Reproducing the Randall-Sundrum KK-graviton resonance pattern in $e^+e^- \to \mu^+\mu^-$

Reproducing warped extra dimension Kaluza-Klein graviton resonance from arXiv:hep-ph/9909255

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?*

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.

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.

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 $\sqrt{s}=m_n$.

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?

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.

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.

Pure SM $e^+e^- \to \mu^+\mu^-$ (Drell-Yan via $\gamma^*/Z$) at the same energy points

Total $\sigma(e^+e^- \to \mu^+\mu^-)$ in pb at each of the 11 $\sqrt{s}$ points.

Reconstructed $\sqrt{s}$ at which the first KK resonance peaks; target = $600 \pm 30$ GeV.

Ratio $\sigma(\sqrt{s}=m_1) / \sigma(\sqrt{s}=m_1 - 200\,\mathrm{GeV})$; should exceed $\sim 10$.

$e^+e^- \to \mu^+\mu^-$ in the RS warped-graviton model.

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).

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.

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.

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.

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.

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.

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.

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.

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.

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.

Code-development bucket: BSM model + process card + PDF/cuts + full pipeline are wired correctly.

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.

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.

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.

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.

Execution-validity bucket: MC sample passes nevents threshold, physics-validity gates clear, MC stats are sufficient.

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.

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.

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.

Results bucket: quantitative comparison of three hypothesis-driven observables to the published figure, plus a reproduced figure artifact and a per-hypothesis writeup.

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.

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.

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.

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.

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.

Reproducibility bucket (new for physics topics; absent in T-rubrics): the artifacts contain everything needed to rerun the analysis from scratch.

UFO model directory (or analytic model Python module) is checked into the artifacts and is loadable by MadGraph (or directly importable for analytic models).

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.

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.


Reproducing $pp \to \mu^\pm N$ cross section vs heavy-Majorana-neutrino mass at $\sqrt{s} = 7, 8, 14$ TeV

Reproducing heavy Majorana neutrino production $pp \to \mu^\pm N$ at LHC 7/8/14 TeV from arXiv:1308.2209

Reproducing the LHC sensitivity to a single heavy Majorana neutrino $N$
in the muon channel as a benchmark of the agent's ability to assemble a
hadron-collider Lagrangian -> MC -> analysis pipeline. The BSM extension
adds a right-handed singlet $N$ mixing with $\nu_\mu$ via the
dimensionless real parameter $V_{\mu N}$, so the relevant interaction is
$\mathcal{L}_N \supset -(g_2/\sqrt{2})\,V_{\mu N}\,(\bar\mu\gamma^\mu P_L
N)\,W^-_\mu + (\text{NC term}) + \text{h.c.}$ The diagnostic observable
is the $W^*$-mediated cross section $\sigma(pp \to \mu^\pm N)$ scanned
over $m_N \in \{100, 200, \ldots, 1000\}$ GeV with $|V_{\mu N}|=1$, at
three LHC energies $\sqrt{s} \in \{7, 8, 14\}$ TeV with the CTEQ6L PDF.

A credible study (a) implements the heavy-Majorana-neutrino Lagrangian
(FeynRules .fr or analytic UFO modification), (b) sets up MadGraph runs
for the 30 (mass, energy) cells with the CTEQ6L PDF, (c) extracts the
cross section per cell, and (d) plots three side-by-side panels of
$\sigma(m_N)$ on a log-y axis over $[100,1000]$ GeV vs $[0.1, 4\times
10^4]$ fb. Research question: *does the agent reproduce the steep
PDF-driven fall-off of $\sigma(pp \to \mu^\pm N)$ with $m_N$ and the
correct ordering between $\sqrt{s}=7$, 8, and 14 TeV predicted by
arXiv:1308.2209 Fig. 3?*

At $m_N = 200$ GeV and $\sqrt{s}=14$ TeV, $\sigma(pp \to \mu^\pm N)$ falls within $\pm 30\%$ of the published reference value.

Cross-section ordering $\sigma(14\,\mathrm{TeV}) > \sigma(8\,\mathrm{TeV}) > \sigma(7\,\mathrm{TeV})$ holds at every mass point, with the 14/7 ratio at $m_N = 500$ GeV in $[5, 30]$.

$\sigma(m_N)$ falls by at least 2 orders of magnitude between $m_N = 100$ GeV and $m_N = 1000$ GeV at every LHC energy.

Does the agent reproduce the cross-section curves for $pp \to \mu^\pm N$ as a function of the heavy-Majorana-neutrino mass at the 7, 8, and 14 TeV LHC, matching Figure 3 of arXiv:1308.2209?

$pp$ collisions at $\sqrt{s}=7$ TeV with CTEQ6L PDF, mass scan $m_N \in \{100, 200, 300, 400, 500, 600, 700, 800, 900, 1000\}$ GeV, $|V_{\mu N}|=1$.

Same setup at $\sqrt{s}=8$ TeV (LHC Run 1 final dataset energy).

Same setup at $\sqrt{s}=14$ TeV (HL-LHC design).

Charged-current SM $pp \to \mu \nu_\mu$ (W production) cross check at the same energies

Total $\sigma(pp \to \mu^\pm N)$ in fb at each (mass, energy) cell.

$\sigma(14\,\mathrm{TeV})/\sigma(7\,\mathrm{TeV})$ at $m_N = 500$ GeV.

$\sigma(m_N=100)/\sigma(m_N=1000)$ at each $\sqrt{s}$.

$pp \to \mu^\pm N$ via $W^*$ at the LHC (CTEQ6L PDF). Three sub-samples for $\sqrt{s} \in \{7,8,14\}$ TeV.

results.json metrics MUST report a numeric `sigma_pp_to_muN_at_mN200_14TeV_fb` (or equivalent) within ±30% of the published reference value at m_N=200 GeV, √s=14 TeV.

A credible HEP collider study reproducing the published reference figure for Heavy Majorana neutrino $pp \to \mu^\pm N$ at LHC 7/8/14 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.

Code-development bucket: BSM model + process card + PDF/cuts + full pipeline are wired correctly.

BSM Lagrangian implemented (FeynRules .fr file + UFO output, or equivalent analytic Python module): BSM single right-handed Majorana neutrino $N$ mixing with the muon flavor: $\mathcal{L}_N \supset -(g_2/\sqrt 2) V_{\mu N} (\bar\mu \gamma^\mu P_L N) W^-_\mu - (g_2/2 c_W) V_{\mu N} (\bar\nu_\mu \gamma^\mu P_L N) Z_\mu + \mathrm{h.c.}$ at $|V_{\mu N}| = 1$.

MadGraph generate-process card or analytic process module matches the paper's process string: $pp \to \mu^\pm N$ via $W^*$ at the LHC, mass scan $m_N \in \{100,\ldots,1000\}$ GeV at three energies.

PDF set and generation-level cuts match the paper exactly: CTEQ6L PDF for all $\sqrt{s}$ values; 30 (mass, energy) cells (10 masses x 3 energies).

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.

Execution-validity bucket: MC sample passes nevents threshold, physics-validity gates clear, MC stats are sufficient.

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.

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.

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.

