credible study (a) reuses the kinetic-mixing B-L $Z'$ model
(FeynRules + UFO), (b) executes 6 MadGraph runs (3 per mass) at
$\sqrt{s}=13$ TeV, (c) solves the linear system for $(A,B,C)$ at each
mass, (d) computes the analytic curves $\sigma(g_1')|_{\tilde g}$ for
the requested slices, and (e) plots two panels with log-y on the
prescribed ranges (Panel A: $g_1' \in [0, 0.20]$, $\sigma \in
[10^{-4}, 10^{-1}]$ pb; Panel B: $g_1' \in [0, 0.70]$, $\sigma \in
[10^{-4}, 10^{1}]$ pb). Research question: *does the agent recover the
quadratic-in-couplings parameterization of $Z'$ production well enough
to reproduce the constant-$\tilde g$ cross-section slices in Figure 10
of arXiv:1605.02910?*

Hypotheses:
statement: At Panel A ($M_{Z'}=2$ TeV, $\tilde g = 0$, $g_1' = 0.10$), the reconstructed $\sigma(pp \to Z')$ lies within $\pm 30\%$ of the published value., statement: The curve at $\tilde g = -0.10$ in Panel A lies above the $\tilde g = 0$ curve at $g_1' = 0.05$ but below at $g_1' = 0.20$, demonstrating the destructive-then-constructive interference pattern of the kinetic mixing., statement: $\sigma$ at ($M_{Z'}=2$ TeV, $g_1'=0.10$, $\tilde g=0$) exceeds $\sigma$ at ($M_{Z'}=3$ TeV, $g_1'=0.10$, $\tilde g=0$) by a factor in $[10, 200]$, reflecting the steep PDF suppression.

Experiment design:
research_question: Does the agent reproduce $\sigma(pp \to Z')$ vs $g_1'$ for fixed-$\tilde g$ slices at $M_{Z'}=2$ and 3 TeV at $\sqrt{s}=13$ TeV (Figure 10 of arXiv:1605.02910)?
conditions: name: mzp_2tev_3runs
description: $M_{Z'}=2$ TeV at $\sqrt{s}=13$ TeV: 3 signal runs at $(g_1', \tilde g) \in \{(0.10, 0), (0.10, -0.10), (0.15, -0.05)\}$., name: mzp_3tev_3runs
description: $M_{Z'}=3$ TeV at $\sqrt{s}=13$ TeV: 3 signal runs at $(g_1', \tilde g) \in \{(0.30, 0), (0.30, -0.30), (0.50, -0.60)\}$.
baselines: Self-consistency cross-check: predicted $\sigma$ at the 3 input points must reproduce the simulated $\sigma$ exactly (closure of the $A,B,C$ fit)
metrics: name: cross_section_pb
direction: match_reference
description: $\sigma(pp \to Z')$ in pb on the requested slice points., name: quadratic_coefficients_ABC_13tev
direction: match_reference
description: $(A, B, C)$ coefficients per mass point at $\sqrt{s}=13$ TeV., name: mass_pdf_suppression_ratio
direction: match_reference
description: $\sigma(M_{Z'}=2)/\sigma(M_{Z'}=3)$ at $\tilde g = 0$, $g_1' = 0.10$.
datasets: process_id: pp_to_Zprime_BL_kinmix_13tev
sqrt_s_TeV: 13
description: $pp \to Z'$ for the kinetic-mixing B-L Z' model at LHC Run 2 energy.
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 `sigma_pp_to_Zprime_2TeV_panelA_fb` (at M_Z'=2 TeV, g̃=0, g1'=0.10) within ±30% of the published Panel A reference cross section., 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 B-L $Z'$ kinetic mixing $\sigma(g_1')$ slices at $\sqrt{s}=13$ 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): Same kinetic-mixing B-L $Z'$ as P03; cross section $\sigma = A g_1'^2 + B g_1'\tilde g + C \tilde g^2$ exact.
task_category: Code Development
finegrained_task_category: Method Implementation, requirements: MadGraph generate-process card or analytic process module matches the paper's process string: $pp \to Z'$ at $\sqrt{s}=13$ TeV; $\sigma$ vs $g_1'$ at fixed $\tilde g$ slices.
task_category: Code Development
finegrained_task_category: Method Implementation, requirements: PDF set and generation-level cuts match the paper exactly: 6 signal runs (3 per mass) at $\sqrt{s}=13$ TeV; standard LHC PDF set.
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 — $\sigma(M_{Z'}=2\,\mathrm{TeV}, \tilde g=0, g_1'=0.10)$ within $\pm 30\%$ of published Panel A value.
task_category: Result Analysis
finegrained_task_category: Logging, Analysis & Presentation, requirements: Quantitative test of H2 — $\tilde g=-0.10$ curve in Panel A lies above $\tilde g=0$ at $g_1'=0.05$ but below at $g_1'=0.20$ (interference sign change). Use the same graded relative-error scale as H1.
task_category: Result Analysis
finegrained_task_category: Logging, Analysis & Presentation, requirements: Quantitative test of H3 — $\sigma(M_{Z'}=2)/\sigma(M_{Z'}=3)$ at $\tilde g=0, g_1'=0.10$ is in $[10, 200]$ (PDF suppression). 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-panel figure (Panel A: $M_{Z'}=2$ TeV, $g_1'\in[0,0.20]$, $\sigma \in [10^{-4}, 10^{-1}]$ pb; Panel B: $M_{Z'}=3$ TeV, $g_1'\in[0,0.70]$, $\sigma \in [10^{-4}, 10^1]$ pb), three colored curves per panel.
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