Module particle_physics 

Relativistic kinematics and scattering for particle collisions.

Invariant mass – the quantity every collider analysis is built on, because it is the same in every frame – along with centre-of-mass energy for colliding and fixed-target geometries, and the Lorentz boost of energy and longitudinal momentum.

The collider coordinates: rapidity, pseudorapidity and transverse momentum, chosen because rapidity differences are boost invariant along the beam. Scattering by the Rutherford cross section and the Breit-Wigner resonance shape, with the width-lifetime relation Γτ = ħ and branching ratios.

Also the conservation-law checks – charge, lepton number, baryon number – that say whether a proposed reaction can happen at all.

Constants

CHARGE_DOWN

CHARGE_UP

FINE_STRUCTURE

Fine-structure constant α ≈ 1/137, re-exported from crate::math::constants::ALPHA. The 7.297e-3 that used to be written here was the same constant to four digits and a different number after them.

M_HIGGS

M_KAON

M_MUON

M_PION_CHARGED

M_PION_NEUTRAL

M_TAU

M_TOP_QUARK

M_W_BOSON

M_Z_BOSON

STRONG_COUPLING

WEAK_MIXING_ANGLE_SIN2

Functions

branching_ratio

Branching ratio BR = Γ_i / Γ_total

breit_wigner

Non-relativistic Breit-Wigner resonance (normalized to peak = 1). BW(E) = (Γ/2)² / ((E - M)² + (Γ/2)²)

center_of_mass_energy

Center-of-mass energy √s for two particles with given energies and momenta. √s = √((E1+E2)² - (p1+p2)²c²)

decay_rate_from_lifetime

Decay rate from lifetime. Γ = ℏ / τ

fixed_target_com_energy

Fixed-target center-of-mass energy (high-energy approximation). √s ≈ √(2 × E_beam × m_target × c²)

four_momentum_magnitude

Four-momentum magnitude (invariant mass × c). √(E² - p²c²) / c = mc

invariant_mass

Invariant mass from total energy and scalar momentum magnitude. m = √(E² - p²c²) / c²

invariant_mass_two_body

Invariant mass of a two-body system from individual four-momenta. m² = (E1+E2)² - |p1+p2|²c², return m/c².

is_baryon_number_conserved

Check baryon number conservation.

is_charge_conserved

Check charge conservation: sum of input charges ≈ sum of output charges.

is_lepton_number_conserved

Check lepton number conservation.

lifetime_from_width

Lifetime from decay width. τ = ℏ / Γ

lorentz_boost_energy

Lorentz boost of energy along z. E’ = γ(E - β pz c)

lorentz_boost_pz

Lorentz boost of z-momentum. pz’ = γ(pz - β E/c)

luminosity_to_event_rate

Event rate R = L × σ

mean_free_path_particle

Mean free path λ = 1 / (n σ)

pseudorapidity

Pseudorapidity η = -ln(tan(θ/2))

rapidity

Rapidity y = 0.5 × ln((E + pz c) / (E - pz c))

rutherford_cross_section

Rutherford scattering differential cross section. dσ/dΩ = (Z1 Z2 k_e e² / (4E))² / sin⁴(θ/2)

transverse_momentum

Transverse momentum pT = √(px² + py²)