Reproducing the Randall-Sundrum KK-graviton resonance pattern in $e^+e^- \to \mu^+\mu^-$
Domain: physics (high-energy-physics, bsm-phenomenology, extra-dimensions)
Topic: Reproducing warped extra dimension Kaluza-Klein graviton resonance from arXiv:hep-ph/9909255
Venue: ARC-Bench Physics 2026
Source paper: arXiv hep-ph/9909255
Headline metric: primary_metric (maximize)

Research briefing:
Reproducing the cross-section vs $\sqrt{s}$ scan of $e^+e^- \to \mu^+\mu^-$
in the Randall-Sundrum warped extra dimension scenario as a benchmark of
the agent's ability to assemble a full Lagrangian -> MC -> analysis
pipeline. The model adds a tower of massive spin-2 KK gravitons
$h^{(n)}_{\alpha\beta}$ ($n=1,\ldots,5$) coupled to the SM
energy-momentum tensor with strength $1/\Lambda_\pi$, on top of the
massless zero-mode coupled with $1/\bar M_{Pl}$. The diagnostic
observable is $\sigma(e^+e^- \to \mu^+\mu^-)$ scanned over
$\sqrt{s}\in\{200,300,\ldots,1200\}$ GeV, which exhibits sharp
resonance peaks at the KK masses $m_n = \{600, 1098, 1592, 2086, 2580\}$
GeV where they sit in the scan window, and an off-resonance continuum
enhancement above SM Drell-Yan elsewhere.

A credible study (a) implements the spin-2 graviton-stress-tensor
Lagrangian (FeynRules + UFO or an equivalent analytic propagator),
(b) generates parton-level events at each of the 11 energy points with
proper handling of the unitary-gauge graviton propagator,
(c) extracts $\sigma(\sqrt{s})$ from the MadGraph banner for each run,
(d) plots $\sigma$ vs $\sqrt{s}$ on a log-y axis over [50, 1500] GeV with
range $[400, 5\times 10^6]$ fb, and (e) compares the resonance positions
and continuum heights against the published Figure 2. Research question:
*to what extent does an autonomous HEP pipeline reproduce the RS
KK-graviton resonance spectrum imprinted on dilepton production at a
500 GeV-1 TeV $e^+e^-$ collider?*

Hypotheses:
statement: The first KK resonance $m_1 = 600$ GeV produces a peak in $\sigma(e^+e^- \to \mu^+\mu^-)$ at $\sqrt{s} = 600$ GeV that lies within 5% of the input mass., statement: Off-resonance cross sections at $\sqrt{s}=200$ and $\sqrt{s}=400$ GeV agree with the published Figure 2 values within 30%, demonstrating correct continuum (zero-mode + virtual KK) interference., statement: At least 2 of the 5 KK resonances within the [50,1500] GeV scan window ($m_1=600$, $m_2=1098$ GeV) are visible as $\geq 1$-decade enhancements above the SM Drell-Yan baseline at $\sqrt{s}=m_n$.

Experiment design:
research_question: Does the agent reproduce the Randall-Sundrum KK-graviton resonance pattern in $e^+e^- \to \mu^+\mu^-$ across the $\sqrt{s}=200$-$1200$ GeV scan, matching the published positions and continuum heights of Figure 2 of arXiv:hep-ph/9909255?
conditions: name: sqrt_s_scan
description: Scan $\sqrt{s} \in \{200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200\}$ GeV with $E^+ = E^- = \sqrt{s}/2$, 100 events per energy point. KK masses fixed at $m_n = \{600, 1098, 1592, 2086, 2580\}$ GeV; $\Lambda_\pi = 522$ GeV; $\bar M_{Pl} = 2.4 \times 10^{18}$ GeV., name: sm_only_baseline
description: Same energy scan with all KK gravitons decoupled ($1/\Lambda_\pi \to 0$) to obtain the pure SM $\gamma^*/Z$ Drell-Yan baseline for resonance-significance comparison.
baselines: Pure SM $e^+e^- \to \mu^+\mu^-$ (Drell-Yan via $\gamma^*/Z$) at the same energy points
metrics: name: cross_section_pb
direction: match_reference
description: Total $\sigma(e^+e^- \to \mu^+\mu^-)$ in pb at each of the 11 $\sqrt{s}$ points., name: peak_position_gev
direction: match_reference
description: Reconstructed $\sqrt{s}$ at which the first KK resonance peaks; target = $600 \pm 30$ GeV., name: resonance_to_continuum_ratio
direction: match_reference
description: Ratio $\sigma(\sqrt{s}=m_1) / \sigma(\sqrt{s}=m_1 - 200\,\mathrm{GeV})$; should exceed $\sim 10$.
datasets: process_id: ee_to_mumu_RS
sqrt_s_TeV: 1.2
description: $e^+e^- \to \mu^+\mu^-$ in the RS warped-graviton model.
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 `peak_position_gev` (or equivalent first-KK-resonance position) within ±5% of 600 GeV — i.e. in the interval [570, 630] GeV — after the RS scan over √s ∈ {200..1200} GeV., 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 RS warped extra dimension KK-graviton resonance in $e^+e^- \to \mu^+\mu^-$. 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): Randall-Sundrum spin-2 KK graviton tower coupled to SM stress-energy tensor with $1/\Lambda_\pi$ (massive modes) and $1/\bar M_{Pl}$ (zero mode); five massive modes $m_n \in \{600, 1098, 1592, 2086, 2580\}$ GeV with $\Lambda_\pi = 522$ GeV.
task_category: Code Development
finegrained_task_category: Method Implementation, requirements: MadGraph generate-process card or analytic process module matches the paper's process string: $e^+e^- \to \mu^+\mu^-$ at energies $\sqrt{s} \in \{200,\ldots,1200\}$ GeV with KK-graviton tower.
task_category: Code Development
finegrained_task_category: Method Implementation, requirements: PDF set and generation-level cuts match the paper exactly: Lepton-collider beams $E^\pm = \sqrt{s}/2$, no proton PDF; widths of all KK gravitons computed automatically (two-body decays only); 100 events per energy point.
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 — First KK resonance peaks within 5% of input $m_1=600$ GeV (i.e. peak in $[570, 630]$ GeV) — score 100% if rel. err. < 3%, 67% if < 10%, 33% if < 30%, 0% otherwise.
task_category: Result Analysis
finegrained_task_category: Logging, Analysis & Presentation, requirements: Quantitative test of H2 — Off-resonance cross sections at $\sqrt{s} \in \{200, 400\}$ GeV agree with the published Figure 2 within $\pm 30\%$. Use the same graded relative-error scale as H1.
task_category: Result Analysis
finegrained_task_category: Logging, Analysis & Presentation, requirements: Quantitative test of H3 — At least 2 of the 5 KK resonances within the [50,1500] GeV scan window appear as $\geq 1$-decade enhancements above the SM Drell-Yan baseline. 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: Reproduced figure shows $\sigma$ vs $\sqrt{s}$ with x-axis $\sqrt{s}$ in GeV (linear, [50,1500]), y-axis $\sigma$ in fb (log, $[400, 5\times 10^6]$), blue line, all resonances visible.
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