[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"skill:01M6CXD4WM7XTMPHPC10PB945X":3,"skill-same:01M6CXD4WM7XTMPHPC10PB945X":83},{"skillNo":4,"name":5,"nameZh":6,"description":7,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":6,"repositoryNo":12,"starsCount":13,"licenseSpdxId":14,"licenseFileUrl":6,"sourceHtmlUrl":15,"categories":16,"keywords":17,"publishedAt":25,"linkOnly":26,"markdownContent":27,"markdownBody":28,"frontMatter":29,"refName":32,"commitSha":33,"skillDirectory":34,"forksCount":35,"repositoryHtmlUrl":36,"repositoryHomepageUrl":6,"ownerHtmlUrl":37,"ownerBlogUrl":6,"ownerDescription":6,"updatedAt":38,"install":39,"resources":52},"01M6CXD4WM7XTMPHPC10PB945X","Particle Physics",null,"Particle physics fundamentals including the Standard Model, Feynman diagrams, detector physics, collider kinematics, and nuclear physics for high-energy physics applications.","ffsshhttiikk\u002Fopencode-agents-skills","ffsshhttiikk","https:\u002F\u002Favatars.githubusercontent.com\u002Fu\u002F226346827?v=4","01M6CWD9RR3Y7VRQX3MXYC8FYH","01M6CWD9WVPYAZW0J82G1VKGHY",3,"MIT","https:\u002F\u002Fgithub.com\u002Fffsshhttiikk\u002Fopencode-agents-skills\u002Fblob\u002Fmain\u002Fparticle-physics\u002FSKILL.md",[],[18,5,19,20,21,22,23,24],"physics","python","applications","model","diagrams","nuclear physics","nuclear","2026-11-10 10:12:30",false,"---\nname: Particle Physics\ndescription: Particle physics fundamentals including the Standard Model, Feynman diagrams, detector physics, collider kinematics, and nuclear physics for high-energy physics applications.\nlicense: MIT\ncompatibility: python>=3.8\naudience: particle-physicists, nuclear-physicists, researchers\ncategory: physics\n---\n\n# Particle Physics\n\n## What I Do\n\nI provide comprehensive particle physics tools including Standard Model interactions, Feynman diagram calculations, detector response, collider kinematics, and nuclear physics for high-energy physics research applications.\n\n## When to Use Me\n\n- Cross section calculations\n- Decay rate predictions\n- Collider physics analysis\n- Detector simulation\n- Neutrino physics\n- Nuclear structure\n\n## Core Concepts\n\n- **Standard Model**: Quarks, leptons, gauge bosons\n- **Feynman Rules**: Vertices, propagators, amplitudes\n- **Cross Sections**: Differential and total\n- **Decay Rates**: Branching ratios, lifetimes\n- **Collider Kinematics**: Mandelstam variables\n- **Detector Physics**: Resolution, efficiency\n- **QCD**: Asymptotic freedom, confinement\n- **Neutrino Oscillations**: PMNS matrix\n\n## Code Examples\n\n### Particle Properties\n\n```python\nimport numpy as np\n\nPARTICLE_MASS = {\n    'e': 0.511,      # MeV\n    'mu': 105.7,\n    'tau': 1777,\n    'u': 2.3,\n    'd': 4.8,\n    's': 95,\n    'c': 1.27,\n    'b': 4.18,\n    't': 173,\n    'W': 80.4,      # GeV\n    'Z': 91.2,\n    'H': 125,\n    'g': 0,\n    'photon': 0,\n    'gluon': 0\n}\n\nQUANTUM_NUMBERS = {\n    'charge': {'u': 2\u002F3, 'd': -1\u002F3, 'e': -1, 'mu': -1},\n    'spin': {'quark': 1\u002F2, 'lepton': 1\u002F2, 'photon': 1, 'W': 1}\n}\n\ndef four_momentum(E, px, py, pz):\n    m = np.sqrt(E**2 - px**2 - py**2 - pz**2)\n    return np.array([E, px, py, pz, m])\n\ndef invariant_mass(p1, p2):\n    p_total = p1 + p2\n    return