Results bucket: quantitative comparison of three hypothesis-driven observables to the published figure, plus a reproduced figure artifact and a per-hypothesis writeup.

Quantitative test of H1 — $\sigma(pp \to \mu^\pm N)$ at $m_N=200$ GeV, $\sqrt{s}=14$ TeV agrees with reference within $\pm 30\%$.

Quantitative test of H2 — Energy ordering $\sigma(14) > \sigma(8) > \sigma(7)$ TeV holds at every mass; 14/7 ratio at $m_N=500$ GeV in $[5, 30]$. Use the same graded relative-error scale as H1.

Quantitative test of H3 — $\sigma(m_N)$ falls $\geq 2$ orders of magnitude from $m_N=100$ to $m_N=1000$ GeV at every $\sqrt{s}$. Use the same graded relative-error scale as H1.

A reproduced figure exists in artifacts (PDF or PNG) with axes, units, ranges, and legend matching the published reference: Three-panel figure (one per $\sqrt{s}$), 1:1 aspect, x-axis $m_N \in [100,1000]$ GeV linear, y-axis $\sigma \in [0.1, 4\times10^4]$ fb log.

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.

Reproducibility bucket (new for physics topics; absent in T-rubrics): the artifacts contain everything needed to rerun the analysis from scratch.

UFO model directory (or analytic model Python module) is checked into the artifacts and is loadable by MadGraph (or directly importable for analytic models).

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.

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.


Reproducing 8 TeV LHC dilepton exclusion contours for a B-L Z' boson with kinetic mixing

Reproducing 8 TeV LHC dilepton exclusion contours for B-L Z' with kinetic mixing from arXiv:1605.02910

high-energy-physics bsm-phenomenology z-prime statistical-recast

Reproducing the LHC Run 1 sensitivity to a B-L gauge boson Z' with
kinetic mixing as a benchmark of the agent's ability to combine MC
parameter scans with an analytic statistical recast. The model has a
Z' coupling to SM fermions via a left/right combination
$C_{f,L/R}(\tilde g, g_1', M_{Z'})$ where $g_1'$ is the B-L gauge
coupling, $\tilde g$ is the kinetic mixing, and the production cross
section is the exact quadratic form
$\sigma(pp \to Z') = A g_1'^2 + B g_1' \tilde g + C \tilde g^2$ — so
three runs per mass point determine $(A,B,C)$ for the entire $(\tilde
g, g_1')$ plane. The diagnostic observable is the three-panel exclusion
contour at $\mathrm{Sig}\equiv 2(\sqrt{S+B}-\sqrt B) = 2$ for
$M_{Z'} \in \{2.0, 2.5, 3.0\}$ TeV at $\mathcal{L} = 20$ fb$^{-1}$.

A credible study (a) implements the kinetic-mixing B-L Lagrangian and
$C_{f,L/R}$ couplings, (b) runs the 9 signal MadGraph runs (3 mass
points x 3 coupling points) plus 3 SM Drell-Yan background runs with
$m_{\ell\ell} > 0.9 M_{Z'}$ generator cut, (c) computes the analytic
$Z' \to e^+e^- + \mu^+\mu^-$ branching ratio including 3 degenerate
heavy Majorana neutrinos $m_{\nu_h}=95$ GeV, (d) applies the published
NNLO k-factors $k\in\{1.35,1.40,1.50\}$ and acceptance
$\epsilon_\mathrm{acc}=0.6$, (e) solves the $\mathrm{Sig}=2$ equation
on a 2D grid in $(\tilde g, g_1')$, and (f) plots three side-by-side
contours. Research question: *does the agent reproduce the three-panel
$(\tilde g, g_1')$ exclusion contours at $M_{Z'}=2.0, 2.5, 3.0$ TeV from
Figure 1 of arXiv:1605.02910?*

For the $M_{Z'}=2$ TeV panel, the exclusion contour crosses the $\tilde g = 0$ axis at $g_1' \in [0.10, 0.20]$ (matching the published value within 30%).

The $(A, B, C)$ quadratic coefficients extracted at $M_{Z'}=2$ TeV satisfy $A > 0$ and $|B| \le 4\sqrt{AC}$ (positivity of the cross section over the full parameter plane).

The maximum reach in $g_1'$ at $\tilde g = 0$ degrades by at least a factor of 2 going from $M_{Z'}=2$ TeV to $M_{Z'}=3$ TeV, reflecting the PDF suppression at high mass.

Does the agent reproduce the three-panel $(\tilde g, g_1')$ 2$\sigma$ exclusion contours at $M_{Z'}=2.0, 2.5, 3.0$ TeV from the LHC Run 1 dilepton search at $\sqrt{s}=8$ TeV with $\mathcal{L}=20$ fb$^{-1}$ (Figure 1 of arXiv:1605.02910)?

$M_{Z'}=2$ TeV: 3 signal runs at $(g_1', \tilde g) \in \{(0.10, 0), (0.10, -0.10), (0.15, -0.05)\}$.

$M_{Z'}=2.5$ TeV: 3 signal runs at the same three $(g_1', \tilde g)$ points.

$M_{Z'}=3$ TeV: 3 signal runs at $(g_1', \tilde g) \in \{(0.30, 0), (0.30, -0.30), (0.50, -0.60)\}$.

SM Drell-Yan $pp \to \ell^+\ell^-$ at $\sqrt{s}=8$ TeV with generator-level cut $m_{\ell\ell} > 0.9 M_{Z'}$, one per mass point

Value of $g_1'$ at which the $\mathrm{Sig}=2$ contour crosses $\tilde g = 0$, per mass point.

$(A, B, C)$ extracted from the 3 signal runs per mass; positive-definite check.

Analytic $\mathrm{BR}(Z' \to e^+e^-+\mu^+\mu^-)$ at the three benchmark masses.

$pp \to Z'$ with kinetic-mixing B-L Z' at the LHC, dilepton final state. Background: SM Drell-Yan with $m_{\ell\ell}$ cut.

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).

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.

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.

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.

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.

results.json metrics MUST report the g1' coordinate where the 2σ exclusion contour at M_Z'=2 TeV crosses the g̃=0 axis, in the interval [0.07, 0.26] (i.e. published [0.10, 0.20] ±30%).

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.

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.

A credible HEP collider study reproducing the published reference figure for B-L $Z'$ kinetic mixing, three-panel exclusion in $(\tilde g, g_1')$. 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.

Code-development bucket: BSM model + process card + PDF/cuts + full pipeline are wired correctly.

BSM Lagrangian implemented (FeynRules .fr file + UFO output, or equivalent analytic Python module): Kinetic-mixing B-L $Z'$ with chiral couplings $C_{f,L/R}(\tilde g, g_1', M_{Z'})$ encoding $g_1'$ (B-L gauge), $\tilde g$ (kinetic mixing), and 3 heavy Majorana neutrinos $\nu_h$ at $m_{\nu_h}=95$ GeV.

MadGraph generate-process card or analytic process module matches the paper's process string: $pp \to Z'$ at $\sqrt{s}=8$ TeV with kinetic mixing; Drell-Yan dilepton search recast.

