ffsshhttiikk Particle Physics
What I Do
I 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.
When to Use Me
- Cross section calculations
- Decay rate predictions
- Collider physics analysis
- Detector simulation
- Neutrino physics
- Nuclear structure
Core Concepts
- Standard Model: Quarks, leptons, gauge bosons
- Feynman Rules: Vertices, propagators, amplitudes
- Cross Sections: Differential and total
- Decay Rates: Branching ratios, lifetimes
- Collider Kinematics: Mandelstam variables
- Detector Physics: Resolution, efficiency
- QCD: Asymptotic freedom, confinement
- Neutrino Oscillations: PMNS matrix
Code Examples
Particle Properties
import numpy as np
PARTICLE_MASS = {
'e': 0.511, # MeV
'mu': 105.7,
'tau': 1777,
'u': 2.3,
'd': 4.8,
's': 95,
'c': 1.27,
'b': 4.18,
't': 173,
'W': 80.4, # GeV
'Z': 91.2,
'H': 125,
'g': 0,
'photon': 0,
'gluon': 0
}
QUANTUM_NUMBERS = {
'charge': {'u': 2/3, 'd': -1/3, 'e': -1, 'mu': -1},
'spin': {'quark': 1/2, 'lepton': 1/2, 'photon': 1, 'W': 1}
}
def four_momentum(E, px, py, pz):
m = np.sqrt(E**2 - px**2 - py**2 - pz**2)
return np.array([E, px, py, pz, m])
def invariant_mass(p1, p2):
p_total = p1 + p2
return np.sqrt(p_total[0]**2 - p_total[1]**2 - p_total[2]**2 - p_total[3]**2)
def lorentz_boost(p, beta):
gamma = 1 / np.sqrt(1 - beta**2)
p_parallel = p[3] * beta * gamma
p_perp = p[1:3]
E = gamma * (p[0] + beta * p[3])
return np.array([E, p_perp[0], p_perp[1], p_parallel])
Kinematics
def mandelstam_s(p1, p2):
return (p1[0] + p2[0])**2 - np.sum((p1[1:] + p2[1:])**2)
def mandelstam_t(p1, p2, p3):
return (p1[0] - p3[0])**2 - np.sum((p1[1:] - p3[1:])**2)
def mandelstam_u(p1, p2, p4):
return (p1[0] - p4[0])**2 - np.sum((p1[1:] - p4[1:])**2)
def transverse_momentum(px, py):
return np.sqrt(px**2 + py**2)
def pseudorapidity(pz, E):
return 0.5 * np.log((E + pz) / (E - pz))
def rapidity(E, pz):
return 0.5 * np.log((E + pz) / (E - pz))
def delta_r(eta1, eta2, phi1, phi2):
d_eta = eta1 - eta2
d_phi = phi1 - phi2
return np.sqrt(d_eta**2 + d_phi**2)
s = mandelstam_s(p1, p2)
print(f"Mandelstam s: {s:.2f} GeV²")
Cross Sections
def rutherford_cross_section(theta, alpha, E):
return (alpha**2 / (16 * E**2 * np.sin(theta/2)**4))
def klein_nishina(Egamma, theta):
re = 2.818e-15 # Classical electron radius
alpha = Egamma / (0.511)
return (re**2 / 2) * (Egamma / (Egamma * (1 + alpha * (1 - np.cos(theta)))))**2 * (1 + np.cos(theta)**2 + alpha**2 * (1 - np.cos(theta))**2 / (1 + alpha * (1 - np.cos(theta))))
def differential_cross_section(dsigma_dcos, cos_theta):
return dsigma_dcos
def total_cross_section(sigma, integration_range):
return np.trapz(sigma, integration_range)
def parton_luminosity(LHC, sqrt_s):
return 1 / sqrt_s
def production_cross_section(parton_luminosity, partonic_cross_section):
return parton_luminosity * partonic_cross_section
Decay Rates
def phase_space_factor(m_parent, m_daughters):
m1, m2 = m_daughters
if m1 + m2 > m_parent:
return 0
E1 = (m_parent**2 + m1**2 - m2**2) / (2 * m_parent)
E2 = (m_parent**2 + m2**2 - m1**2) / (2 * m_parent)
p = np.sqrt(E1**2 - m1**2)
return p / m_parent
def decay_width(width_matrix, phase_space):
return width_matrix * phase_space
def branching_ratio(width_i, total_width):
return width_i / total_width
def lifetime_hbar(width):
return 6.582e-22 / width
def muon_lifetime():
G_F = 1.166e-5 # GeV^-2
m_mu = 0.1057
width = G_F**2 * m_mu**5 / (192 * np.pi**3)
return 1 / width
width_mu = muon_lifetime()
print(f"Muon decay width: {width_mu:.4e} GeV")
tau_mu = lifetime_hbar(width_mu)
print(f"Muon lifetime: {tau_mu:.2e} s")
Detector Response
def energy_resolution(sigma_E, E):
return sigma_E / E
def momentum_resolution(sigma_pT, pT):
return sigma_pT / pT
def tracking_efficiency(hits, tracks):
return hits / tracks
def particle_identification_probability(PID_response, threshold):
return np.where(PID_response > threshold, 1, 0)
def jet_energy_correction(jet_pt, eta, MC_data):
correction_factor = 1 + 0.05 * np.abs(eta)
return jet_pt * correction_factor
def pileup_subtraction(n_pileup, correction):
return correction - n_pileup * correction
def missing_ET_resolution(MET, sumET):
return 0.5 * np.sqrt(sumET)
Best Practices
- Renormalization: Use appropriate renormalization scheme
- Higher Orders: Include NLO/NNLO corrections
- PDFs: Use appropriate parton distribution functions
- Backgrounds: Estimate all backgrounds
- Systematics: Include systematic uncertainties
Common Patterns
# Event generation
def generate_event(process, kinematics):
return event
# Cut optimization
def optimize_cuts(signal, background):
return optimal_cuts
Core Competencies
- Standard Model interactions
- Feynman diagram calculations
- Collider kinematics
- Detector response
- Statistical analysis