np.sqrt(p_total[0]**2 - p_total[1]**2 - p_total[2]**2 - p_total[3]**2)\n\ndef lorentz_boost(p, beta):\n    gamma = 1 \u002F np.sqrt(1 - beta**2)\n    p_parallel = p[3] * beta * gamma\n    p_perp = p[1:3]\n    E = gamma * (p[0] + beta * p[3])\n    return np.array([E, p_perp[0], p_perp[1], p_parallel])\n```\n\n### Kinematics\n\n```python\ndef mandelstam_s(p1, p2):\n    return (p1[0] + p2[0])**2 - np.sum((p1[1:] + p2[1:])**2)\n\ndef mandelstam_t(p1, p2, p3):\n    return (p1[0] - p3[0])**2 - np.sum((p1[1:] - p3[1:])**2)\n\ndef mandelstam_u(p1, p2, p4):\n    return (p1[0] - p4[0])**2 - np.sum((p1[1:] - p4[1:])**2)\n\ndef transverse_momentum(px, py):\n    return np.sqrt(px**2 + py**2)\n\ndef pseudorapidity(pz, E):\n    return 0.5 * np.log((E + pz) \u002F (E - pz))\n\ndef rapidity(E, pz):\n    return 0.5 * np.log((E + pz) \u002F (E - pz))\n\ndef delta_r(eta1, eta2, phi1, phi2):\n    d_eta = eta1 - eta2\n    d_phi = phi1 - phi2\n    return np.sqrt(d_eta**2 + d_phi**2)\n\ns = mandelstam_s(p1, p2)\nprint(f\"Mandelstam s: {s:.2f} GeV²\")\n```\n\n### Cross Sections\n\n```python\ndef rutherford_cross_section(theta, alpha, E):\n    return (alpha**2 \u002F (16 * E**2 * np.sin(theta\u002F2)**4))\n\ndef klein_nishina(Egamma, theta):\n    re = 2.818e-15  # Classical electron radius\n    alpha = Egamma \u002F (0.511)\n    return (re**2 \u002F 2) * (Egamma \u002F (Egamma * (1 + alpha * (1 - np.cos(theta)))))**2 * (1 + np.cos(theta)**2 + alpha**2 * (1 - np.cos(theta))**2 \u002F (1 + alpha * (1 - np.cos(theta))))\n\ndef differential_cross_section(dsigma_dcos, cos_theta):\n    return dsigma_dcos\n\ndef total_cross_section(sigma, integration_range):\n    return np.trapz(sigma, integration_range)\n\ndef parton_luminosity(LHC, sqrt_s):\n    return 1 \u002F sqrt_s\n\ndef production_cross_section(parton_luminosity, partonic_cross_section):\n    return parton_luminosity * partonic_cross_section\n```\n\n### Decay Rates\n\n```python\ndef phase_space_factor(m_parent, m_daughters):\n    m1, m2 = m_daughters\n    if m1 + m2 > m_parent:\n        return 0\n    \n    E1 = (m_parent**2 + m1**2 - m2**2) \u002F (2 * m_parent)\n    E2 = (m_parent**2 + m2**2 - m1**2) \u002F (2 * m_parent)\n    \n    p = np.sqrt(E1**2 - m1**2)\n    return p \u002F m_parent\n\ndef decay_width(width_matrix, phase_space):\n    return width_matrix * phase_space\n\ndef branching_ratio(width_i, total_width):\n    return width_i \u002F total_width\n\ndef lifetime_hbar(width):\n    return 6.582e-22 \u002F width\n\ndef muon_lifetime():\n    G_F = 1.166e-5  # GeV^-2\n    m_mu = 0.1057\n    width = G_F**2 * m_mu**5 \u002F (192 * np.pi**3)\n    return 1 \u002F width\n\nwidth_mu = muon_lifetime()\nprint(f\"Muon decay width: {width_mu:.4e} GeV\")\ntau_mu = lifetime_hbar(width_mu)\nprint(f\"Muon lifetime: {tau_mu:.2e} s\")\n```\n\n### Detector Response\n\n```python\ndef energy_resolution(sigma_E, E):\n    return sigma_E \u002F E\n\ndef momentum_resolution(sigma_pT, pT):\n    return sigma_pT \u002F pT\n\ndef tracking_efficiency(hits, tracks):\n    return hits \u002F tracks\n\ndef particle_identification_probability(PID_response, threshold):\n    return np.where(PID_response > threshold, 1, 0)\n\ndef jet_energy_correction(jet_pt, eta, MC_data):\n    correction_factor = 1 + 0.05 * np.abs(eta)\n    return jet_pt * correction_factor\n\ndef pileup_subtraction(n_pileup, correction):\n    return correction - n_pileup * correction\n\ndef missing_ET_resolution(MET, sumET):\n    return 0.5 * np.sqrt(sumET)\n```\n\n## Best Practices\n\n1. **Renormalization**: Use appropriate renormalization scheme\n2. **Higher Orders**: Include NLO\u002FNNLO corrections\n3. **PDFs**: Use appropriate parton distribution functions\n4. **Backgrounds**: Estimate all backgrounds\n5. **Systematics**: Include systematic uncertainties\n\n## Common Patterns\n\n```python\n# Event generation\ndef generate_event(process, kinematics):\n    return event\n\n# Cut optimization\ndef optimize_cuts(signal, background):\n    return optimal_cuts\n```\n\n## Core Competencies\n\n1. Standard Model interactions\n2. Feynman diagram calculations\n3. Collider kinematics\n4. Detector response\n5. Statistical analysis\n","# Particle Physics\n\n## What I Do\n\nI provide comprehensive particle physics tools including Standard Model interactions, Feynman diagram calculations, detector response, collider kinematics, and nuclear physics for high-energy physics research applications.\n\n## When to Use Me\n\n- Cross section calculations\n- Decay rate predictions\n- Collider physics analysis\n- Detector simulation\n- Neutrino physics\n- Nuclear structure\n\n## Core Concepts\n\n- **Standard Model**: Quarks, leptons, gauge bosons\n- **Feynman Rules**: Vertices, propagators, amplitudes\n- **Cross Sections**: Differential and total\n- **Decay Rates**: Branching ratios, lifetimes\n- **Collider Kinematics**: Mandelstam variables\n- **Detector Physics**: Resolution, efficiency\n- **QCD**: Asymptotic freedom, confinement\n- **Neutrino Oscillations**: PMNS matrix\n\n## Code Examples\n\n### Particle Properties\n\n```python\nimport numpy as np\n\nPARTICLE_MASS = {\n    'e': 0.511,      # MeV\n    'mu': 105.7,\n    'tau': 1777,\n    'u': 2.3,\n    'd': 4.8,\n    's': 95,\n    'c': 1.27,\n    'b': 4.18,\n    't': 173,\n    'W': 80.4,      # GeV\n    'Z': 91.2,\n    'H': 125,\n    'g': 0,\n    'photon': 0,\n    'gluon': 0\n}\n\nQUANTUM_NUMBERS = {\n    'charge': {'u': 2\u002F3, 'd': -1\u002F3, 'e': -1, 'mu': -1},\n    'spin': {'quark': 1\u002F2, 'lepton': 1\u002F2, 'photon': 1, 'W': 1}\n}\n\ndef four_momentum(E, px, py, pz):\n    m = np.sqrt(E**2 - px**2 - py**2 - pz**2)\n    return np.array([E, px, py, pz, m])\n\ndef invariant_mass(p1, p2):\n    p_total = p1 + p2\n    return np.sqrt(p_total[0]**2 - p_total[1]**2 - p_total[2]**2 - p_total[3]**2)\n\ndef lorentz_boost(p, beta):\n    gamma = 1 \u002F np.sqrt(1 - beta**2)\n    p_parallel = p[3] * beta * gamma\n    p_perp = p[1:3]\n    E = gamma * (p[0] + beta * p[3])\n    return np.array([E, p_perp[0], p_perp[1], p_parallel])\n```\n\n### Kinematics\n\n```python\ndef mandelstam_s(p1, p2):\n    return (p1[0] + p2[0])**2 - np.sum((p1[1:] + p2[1:])**2)\n\ndef mandelstam_t(p1, p2, p3):\n    return (p1[0] - p3[0])**2 - np.sum((p1[1:] - p3[1:])**2)\n\ndef mandelstam_u(p1, p2, p4):\n    return (p1[0] - p4[0])**2 - np.sum((p1[1:] - p4[1:])**2)\n\ndef transverse_momentum(px, py):\n    return np.sqrt(px**2 + py**2)\n\ndef pseudorapidity(pz, E):\n    return 0.5 * np.log((E + pz) \u002F (E - pz))\n\ndef rapidity(E, pz):\n    return 0.5 * np.log((E + pz) \u002F (E - pz))\n\ndef delta_r(eta1, eta2, phi1, phi2):\n    d_eta = eta1 - eta2\n    d_phi = phi1 - phi2\n    return np.sqrt(d_eta**2 + d_phi**2)\n\ns = mandelstam_s(p1, p2)\nprint(f\"Mandelstam s: {s:.2f} GeV²\")\n```\n\n### Cross Sections\n\n```python\ndef rutherford_cross_section(theta, alpha, E):\n    return (alpha**2 \u002F (16 * E**2 * np.sin(theta\u002F2)**4))\n\ndef klein_nishina(Egamma, theta):\n    re = 2.818e-15  # Classical electron radius\n    alpha = Egamma \u002F (0.511)\n    return (re**2 \u002F 2) * (Egamma \u002F (Egamma * (1 + alpha * (1 - np.cos(theta)))))**2 * (1 + np.cos(theta)**2 + alpha**2 * (1 - np.cos(theta))**2 \u002F (1 + alpha * (1 - np.cos(theta))))\n\ndef differential_cross_section(dsigma_dcos, cos_theta):\n    return dsigma_dcos\n\ndef total_cross_section(sigma, integration_range):\n    return np.trapz(sigma, integration_range)\n\ndef parton_luminosity(LHC, sqrt_s):\n    return 1 \u002F sqrt_s\n\ndef production_cross_section(parton_luminosity, partonic_cross_section):\n    return parton_luminosity * partonic_cross_section\n```\n\n### Decay Rates\n\n```python\ndef phase_space_factor(m_parent, m_daughters):\n    m1, m2 = m_daughters\n    if m1 + m2 > m_parent:\n        return 0\n    \n    E1 = (m_parent**2 + m1**2 - m2**2) \u002F (2 * m_parent)\n    E2 = (m_parent**2 + m2**2 - m1**2) \u002F (2 * m_parent)\n    \n    p = np.sqrt(E1**2 - m1**2)\n    return p \u002F m_parent\n\ndef decay_width(width_matrix, phase_space):\n    return width_matrix * phase_space\n\ndef branching_ratio(width_i, total_width):\n    return width_i \u002F total_width\n\ndef lifetime_hbar(width):\n    return 6.582e-22 \u002F width\n\ndef muon_lifetime():\n    G_F = 1.166e-5  # GeV^-2\n    m_mu = 0.1057\n    width = G_F**2 * m_mu**5 \u002F (192 * np.pi**3)\n    return 1 \u002F width\n\nwidth_mu = muon_lifetime()\nprint(f\"Muon decay width: {width_mu:.4e} GeV\")\ntau_mu = lifetime_hbar(width_mu)\nprint(f\"Muon lifetime: {tau_mu:.2e} s\")\n```\n\n### Detector Response\n\n```python\ndef energy_resolution(sigma_E, E):\n    return sigma_E \u002F E\n\ndef momentum_resolution(sigma_pT, pT):\n    return sigma_pT \u002F pT\n\ndef tracking_efficiency(hits, tracks):\n    return hits \u002F tracks\n\ndef particle_identification_probability(PID_response, threshold):\n    return np.where(PID_response > threshold, 1, 0)\n\ndef jet_energy_correction(jet_pt, eta, MC_data):\n    correction_factor = 1 + 0.05 * np.abs(eta)\n    return jet_pt * correction_factor\n\ndef pileup_subtraction(n_pileup, correction):\n    return correction - n_pileup * correction\n\ndef missing_ET_resolution(MET, sumET):\n    return 0.5 * np.sqrt(sumET)\n```\n\n## Best Practices\n\n1. **Renormalization**: Use appropriate renormalization scheme\n2. **Higher Orders**: Include NLO\u002FNNLO corrections\n3. **PDFs**: Use appropriate parton distribution functions\n4. **Backgrounds**: Estimate all backgrounds\n5. **Systematics**: Include systematic uncertainties\n\n## Common Patterns\n\n```python\n# Event generation\ndef generate_event(process, kinematics):\n    return event\n\n# Cut optimization\ndef optimize_cuts(signal, background):\n    return optimal_cuts\n```\n\n## Core Competencies\n\n1. 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