PDF set and generation-level cuts match the paper exactly: 9 signal runs (3 mass x 3 coupling points), 3 SM Drell-Yan background runs with generator cut $m_{\ell\ell} > 0.9 M_{Z'}$ at $\sqrt{s}=8$ TeV; mass-dependent NNLO k-factors $\{1.35, 1.40, 1.50\}$ and $\epsilon_\mathrm{acc}=0.6$.

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.

Execution-validity bucket: MC sample passes nevents threshold, physics-validity gates clear, MC stats are sufficient.

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.

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.

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.

Results bucket: quantitative comparison of three hypothesis-driven observables to the published figure, plus a reproduced figure artifact and a per-hypothesis writeup.

Quantitative test of H1 — $M_{Z'}=2$ TeV exclusion contour crosses the $\tilde g=0$ axis at $g_1' \in [0.10, 0.20]$ (within 30% of published).

Quantitative test of H2 — Quadratic coefficients $(A,B,C)$ at $M_{Z'}=2$ TeV satisfy $A>0$ and $|B| \le 4\sqrt{AC}$ (positive-definite cross section everywhere in plane). Use the same graded relative-error scale as H1.

Quantitative test of H3 — Maximum reach in $g_1'$ at $\tilde g=0$ degrades by $\geq 2\times$ from $M_{Z'}=2$ TeV to $M_{Z'}=3$ TeV. Use the same graded relative-error scale as H1.

A reproduced figure exists in artifacts (PDF or PNG) with axes, units, ranges, and legend matching the published reference: Three side-by-side panels (one per $M_{Z'}$), 1:1 aspect, exclusion contour at $\mathrm{Sig}\equiv 2(\sqrt{S+B}-\sqrt B)=2$ in the $(\tilde g, g_1')$ plane.

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.

Reproducibility bucket (new for physics topics; absent in T-rubrics): the artifacts contain everything needed to rerun the analysis from scratch.

UFO model directory (or analytic model Python module) is checked into the artifacts and is loadable by MadGraph (or directly importable for analytic models).

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.

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.


Reproducing $\sigma(pp \to Z')$ vs $g_1'$ slices for kinetic-mixing B-L Z' at $\sqrt{s}=13$ TeV

Reproducing $\sigma(pp \to Z')$ vs $g_1'$ slices for kinetic-mixing B-L Z' at 13 TeV from arXiv:1605.02910

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?*

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.

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.

$\sigma$ 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.

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)?

$M_{Z'}=2$ TeV at $\sqrt{s}=13$ TeV: 3 signal runs at $(g_1', \tilde g) \in \{(0.10, 0), (0.10, -0.10), (0.15, -0.05)\}$.

$M_{Z'}=3$ TeV at $\sqrt{s}=13$ TeV: 3 signal runs at $(g_1', \tilde g) \in \{(0.30, 0), (0.30, -0.30), (0.50, -0.60)\}$.

Self-consistency cross-check: predicted $\sigma$ at the 3 input points must reproduce the simulated $\sigma$ exactly (closure of the $A,B,C$ fit)

$\sigma(pp \to Z')$ in pb on the requested slice points.

$(A, B, C)$ coefficients per mass point at $\sqrt{s}=13$ TeV.

$\sigma(M_{Z'}=2)/\sigma(M_{Z'}=3)$ at $\tilde g = 0$, $g_1' = 0.10$.

$pp \to Z'$ for the kinetic-mixing B-L Z' model at LHC Run 2 energy.

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.

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.

Code-development bucket: BSM model + process card + PDF/cuts + full pipeline are wired correctly.

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.

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.

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.

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.

Execution-validity bucket: MC sample passes nevents threshold, physics-validity gates clear, MC stats are sufficient.

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.

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.

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.

Results bucket: quantitative comparison of three hypothesis-driven observables to the published figure, plus a reproduced figure artifact and a per-hypothesis writeup.

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.

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.

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.

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.

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.

Reproducibility bucket (new for physics topics; absent in T-rubrics): the artifacts contain everything needed to rerun the analysis from scratch.

UFO model directory (or analytic model Python module) is checked into the artifacts and is loadable by MadGraph (or directly importable for analytic models).

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.

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.


Reproducing the normalized $E_T^\mathrm{miss}$ shape in $pp \to a W^\pm \gamma$ from a photophobic ALP EFT

Reproducing photophobic ALP EFT $E_T^\mathrm{miss}$ shape in $pp \to a W^\pm \gamma$ from arXiv:1701.05379

high-energy-physics bsm-phenomenology axion-like-particles effective-field-theory

Reproducing the normalized $E_T^\mathrm{miss}$ distribution for the
process $pp \to a W^\pm (\to \ell^\pm \nu)\, \gamma$ at $\sqrt{s}=13$
TeV in the bosonic ALP EFT, as a benchmark of the agent's ability to
handle a higher-dimensional EFT operator and parton-level missing-energy
reconstruction. The Lagrangian is
$\delta\mathcal{L}_a = c_{\tilde W} \mathcal{A}_{\tilde W} +
c_{\tilde B} \mathcal{A}_{\tilde B}$ with the photophobic constraint
$c_{\tilde B} = -\tan^2\theta_W \cdot c_{\tilde W}$ (so the
$a\gamma\gamma$ coupling vanishes), giving a single free Wilson
coefficient $c_{\tilde W}$. The diagnostic observable is the
normalized parton-level $E_T^\mathrm{miss} = |\vec p_T^{\,a} +
\vec p_T^{\,\nu}|$ shape in 50 bins over [0, 1000] GeV, with
generation cuts $p_T^{\gamma,\ell} > 20$ GeV, $|\eta^{\gamma,\ell}| < 2.5$.

A credible study (a) implements the photophobic ALP EFT (FeynRules
bosonic operators with $c_{\tilde B} = -\tan^2\theta_W \cdot c_{\tilde W}$),
(b) generates 500k LHE events at $f_a = 1000$ GeV, $m_a = 0.001$ GeV,
$c_{\tilde W} = 1$ with the nn23lo1 PDF, (c) sums $\vec p_T^{\,a}$ +
$\vec p_T^{\,\nu}$ from invisible final-state particles to reconstruct
$E_T^\mathrm{miss}$, and (d) plots the normalized histogram on log-y
$[10^{-4}, 1]$ over [0, 1000] GeV. Research question: *does the agent
reproduce the falling-then-flattening MET shape characteristic of a
derivative ALP coupling versus the steeply falling SM-like baseline,
matching Figure 8 of arXiv:1701.05379?*

The peak of the normalized $E_T^\mathrm{miss}$ distribution lies in the bin range $[100, 250]$ GeV, consistent with the published shape.

The integrated normalized fraction of events with $E_T^\mathrm{miss} > 500$ GeV is in $[0.05, 0.30]$ at $c_{\tilde W}=1$, $f_a=1$ TeV (long high-MET tail from the derivative ALP coupling).

Acceptance after the published photon and lepton cuts ($p_T > 20$ GeV, $|\eta| < 2.5$) is $\geq 50\%$ of generated events.

