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| id: P09 |
| title: "Reproducing the normalized $|\\eta|$ shape in $\\mu^+\\mu^- \\to b\\bar b$ from a $U_1$ vector leptoquark at $\\sqrt{s}=3$ TeV" |
| arxiv_id: "2104.05720" |
| venue: "ARC-Bench Physics 2026" |
| paper_asset: null |
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| synthesis: | |
| Reproducing the normalized pseudorapidity shape of the $b$ quark in |
| $\mu^+\mu^- \to b\bar b$ at a 3 TeV muon collider, comparing SM |
| ($s$-channel $\gamma^*/Z^*$) against $U_1$ vector-leptoquark |
| $t$-channel exchange. The Lagrangian has the standard vector-LQ |
| kinetic term plus |
| $\mathcal{L} \supset (g_U/\sqrt{2})\,U_1^\mu (\beta_L^{ij}\, |
| \bar Q_L^i \gamma_\mu L_L^j) + \mathrm{h.c.}$, with only |
| $\beta_L^{32}$ (b-quark to muon) non-zero. The diagnostic observable |
| is the normalized $|\eta|$ distribution of the $b$ quark binned in 13 |
| bins from 0 to 2.5 (narrow [0, 0.1] first bin then uniform 0.2-wide |
| bins), shown in two side-by-side panels at $\beta_L^{32} = 1.0$ and |
| $\beta_L^{32} = 0.1$, each overlaying SM (gray bar histogram) with |
| $m_\mathrm{LQ}=1$ TeV (blue dashed) and $m_\mathrm{LQ}=10$ TeV |
| (orange dashed). |
| |
| A credible study (a) implements the $U_1$ vector-LQ Lagrangian with |
| $\kappa_U=\tilde\kappa_U=0$ (FeynRules + UFO), (b) runs 5 parton-level |
| MadGraph runs (1 SM baseline at 500k events with $\beta_L^{32}=0$ and |
| $m_\mathrm{LQ}=10^5$ GeV; 4 LQ signal runs at $\beta_L^{32}\in |
| \{1.0, 0.1\}$ x $m_\mathrm{LQ}\in\{1, 10\}$ TeV with 50k events |
| each), (c) extracts the $b$-quark $|\eta|$ from each event, (d) |
| histograms into the 13 bins and normalizes to total events per run, |
| (e) plots two panels side by side with the prescribed style. Research |
| question: *does the agent reproduce the central-vs-forward angular |
| redistribution induced by the $t$-channel $U_1$ exchange in |
| $\mu^+\mu^- \to b\bar b$ from Figure 11 of arXiv:2104.05720?* |
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| hypotheses: |
| - id: H1 |
| statement: "At $\\beta_L^{32} = 1.0$, $m_\\mathrm{LQ} = 1$ TeV, the central-bin ($|\\eta| < 0.1$) normalized fraction exceeds the SM by $\\geq 50\\%$ (LQ $t$-channel pulls events forward+central)." |
| measurable: true |
| - id: H2 |
| statement: "At $\\beta_L^{32}=0.1$, the normalized $|\\eta|$ shape differs from the SM baseline by $\\leq 10\\%$ in every bin (small-coupling regime collapses to SM)." |
| measurable: true |
| - id: H3 |
| statement: "At $\\beta_L^{32}=1.0$, $m_\\mathrm{LQ}=10$ TeV the normalized shape lies between the SM and the $m_\\mathrm{LQ}=1$ TeV curves (decoupling limit)." |
| measurable: true |
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| experiment_design: |
| research_question: "Does the agent reproduce the normalized $|\\eta|$ distributions of $\\mu^+\\mu^- \\to b\\bar b$ for SM and $U_1$ leptoquark signal at $\\sqrt{s}=3$ TeV muon collider, in the two coupling regimes $\\beta_L^{32} \\in \\{1.0, 0.1\\}$ (Figure 11 of arXiv:2104.05720)?" |
| conditions: |
| - name: "sm_baseline_3tev" |
| description: "All $\\beta_L^{ij} = 0$ (LQ decoupled), $m_\\mathrm{LQ} = 10^5$ GeV. 500k events at $\\sqrt{s}=3$ TeV, parton level." |
| - name: "lq_beta1_3tev" |
| description: "$\\beta_L^{32} = 1.0$, mass scan $m_\\mathrm{LQ} \\in \\{1, 10\\}$ TeV, 50k events each at $\\sqrt{s}=3$ TeV." |
| - name: "lq_beta01_3tev" |
| description: "$\\beta_L^{32} = 0.1$, mass scan $m_\\mathrm{LQ} \\in \\{1, 10\\}$ TeV, 50k events each at $\\sqrt{s}=3$ TeV." |
| baselines: |
| - "SM $s$-channel $\\mu^+\\mu^- \\to \\gamma^*/Z^* \\to b\\bar b$ (the $\\beta_L^{32}=0$ run)" |
| metrics: |
| - name: "central_bin_excess_fraction" |
| direction: "match_reference" |
| description: "Ratio of central-bin ($|\\eta| < 0.1$) normalized event fraction in LQ signal vs SM." |
| - name: "shape_deviation_l1norm" |
| direction: "match_reference" |
| description: "$L^1$ norm $\\sum_i |f_i^\\mathrm{LQ} - f_i^\\mathrm{SM}|$ of normalized shape difference per (mass, coupling)." |
| - name: "decoupling_distance" |
| direction: "match_reference" |
| description: "Shape distance between $m_\\mathrm{LQ}=10$ TeV signal and SM should be smaller than for $m_\\mathrm{LQ}=1$ TeV signal." |
| datasets: |
| - process_id: "mumu_to_bbbar_U1" |
| sqrt_s_TeV: 3 |
| description: "$\\mu^+\\mu^- \\to b\\bar b$ via SM ($s$-channel) + $U_1$ ($t$-channel) at a 3 TeV muon collider, parton level." |
| compute_requirements: |
| gpu_required: false |
| estimated_wall_clock_sec: 3600 |
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| rubric_path: "experiments/arc_bench/config/physics/rubrics/P09.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 |
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|
| - 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 |
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| - 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 |
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| - 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_central_bin_excess |
| type: numeric |
| description: >- |
| results.json metrics MUST report the normalized central-|η|<0.1 fraction for β_L^32=1.0, m_LQ=1 TeV, AND the same fraction for SM, AND the LQ fraction MUST exceed SM by ≥50%. |
| must_pass: true |
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| - 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 |
|
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| - 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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