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| id: P10 |
| title: "Reproducing $\\beta_L^{32}$-vs-$m_\\mathrm{LQ}$ exclusion + 5$\\sigma$ discovery contours for $U_1$ at 3 TeV (1 ab$^{-1}$) and 14 TeV (20 ab$^{-1}$) muon colliders" |
| arxiv_id: "2104.05720" |
| venue: "ARC-Bench Physics 2026" |
| paper_asset: null |
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| synthesis: | |
| Reproducing the muon-collider sensitivity to a $U_1$ vector |
| leptoquark in the coupling-vs-mass plane via a binned-likelihood |
| recast of $\mu^+\mu^- \to b\bar b$, as a benchmark of the agent's |
| ability to combine MC parameter scans with statistical recasting |
| spanning two orders of magnitude in mass and four orders in coupling. |
| The same $U_1$ Lagrangian as P09 (only $\beta_L^{32}$ non-zero), |
| but here the per-bin cross section is parameterized as |
| $\sigma_i(m, \beta) = b_i + \beta^2 I_i(m) + \beta^4 J_i(m)$, with |
| $I_i(m), J_i(m)$ extracted by solving a $2\times 2$ linear system from |
| two reference $\beta$ values. The diagnostic figure shows 95% CL |
| exclusion (dashed) and 5$\sigma$ discovery (solid) contours in |
| ($m_\mathrm{LQ}$, $\beta_L^{32}$) at $\sqrt{s}=3$ TeV (1 ab$^{-1}$, |
| red) and $\sqrt{s}=14$ TeV (20 ab$^{-1}$, purple). |
| |
| A credible study (a) implements the $U_1$ Lagrangian (FeynRules + UFO), |
| (b) runs SM baselines (100k events at 3 and 14 TeV) plus 4 LQ signal |
| scans ($\sqrt{s}\in\{3,14\}$ TeV x $\beta_L^{32}\in\{1.0, 2.0\}$) over |
| 17 mass points $m_\mathrm{LQ} \in \{1.0, 1.5, 2.0, 3.0, 4.0, 5.0, |
| 6.0, 7.0, 8.0, 10, 15, 20, 30, 40, 50, 60, 70\}$ TeV with 50k events |
| each, (c) bins each run in 10 equal-width $|\eta|$ bins, (d) extracts |
| $I_i, J_i$ per (mass, $\sqrt{s}$), (e) computes the binned |
| log-likelihood ratio for both the exclusion null hypothesis ($n_i |
| = b_i^\mathrm{events}$) and the discovery null ($n_i = \mu_i$), |
| (f) finds the $\beta$ where $-2\log\lambda$ crosses $\chi^2(10, |
| 0.95) = 18.307$ (exclusion) or 48.2 (5$\sigma$ discovery), and |
| (g) plots the four contours on log-log axes ($m_\mathrm{LQ}\in |
| [1, 75]$ TeV, $\beta\in[10^{-3}, 2]$). Research question: *does the |
| agent reproduce the muon-collider $U_1$ exclusion + discovery |
| contours from Figure 12 of arXiv:2104.05720?* |
|
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| hypotheses: |
| - id: H1 |
| statement: "At $\\sqrt{s}=14$ TeV with 20 ab$^{-1}$, the 95% CL exclusion contour reaches $\\beta_L^{32} \\leq 0.01$ at $m_\\mathrm{LQ} = 10$ TeV (matching the published value within a factor of 2)." |
| measurable: true |
| - id: H2 |
| statement: "The 14 TeV exclusion contour extends to higher $m_\\mathrm{LQ}$ than the 3 TeV exclusion contour at every fixed $\\beta_L^{32}$ in $[10^{-2}, 1]$ (higher energy + luminosity gives more reach)." |
| measurable: true |
| - id: H3 |
| statement: "5$\\sigma$ discovery contours always lie above the corresponding exclusion contours in $\\beta_L^{32}$ at every mass (discovery requires stronger signal than exclusion)." |
| measurable: true |
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| experiment_design: |
| research_question: "Does the agent reproduce the 95% CL exclusion and 5$\\sigma$ discovery contours for the $U_1$ leptoquark in the $(m_\\mathrm{LQ}, \\beta_L^{32})$ plane at 3 TeV (1 ab$^{-1}$) and 14 TeV (20 ab$^{-1}$) muon colliders (Figure 12 of arXiv:2104.05720)?" |
| conditions: |
| - name: "sm_baselines" |
| description: "Two SM-only runs (100k events each) at $\\sqrt{s}\\in\\{3, 14\\}$ TeV, $\\beta_L^{ij}=0$. Define per-bin SM cross section $b_i$ in 10 $|\\eta|$ bins." |
| - name: "lq_signal_3tev" |
| description: "Mass scan over 17 points $m_\\mathrm{LQ} \\in [1, 70]$ TeV at $\\sqrt{s}=3$ TeV, with $\\beta_L^{32}\\in\\{1.0, 2.0\\}$, 50k events each." |
| - name: "lq_signal_14tev" |
| description: "Same mass scan at $\\sqrt{s}=14$ TeV with $\\beta_L^{32}\\in\\{1.0, 2.0\\}$, 50k events each." |
| baselines: |
| - "SM $\\mu^+\\mu^- \\to \\gamma^*/Z^* \\to b\\bar b$ at $\\sqrt{s} = 3$ TeV and 14 TeV" |
| metrics: |
| - name: "exclusion_beta_at_10tev_14tev" |
| direction: "match_reference" |
| description: "$\\beta_L^{32}$ at the 95% CL exclusion contour at $m_\\mathrm{LQ}=10$ TeV, $\\sqrt{s}=14$ TeV." |
| - name: "discovery_beta_at_10tev_14tev" |
| direction: "match_reference" |
| description: "$\\beta_L^{32}$ at the 5$\\sigma$ discovery contour at $m_\\mathrm{LQ}=10$ TeV, $\\sqrt{s}=14$ TeV." |
| - name: "I_J_coefficients_per_mass" |
| direction: "match_reference" |
| description: "$(I_i, J_i)$ per $|\\eta|$ bin and mass point, extracted from the $\\beta\\in\\{1, 2\\}$ runs; positive-definite check on $J_i$." |
| datasets: |
| - process_id: "mumu_to_bbbar_U1_3and14tev" |
| sqrt_s_TeV: 14 |
| description: "$\\mu^+\\mu^- \\to b\\bar b$ via SM + $U_1$ exchange at muon colliders, two energy points." |
| compute_requirements: |
| gpu_required: false |
| estimated_wall_clock_sec: 3600 |
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| rubric_path: "experiments/arc_bench/config/physics/rubrics/P10.json" |
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| requirements: |
| - id: req_results_json |
| 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). |
| must_pass: true |
|
|
| - id: req_metrics_numeric |
| 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. |
| must_pass: true |
|
|
| - id: req_hypotheses_supported_flags |
| 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. |
| must_pass: true |
|
|
| - id: req_publication_figure |
| 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. |
| must_pass: true |
|
|
| - id: req_model_implementation |
| 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. |
| must_pass: true |
|
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| - id: req_14tev_excl_reach |
| type: numeric |
| description: >- |
| results.json metrics MUST report the 95% CL exclusion β_L^32 reach at m_LQ=10 TeV, √s=14 TeV, 20 ab^-1; the value MUST be ≤ 0.02 (published ≤0.01 within a factor of 2). |
| must_pass: true |
|
|
| - id: req_mechanistic_writeup |
| 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. |
| must_pass: false |
|
|
| - id: req_mc_reproducibility |
| 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. |
| must_pass: false |
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