Does the agent reproduce the parton-level $E_T^\mathrm{miss}$ shape for $pp \to a W^\pm \gamma$, $W \to \ell\nu$ at $\sqrt{s}=13$ TeV under the photophobic ALP EFT (Figure 8 of arXiv:1701.05379)?

Bosonic ALP EFT at $c_{\tilde W}=1$, $c_{\tilde B}=-\tan^2\theta_W$, $f_a=1000$ GeV, $m_a=0.001$ GeV, 500k events at $\sqrt{s}=13$ TeV with nn23lo1 PDF.

Sanity-check run at $c_{\tilde W}=2$, $f_a=1000$ GeV; cross section should scale as $c_{\tilde W}^2$ but normalized shape should be invariant.

Shape-only normalization is its own baseline: deviation between $c_{\tilde W}=1$ and $c_{\tilde W}=2$ shapes should be statistical only

$E_T^\mathrm{miss}$ bin center of the peak of the normalized histogram.

Fraction of normalized events with $E_T^\mathrm{miss} > 500$ GeV.

Acceptance fraction after photon + lepton fiducial cuts.

Parton-level $pp \to a W^\pm \gamma$ with $W \to \ell\nu$ in the photophobic ALP EFT.

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).

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.

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.

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.

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.

results.json metrics MUST report the peak bin of the normalized E_T^miss distribution; the bin center must lie in [100, 250] GeV and the distribution must integrate to 1.0 (normalized).

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.

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.

A credible HEP collider study reproducing the published reference figure for Photophobic ALP EFT $E_T^\mathrm{miss}$ in $pp \to a W^\pm \gamma$. 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.

Code-development bucket: BSM model + process card + PDF/cuts + full pipeline are wired correctly.

BSM Lagrangian implemented (FeynRules .fr file + UFO output, or equivalent analytic Python module): Bosonic ALP EFT operators $\mathcal{A}_{\tilde W}, \mathcal{A}_{\tilde B}$ with photophobic relation $c_{\tilde B} = -\tan^2\theta_W \cdot c_{\tilde W}$; $f_a = 1$ TeV, $m_a = 1$ MeV, $c_{\tilde W} = 1$.

MadGraph generate-process card or analytic process module matches the paper's process string: Parton-level $pp \to a W^\pm (\to \ell^\pm\nu) \gamma$ at $\sqrt{s}=13$ TeV.

PDF set and generation-level cuts match the paper exactly: nn23lo1 PDF; photon $p_T > 20$ GeV, $|\eta_\gamma| < 2.5$; lepton $p_T > 20$ GeV, $|\eta_\ell| < 2.5$; 500k events, parton level (no shower/detector).

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.

Execution-validity bucket: MC sample passes nevents threshold, physics-validity gates clear, MC stats are sufficient.

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.

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.

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.

Results bucket: quantitative comparison of three hypothesis-driven observables to the published figure, plus a reproduced figure artifact and a per-hypothesis writeup.

Quantitative test of H1 — Peak of normalized $E_T^\mathrm{miss}$ in $[100, 250]$ GeV bin range.

Quantitative test of H2 — Integrated normalized fraction with $E_T^\mathrm{miss} > 500$ GeV in $[0.05, 0.30]$ (long high-MET tail from derivative coupling). Use the same graded relative-error scale as H1.

Quantitative test of H3 — Acceptance after photon + lepton cuts $\geq 50\%$. Use the same graded relative-error scale as H1.

A reproduced figure exists in artifacts (PDF or PNG) with axes, units, ranges, and legend matching the published reference: Normalized $E_T^\mathrm{miss}$ histogram, 50 bins over [0,1000] GeV, log-y $[10^{-4}, 1]$, 4:3 aspect.

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.

Reproducibility bucket (new for physics topics; absent in T-rubrics): the artifacts contain everything needed to rerun the analysis from scratch.

UFO model directory (or analytic model Python module) is checked into the artifacts and is loadable by MadGraph (or directly importable for analytic models).

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.

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.


Reproducing $U_1$ vector-leptoquark $\sqrt{|g_c^* g_b|}$ vs $M_{U_1}$ exclusion from ATLAS+CMS $pp \to \tau\nu$

Reproducing $U_1$ vector leptoquark exclusion from combined ATLAS+CMS $pp \to \tau\nu$ recast from arXiv:1811.07920

high-energy-physics bsm-phenomenology leptoquark flavor-anomaly statistical-recast

Reproducing the LHC sensitivity to a $U_1$ vector leptoquark from the
$pp \to \tau\nu$ channel via $bc \to U_1 \to \tau\nu$ exchange,
combining ATLAS + CMS searches in a binned profile-likelihood, as a
benchmark of the agent's ability to (i) generate LQ events with
bottom-quark and charm-quark initial-state partons, (ii) run two
parallel detector-card simulations (Delphes ATLAS card vs CMS card),
(iii) recast experimental data into a profile-likelihood fit. The
Lagrangian couples $U_1$ to $(\bar c \gamma^\mu P_L \nu_\tau)$ and
$(\bar b \gamma^\mu P_L \tau)$ with couplings $g_c, g_b$, and the
diagnostic figure is the 2$\sigma$ exclusion contour in the
$(\sqrt{|g_c^* g_b|}, M_{U_1})$ plane along with the LH and RH
$R_{D^{(*)}}$ flavor-anomaly bands.

A credible study (a) implements the $U_1$ Lagrangian (FeynRules .fr +
UFO), (b) runs MadGraph + Pythia8 + Delphes for $M_{U_1} \in \{750,
1000, 1250, 1500, 2000, 2500, 3000, 4000, 5000\}$ GeV with both ATLAS
and CMS cards (LHCO output), (c) applies the published ATLAS and CMS
$\tau$-channel selections (lepton veto, hadronic-$\tau$ requirement,
$E_T^\mathrm{miss}$ cut, $m_T$ cut), (d) builds a binned signal
template that scales as $g^4$ and runs the per-bin profile likelihood
with nuisance parameters $\theta_i$, (e) combines ATLAS + CMS, finds
the 2$\sigma$ exclusion via $-2\Delta\ln\mathcal{L} = 4$, and (f)
overlays the analytic LH band $g_\mathrm{LH}(M) = (M/v)\sqrt{2 V_{cb}\,
\epsilon_L}$ with $\epsilon_L = 0.11 \pm 0.02$ and the analogous RH band.
Research question: *does the agent reproduce the $(\sqrt{|g_c^* g_b|},
M_{U_1})$ exclusion contour and the $R_{D^{(*)}}$ overlay bands of
Figure 3 of arXiv:1811.07920?*

The combined ATLAS+CMS 2$\sigma$ exclusion at $M_{U_1} = 1$ TeV gives $\sqrt{|g_c^* g_b|} \in [0.3, 1.5]$, matching the published value within 30%.

The reconstructed exclusion contour intersects the LH $R_{D^{(*)}}$ band ($\epsilon_L = 0.11$) at an excluded mass $M_{U_1}^* \in [1.0, 2.5]$ TeV.

Selection efficiency on signal events is $\geq 5\%$ at $M_{U_1}=1$ TeV in both ATLAS and CMS analyses (gauge of pipeline working end-to-end through Delphes).

