# ============================================================================ # P10 — $U_1$ leptoquark exclusion + discovery contours at 3+14 TeV muon collider # ---------------------------------------------------------------------------- # Adapts ColliderAgent paper-reproduction prompt: # /home/shiqiu/ColliderAgent/paper-reproduction/2104.05720/prompt_figure_12.md # Source: arXiv:2104.05720 — same $U_1$ LQ as P09 but the diagnostic # figure is $\beta_L^{32}$ vs $m_\mathrm{LQ}$ exclusion + discovery from # binned likelihood ratio at two muon-collider energies. # ============================================================================ 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 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?* 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 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 rubric_path: "experiments/arc_bench/config/physics/rubrics/P10.json" # --------------------------------------------------------------------------- # Agent-mode requirements (consumed by researchclaw.pipeline.requirements_judge # at stage 15 RESEARCH_DECISION). Schema mirrors B01.yaml: # id — stable identifier # type — advisory hint to the LLM judge (numeric | artifact | discussion) # description — natural-language statement of what must be true post-run # must_pass — true → unmet ⇒ rerun (1 retry max); false → optional # # The five generic must_pass items apply uniformly across P01-P10; the sixth # is topic-specific (mirrors this manifest's H1). The two must_pass=false # items reward mechanistic interpretation and MC-reproducibility metadata # without blocking proceed-vs-rerun on them. # --------------------------------------------------------------------------- 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 - 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