Does the agent reproduce the 2$\sigma$ exclusion contour for the $U_1$ vector leptoquark in the $(\sqrt{|g_c^* g_b|}, M_{U_1})$ plane from combined ATLAS+CMS $pp \to \tau\nu$ recast (Figure 3 of arXiv:1811.07920)?

Mass scan $M_{U_1} \in \{750, 1000, 1250, 1500, 2000, 2500, 3000, 4000, 5000\}$ GeV at $\sqrt{s}=13$ TeV, 10k events each, Pythia8 shower, Delphes ATLAS card, LHCO output. Selection: lepton veto, hadronic-$\tau$ $p_T > 80$ GeV, $|\eta_\tau| < 2.3$, $E_T^\mathrm{miss} > 150$ GeV, $m_T > 250$ GeV.

Same mass scan with Delphes CMS card; selection: lepton veto, $\tau$ $p_T>80$ GeV, $|\eta|<2.1$, $E_T^\mathrm{miss}>200$ GeV, $0.7 < p_T^\tau / E_T^\mathrm{miss} < 1.3$, $\Delta\phi(\tau, E_T^\mathrm{miss}) > 2.4$, $m_T > 320$ GeV.

Published ATLAS background table (22 bins, 250-3200 GeV log-spaced) and CMS background table (3 bins) act as the SM-only null hypothesis

$\sqrt{|g_c^* g_b|}$ at the 2$\sigma$ exclusion boundary at $M_{U_1}=1$ TeV from combined fit.

Fraction of generated signal events passing the ATLAS or CMS selection at $M_{U_1}=1$ TeV.

Mass at which the LH $R_{D^{(*)}}$ band crosses the exclusion contour.

$pp \to \tau\nu$ via $bc \to U_1$ exchange. Two detector simulations (Delphes ATLAS, Delphes CMS).

results.json metrics MUST report the 2σ combined ATLAS+CMS √(g_c* g_b) exclusion band at M_U1=1 TeV; the band lower edge must be in [0.21, 0.39] and the upper edge in [1.05, 1.95] (published [0.3, 1.5] ±30%).

A credible HEP collider study reproducing the published reference figure for $U_1$ vector-leptoquark recast of LHC $pp \to \tau\nu$ (ATLAS+CMS). 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.

Code-development bucket: BSM model + process card + PDF/cuts + full pipeline are wired correctly.

BSM Lagrangian implemented (FeynRules .fr file + UFO output, or equivalent analytic Python module): $U_1$ vector LQ in $(\mathbf{3},\mathbf{1},2/3)$ rep coupling to $(\bar c\gamma^\mu P_L\nu_\tau)$ and $(\bar b\gamma^\mu P_L\tau)$ with couplings $g_c, g_b$.

MadGraph generate-process card or analytic process module matches the paper's process string: $pp \to \tau\nu$ via $bc \to U_1 \to \tau\nu$ exchange at $\sqrt{s}=13$ TeV, mass scan.

PDF set and generation-level cuts match the paper exactly: Standard 13 TeV proton PDF; 9 mass points $\{750,\ldots,5000\}$ GeV with $b$ and $c$ parton initial states; 10k events per (mass, detector); Pythia8 shower; Delphes ATLAS card and Delphes CMS card runs in parallel; LHCO output.

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.

Execution-validity bucket: MC sample passes nevents threshold, physics-validity gates clear, MC stats are sufficient.

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.

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.

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.

Results bucket: quantitative comparison of three hypothesis-driven observables to the published figure, plus a reproduced figure artifact and a per-hypothesis writeup.

Quantitative test of H1 — Combined ATLAS+CMS 2$\sigma$ exclusion at $M_{U_1}=1$ TeV gives $\sqrt{|g_c^* g_b|} \in [0.3, 1.5]$.

Quantitative test of H2 — Reconstructed exclusion contour intersects the LH $R_{D^{(*)}}$ band ($\epsilon_L=0.11$) at excluded mass $M_{U_1}^* \in [1.0, 2.5]$ TeV. Use the same graded relative-error scale as H1.

Quantitative test of H3 — Selection efficiency $\geq 5\%$ on signal at $M_{U_1}=1$ TeV in both ATLAS and CMS recasts. Use the same graded relative-error scale as H1.

A reproduced figure exists in artifacts (PDF or PNG) with axes, units, ranges, and legend matching the published reference: Exclusion contour in $(\sqrt{|g_c^* g_b|}, M_{U_1})$ plane, 4:3 aspect, x in TeV $[0.8, 5.0]$, y $[0, 4.0]$, with LH band (blue dashed + light-blue band) and RH band (red dashed + light-red band).

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.

Reproducibility bucket (new for physics topics; absent in T-rubrics): the artifacts contain everything needed to rerun the analysis from scratch.

UFO model directory (or analytic model Python module) is checked into the artifacts and is loadable by MadGraph (or directly importable for analytic models).

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.

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.


Reproducing the $m_{ej}$ resonance in $pp \to \mathrm{LQ} \to ej$ via the LUXlep proton lepton PDF

Reproducing scalar leptoquark $m_{ej}$ resonance via LUXlep proton lepton PDF from arXiv:2005.06475

high-energy-physics bsm-phenomenology leptoquark lepton-pdf

Reproducing the LHC sensitivity to a scalar leptoquark in the
$pp \to \mathrm{LQ} \to ej$ channel as a benchmark of the agent's
ability to assemble a full Lagrangian -> MC -> shower -> detector ->
analysis pipeline using a non-trivial PDF (LUXlep, with electrons inside
the proton). The Lagrangian
$\mathcal{L} = \lambda_{eu}\,\mathrm{LQ}_{eu}\,e_R^T i\sigma^2 u_R +
\mathrm{h.c.}$ describes an $SU(2)_L$-singlet, color-triplet,
$Q=-1/3$ scalar leptoquark coupling to a right-handed lepton-quark pair.
The diagnostic observable is the reconstructed invariant mass $m_{ej}$
of the leading electron and leading jet, peaked at the input
$M_\mathrm{LQ}=3$ TeV with $\Gamma_\mathrm{LQ}=60$ GeV after Pythia8 +
Delphes ATLAS detector smearing.

A credible study (a) implements the scalar-LQ Lagrangian (FeynRules .fr
+ UFO), (b) generates 100k events at $\sqrt{s}=13$ TeV with the LUXlep
PDF (proton content redefined to include leptons + photon) and
generation cuts $p_T(\ell, j) > 500$ GeV, $|\eta| < 2.5$, (c) applies
the Pythia8 lepton-to-photon workaround (replace initial-state leptons
with photons in the LHE; set Check:event=off; shower; Delphes ATLAS
card with anti-$k_T$ R=0.4 jets; LHCO output), (d) selects events with
exactly one $e$ ($p_T>500$ GeV, $|\eta|<2.5$), one $j$ ($p_T>500$ GeV,
$|\eta|<2.5$), $E_T^\mathrm{miss} < 50$ GeV, lepton veto, jet veto,
(e) histograms $m_{ej}$ in 100 GeV bins from 0 to 5000 GeV weighted by
$\sigma\mathcal{L}/N_\mathrm{gen}$ at $\mathcal{L}=100$ fb$^{-1}$, and
(f) plots on log-y $[10^{-3}, 5\times 10^2]$ events/bin over [1000,
5000] GeV. Research question: *does the agent reproduce the scalar-LQ
resonance peak at $m_{ej} \approx 3$ TeV from Figure 2 of arXiv:2005.06475?*

Reconstructed $m_{ej}$ peaks within $\pm 5\%$ of the input $M_\mathrm{LQ}=3000$ GeV after Pythia8+Delphes smearing (i.e., peak in [2850, 3150] GeV).

The generation-level $p_T(\ell, j) > 500$ GeV cut yields $\geq 50\%$ acceptance for the benchmark $M_\mathrm{LQ}=3$ TeV signal.

Total event count in the [2.5, 3.5] TeV $m_{ej}$ window at $\mathcal{L} = 100$ fb$^{-1}$ matches the published value within $\pm 30\%$.

Does the agent reproduce the $m_{ej}$ invariant-mass distribution for $pp \to \mathrm{LQ} \to ej$ at $\sqrt{s}=13$ TeV with LUXlep PDF and $M_\mathrm{LQ}=3$ TeV (Figure 2 of arXiv:2005.06475)?

Scalar LQ at $M_\mathrm{LQ}=3000$ GeV, $\Gamma_\mathrm{LQ}=60$ GeV, $\lambda_{eu}=1$, 100k events at $\sqrt{s}=13$ TeV, LUXlep PDF, $p_T > 500$ GeV gen cuts, Pythia8 + Delphes ATLAS, LHCO output.

Cross-check at $M_\mathrm{LQ}=2000$ GeV with $\lambda_{eu}=1$, same setup; verify that $m_{ej}$ peak shifts to 2 TeV.

Background-only sanity check: $\lambda_{eu}=0$ (LQ decoupled) should produce zero $m_{ej}$ events above the gen-level cut

Bin-center of the maximum of the reconstructed $m_{ej}$ histogram for the 3 TeV signal.

Fraction of generated events with both lepton and jet $p_T > 500$ GeV at $M_\mathrm{LQ}=3$ TeV.

Sum of weighted events in $m_{ej} \in [2500, 3500]$ GeV at $\mathcal{L}=100$ fb$^{-1}$.

Single resonant scalar leptoquark production via lepton-quark fusion using LUXlep proton PDF.

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).

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.

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.

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.

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.

results.json metrics MUST report the reconstructed m_ej peak position (after Pythia8+Delphes smearing) in the interval [2850, 3150] GeV (input M_LQ=3 TeV ±5%).

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.

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.

A credible HEP collider study reproducing the published reference figure for Scalar leptoquark resonance $m_{ej}$ via LUXlep proton lepton PDF. 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.

Code-development bucket: BSM model + process card + PDF/cuts + full pipeline are wired correctly.

BSM Lagrangian implemented (FeynRules .fr file + UFO output, or equivalent analytic Python module): Scalar LQ in $SU(2)_L$ singlet, color triplet, $Q=-1/3$; $\mathcal{L} = \lambda_{eu}\,\mathrm{LQ}_{eu}\,e_R^T i\sigma^2 u_R + \mathrm{h.c.}$; $M_\mathrm{LQ}=3$ TeV, $\Gamma=60$ GeV, $\lambda_{eu}=1$.

MadGraph generate-process card or analytic process module matches the paper's process string: $pp \to \mathrm{LQ} \to ej$ resonant single LQ production at $\sqrt{s}=13$ TeV.

PDF set and generation-level cuts match the paper exactly: LUXlep PDF (proton content includes electrons and photon); generation cuts $p_T(\ell, j) > 500$ GeV, $|\eta|<2.5$; Pythia8 with lepton-to-photon LHE workaround (Check:event=off); Delphes ATLAS card with anti-$k_T$ R=0.4 jets; LHCO output.

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.

Execution-validity bucket: MC sample passes nevents threshold, physics-validity gates clear, MC stats are sufficient.

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.

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.

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.

Results bucket: quantitative comparison of three hypothesis-driven observables to the published figure, plus a reproduced figure artifact and a per-hypothesis writeup.

Quantitative test of H1 — Reconstructed $m_{ej}$ peaks within $\pm 5\%$ of input $M_\mathrm{LQ}=3000$ GeV (peak in $[2850, 3150]$ GeV).

Quantitative test of H2 — Generation-level $p_T > 500$ GeV cut yields $\geq 50\%$ acceptance on the 3 TeV signal. Use the same graded relative-error scale as H1.

Quantitative test of H3 — Total weighted yield in $m_{ej} \in [2500, 3500]$ GeV at $\mathcal{L}=100$ fb$^{-1}$ within $\pm 30\%$ of published value. Use the same graded relative-error scale as H1.

A reproduced figure exists in artifacts (PDF or PNG) with axes, units, ranges, and legend matching the published reference: Reconstructed $m_{ej}$ histogram, 100 GeV bins from 0 to 5000 GeV, weighted by $\sigma\mathcal{L}/N_\mathrm{gen}$, log-y $[10^{-3}, 5\times 10^2]$ events/bin, 1:1 aspect, title 'LHC, $\sqrt{s}=13$ TeV'.

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.

Reproducibility bucket (new for physics topics; absent in T-rubrics): the artifacts contain everything needed to rerun the analysis from scratch.

UFO model directory (or analytic model Python module) is checked into the artifacts and is loadable by MadGraph (or directly importable for analytic models).

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.

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.


Reproducing $\sigma(pp \to Z' \to \mu^+\mu^-)$ vs $M_{Z'}$ for SSM and E6-$\psi$ scenarios at $\sqrt{s}=13$ TeV

Reproducing SSM and $E_6$-$\psi$ Z' dimuon cross sections at 13 TeV LHC from arXiv:2103.02708

Reproducing the dimuon production cross section $\sigma(pp \to Z' \to
\mu^+\mu^-)$ as a function of $M_{Z'}$ for two canonical $Z'$ benchmarks
- the Sequential Standard Model (SSM) where the $Z'$ inherits SM
electroweak couplings, and the $E_6$-derived $Z'_\psi$ with universal
coupling $g_\psi = 0.0942$. The general Lagrangian
$\mathcal{L}_{NP} \supset -Z'_\mu \sum_f \bar f \gamma^\mu (g_{Lf} P_L
+ g_{Rf} P_R) f$ has 7 free chiral couplings $g_{Lu}, g_{Ru}, g_{Ld},
g_{Rd}, g_{Le}, g_{Re}, g_{Lv}$, fixed differently in each benchmark.
The diagnostic observable is the dimuon production cross section
scanned over $M_{Z'} \in \{200, 400, 600, \ldots, 5500\}$ GeV at
$\sqrt{s}=13$ TeV.

A credible study (a) implements the general $Z'$ model (FeynRules + UFO)
with the 7 couplings as inputs, (b) sets up two parameter cards
encoding the SSM and $E_6$-$\psi$ coupling tables, (c) scans 14 mass
points per benchmark with auto-computed $\Gamma_{Z'}$ (two-body decays
only), (d) extracts the cross section per (mass, scenario) cell, and
(e) plots two curves (SSM = green dotted, $Z'_\psi$ = blue solid) on
log-y over $M_{Z'} \in [200, 5500]$ GeV, $\sigma \in [5\times 10^{-6},
5\times 10^{-1}]$ pb. Research question: *does the agent reproduce the
cross-section curves and the well-known SSM $\gtrsim Z'_\psi$ ordering
in dilepton production from Figure 4 of arXiv:2103.02708?*

$\sigma_\mathrm{SSM}(M_{Z'}=2\,\mathrm{TeV}) > \sigma_\psi(M_{Z'}=2\,\mathrm{TeV})$ by a factor in $[3, 30]$ at $\sqrt{s}=13$ TeV (SSM has larger couplings).

$\sigma_\mathrm{SSM}(M_{Z'}=1\,\mathrm{TeV})$ falls within $\pm 30\%$ of the published reference value.

The SSM cross section drops by $\geq 4$ orders of magnitude between $M_{Z'}=200$ GeV and $M_{Z'}=5500$ GeV (PDF + propagator suppression).

Does the agent reproduce $\sigma(pp \to Z' \to \mu^+\mu^-)$ vs $M_{Z'}$ for the SSM ($Z'_\mathrm{SSM}$) and $E_6$-derived $Z'_\psi$ benchmarks at the 13 TeV LHC (Figure 4 of arXiv:2103.02708)?

$Z'_\mathrm{SSM}$ with electroweak couplings $g_{Lu} = (e/s_W c_W)(1/2 - 2 s_W^2/3)$, etc. (SM-like). Scan $M_{Z'} \in \{200, 400, 600, 800, 1000, 1500, 2000, 2500, 3000, 3500, 4000, 4500, 5000, 5500\}$ GeV at $\sqrt{s}=13$ TeV.

$Z'_\psi$ from $E_6$ with universal coupling $g_\psi = 0.0942$ for all SM fermions. Same mass scan.

Internal cross-check: SSM/E6-$\psi$ ratio should be approximately mass-independent (set by the ratio of squared couplings) far from mass thresholds

$\sigma(pp \to Z' \to \mu^+\mu^-)$ in pb at each (mass, benchmark) cell.

$\sigma_\mathrm{SSM}/\sigma_\psi$ at $M_{Z'}=2$ TeV.

$\sigma_\mathrm{SSM}(M=200)/\sigma_\mathrm{SSM}(M=5500)$.

$pp \to Z' \to \mu^+\mu^-$ in the general 7-coupling $Z'$ model. Two benchmark coupling tables: SSM and $E_6$-$\psi$.

results.json metrics MUST report the ratio σ_SSM/σ_ψ at M_Z'=2 TeV, √s=13 TeV, and that ratio MUST be in [3, 30].

A credible HEP collider study reproducing the published reference figure for General $Z'$: SSM vs $E_6$-$\psi$ dimuon cross section vs mass at LHC. 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.

Code-development bucket: BSM model + process card + PDF/cuts + full pipeline are wired correctly.

BSM Lagrangian implemented (FeynRules .fr file + UFO output, or equivalent analytic Python module): General $Z'$ with 7 chiral couplings $g_{Lu/Ru/Ld/Rd/Le/Re/Lv}$; SSM tabulated values vs $E_6$-$\psi$ universal $g_\psi=0.0942$.

MadGraph generate-process card or analytic process module matches the paper's process string: $pp \to Z' \to \mu^+\mu^-$ at $\sqrt{s}=13$ TeV, mass scan over 14 points $\{200,\ldots,5500\}$ GeV.

PDF set and generation-level cuts match the paper exactly: Standard 13 TeV proton PDF; widths auto-computed (two-body decays only); 14 mass points x 2 benchmarks = 28 runs.

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.

Execution-validity bucket: MC sample passes nevents threshold, physics-validity gates clear, MC stats are sufficient.

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.

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.

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.

Results bucket: quantitative comparison of three hypothesis-driven observables to the published figure, plus a reproduced figure artifact and a per-hypothesis writeup.

Quantitative test of H1 — $\sigma_\mathrm{SSM}(2\,\mathrm{TeV}) / \sigma_\psi(2\,\mathrm{TeV})$ in $[3, 30]$.

Quantitative test of H2 — $\sigma_\mathrm{SSM}(M_{Z'}=1\,\mathrm{TeV})$ within $\pm 30\%$ of published value. Use the same graded relative-error scale as H1.

Quantitative test of H3 — $\sigma_\mathrm{SSM}$ drops $\geq 4$ orders of magnitude from $M=200$ GeV to $M=5500$ GeV. Use the same graded relative-error scale as H1.

A reproduced figure exists in artifacts (PDF or PNG) with axes, units, ranges, and legend matching the published reference: Two curves on log-y $\sigma \in [5\times 10^{-6}, 5\times 10^{-1}]$ pb vs $M_{Z'}\in[200,5500]$ GeV linear: $Z'_\mathrm{SSM}$ green dotted, $Z'_\psi$ blue solid.

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.

Reproducibility bucket (new for physics topics; absent in T-rubrics): the artifacts contain everything needed to rerun the analysis from scratch.

UFO model directory (or analytic model Python module) is checked into the artifacts and is loadable by MadGraph (or directly importable for analytic models).

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.

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.


Reproducing the normalized $|\eta|$ shape in $\mu^+\mu^- \to b\bar b$ from a $U_1$ vector leptoquark at $\sqrt{s}=3$ TeV

Reproducing $U_1$ leptoquark $|\eta|$ shape in $\mu^+\mu^- \to b\bar b$ at 3 TeV muon collider from arXiv:2104.05720

high-energy-physics bsm-phenomenology leptoquark muon-collider

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?*

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).

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).

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).

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)?

All $\beta_L^{ij} = 0$ (LQ decoupled), $m_\mathrm{LQ} = 10^5$ GeV. 500k events at $\sqrt{s}=3$ TeV, parton level.

$\beta_L^{32} = 1.0$, mass scan $m_\mathrm{LQ} \in \{1, 10\}$ TeV, 50k events each at $\sqrt{s}=3$ TeV.

$\beta_L^{32} = 0.1$, mass scan $m_\mathrm{LQ} \in \{1, 10\}$ TeV, 50k events each at $\sqrt{s}=3$ TeV.

SM $s$-channel $\mu^+\mu^- \to \gamma^*/Z^* \to b\bar b$ (the $\beta_L^{32}=0$ run)

Ratio of central-bin ($|\eta| < 0.1$) normalized event fraction in LQ signal vs SM.

$L^1$ norm $\sum_i |f_i^\mathrm{LQ} - f_i^\mathrm{SM}|$ of normalized shape difference per (mass, coupling).

Shape distance between $m_\mathrm{LQ}=10$ TeV signal and SM should be smaller than for $m_\mathrm{LQ}=1$ TeV signal.

$\mu^+\mu^- \to b\bar b$ via SM ($s$-channel) + $U_1$ ($t$-channel) at a 3 TeV muon collider, parton level.

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).

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.

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.

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.

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.

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%.

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.

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.

A credible HEP collider study reproducing the published reference figure for $U_1$ vector-LQ angular shape in $\mu^+\mu^- \to b\bar b$ at 3 TeV muon collider. 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.

Code-development bucket: BSM model + process card + PDF/cuts + full pipeline are wired correctly.

BSM Lagrangian implemented (FeynRules .fr file + UFO output, or equivalent analytic Python module): $U_1$ vector LQ in $(\mathbf{3},\mathbf{1},2/3)$ rep with $\kappa_U=\tilde\kappa_U=0$; only $\beta_L^{32}$ (b-quark to muon) non-zero; $g_U=1$.

MadGraph generate-process card or analytic process module matches the paper's process string: $\mu^+\mu^- \to b\bar b$ at $\sqrt{s}=3$ TeV via SM $s$-channel and $U_1$ $t$-channel exchange, parton level.

PDF set and generation-level cuts match the paper exactly: Lepton-collider beams (no PDF); 1 SM run (500k events with $\beta_L^{32}=0$, $m_\mathrm{LQ}=10^5$ GeV) + 4 LQ signal runs ($\beta_L^{32}\in\{1.0, 0.1\}$ x $m_\mathrm{LQ}\in\{1, 10\}$ TeV, 50k events each).

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.

Execution-validity bucket: MC sample passes nevents threshold, physics-validity gates clear, MC stats are sufficient.

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.

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.

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.

Results bucket: quantitative comparison of three hypothesis-driven observables to the published figure, plus a reproduced figure artifact and a per-hypothesis writeup.

Quantitative test of H1 — At $\beta_L^{32}=1.0$, $m_\mathrm{LQ}=1$ TeV, central-bin $|\eta|<0.1$ normalized fraction exceeds SM by $\geq 50\%$.

Quantitative test of H2 — At $\beta_L^{32}=0.1$, normalized $|\eta|$ shape differs from SM by $\leq 10\%$ in every bin. Use the same graded relative-error scale as H1.

Quantitative test of H3 — At $\beta_L^{32}=1.0$, $m_\mathrm{LQ}=10$ TeV shape lies between SM and $m_\mathrm{LQ}=1$ TeV (decoupling). Use the same graded relative-error scale as H1.

A reproduced figure exists in artifacts (PDF or PNG) with axes, units, ranges, and legend matching the published reference: Two side-by-side panels (left: $\beta_L^{32}=1.0$, right: $\beta_L^{32}=0.1$); each panel has SM gray bar histogram + $m_\mathrm{LQ}=1$ TeV blue dashed + $m_\mathrm{LQ}=10$ TeV orange dashed; 13 bins from 0 to 2.5 (narrow [0,0.1] first); $14\times 6$ figure size; y in [0, 0.20].

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.

Reproducibility bucket (new for physics topics; absent in T-rubrics): the artifacts contain everything needed to rerun the analysis from scratch.

UFO model directory (or analytic model Python module) is checked into the artifacts and is loadable by MadGraph (or directly importable for analytic models).

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.

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.


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

Reproducing $U_1$ exclusion + 5$\sigma$ discovery contours at 3 and 14 TeV muon colliders from arXiv:2104.05720

high-energy-physics bsm-phenomenology leptoquark muon-collider statistical-recast

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?*

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).

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).

5$\sigma$ discovery contours always lie above the corresponding exclusion contours in $\beta_L^{32}$ at every mass (discovery requires stronger signal than exclusion).

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)?

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.

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.

Same mass scan at $\sqrt{s}=14$ TeV with $\beta_L^{32}\in\{1.0, 2.0\}$, 50k events each.

SM $\mu^+\mu^- \to \gamma^*/Z^* \to b\bar b$ at $\sqrt{s} = 3$ TeV and 14 TeV

$\beta_L^{32}$ at the 95% CL exclusion contour at $m_\mathrm{LQ}=10$ TeV, $\sqrt{s}=14$ TeV.

$\beta_L^{32}$ at the 5$\sigma$ discovery contour at $m_\mathrm{LQ}=10$ TeV, $\sqrt{s}=14$ TeV.

$(I_i, J_i)$ per $|\eta|$ bin and mass point, extracted from the $\beta\in\{1, 2\}$ runs; positive-definite check on $J_i$.

$\mu^+\mu^- \to b\bar b$ via SM + $U_1$ exchange at muon colliders, two energy points.

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).

A credible HEP collider study reproducing the published reference figure for $U_1$ exclusion + 5$\sigma$ discovery contours at 3 TeV (1 ab$^{-1}$) and 14 TeV (20 ab$^{-1}$) muon colliders. 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.

Code-development bucket: BSM model + process card + PDF/cuts + full pipeline are wired correctly.

BSM Lagrangian implemented (FeynRules .fr file + UFO output, or equivalent analytic Python module): Same $U_1$ Lagrangian as P09; per-bin cross section parameterized as $\sigma_i(m, \beta) = b_i + \beta^2 I_i(m) + \beta^4 J_i(m)$.

MadGraph generate-process card or analytic process module matches the paper's process string: $\mu^+\mu^- \to b\bar b$ at $\sqrt{s}\in\{3, 14\}$ TeV, parton-level.

PDF set and generation-level cuts match the paper exactly: Lepton-collider beams; 2 SM baselines (100k events each at 3 and 14 TeV) + 4 LQ signal scans ($\sqrt{s}\in\{3,14\}$ x $\beta_L^{32}\in\{1.0, 2.0\}$) over 17 mass points $m_\mathrm{LQ}\in\{1.0,\ldots,70\}$ TeV with 50k events each.

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.

Execution-validity bucket: MC sample passes nevents threshold, physics-validity gates clear, MC stats are sufficient.

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.

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.

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.

Results bucket: quantitative comparison of three hypothesis-driven observables to the published figure, plus a reproduced figure artifact and a per-hypothesis writeup.

Quantitative test of H1 — At $\sqrt{s}=14$ TeV with 20 ab$^{-1}$, 95% CL exclusion reaches $\beta_L^{32} \leq 0.01$ at $m_\mathrm{LQ}=10$ TeV (within factor 2 of published).

Quantitative test of H2 — 14 TeV exclusion contour extends to higher $m_\mathrm{LQ}$ than 3 TeV contour at every fixed $\beta_L^{32}\in[10^{-2}, 1]$. Use the same graded relative-error scale as H1.

Quantitative test of H3 — 5$\sigma$ discovery contours always lie above (i.e. require larger $\beta_L^{32}$ than) corresponding exclusion contours at every mass. Use the same graded relative-error scale as H1.

A reproduced figure exists in artifacts (PDF or PNG) with axes, units, ranges, and legend matching the published reference: Log-log plot, x-axis $m_\mathrm{LQ}\in[1,75]$ TeV log, y-axis $\beta_L^{32}\in[10^{-3}, 2]$ log, 1:1 aspect; 3 TeV (red) and 14 TeV (purple) contours; dashed = exclusion, solid = discovery (4 contours total).

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.

Reproducibility bucket (new for physics topics; absent in T-rubrics): the artifacts contain everything needed to rerun the analysis from scratch.

UFO model directory (or analytic model Python module) is checked into the artifacts and is loadable by MadGraph (or directly importable for analytic models).

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.

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.