src.kinematics module#

Event kinematics for pi^- p -> X n with X-> gamma gamma.

Calculation steps:

  • Build initial-state 4-vectors in the LAB frame.

  • Sample cos(theta*) in the CM frame using t-distribution.

  • Build outgoing meson 4-vector in CM frame.

  • Boost meson 4-vector to LAB frame.

  • Isotropic two-body decay of meson to two photons in LAB frame.

  • Compute kinematic variables and plot distributions.

src.kinematics.build_initial_state()[source]#

Build initial-state 4-vectors in the LAB frame for beam + target.

Returns:

  • p_beam (ROOT.TLorentzVector) – Beam 4-vector in LAB (along +z).

  • p_target (ROOT.TLorentzVector) – Target 4-vector in LAB (at rest).

  • p_tot (ROOT.TLorentzVector) – Total initial 4-vector in LAB.

  • s (float) – Mandelstam s in (GeV)^2.

  • beta_cm (ROOT.TVector3) – Boost vector that takes CM -> LAB (i.e. +beta_cm).

src.kinematics.two_body_momentum_cm(s, m_c, m_d)[source]#

Compute the CM momentum magnitude p* for a -> c+d at fixed s.

Parameters:

  • s (float) – Mandelstam s in (GeV)^2.

  • m_c (float) – Final-state masses in GeV.

  • m_d (float) – Final-state masses in GeV.

Returns:

p_star (float) – CM momentum magnitude in GeV.

src.kinematics.meson_fourvec_cm(s, m_meson, cos_th, rng)[source]#

Build the outgoing meson 4-vector in the CM frame using sampled t.

Parameters:

  • s (float) – Mandelstam s in (GeV)^2.

  • m_meson (float) – Outgoing meson mass (pi0 or eta) in GeV.

  • cos_th (float) – cos(theta*) used for the direction.

  • rng (np.random.Generator) – Random number generator.

Returns:

  • p_meson_cm (ROOT.TLorentzVector) – Meson 4-vector in CM.

  • cos_th (float) – cos(theta*) used for the direction.

  • phi (float) – Azimuth in radians.

src.kinematics.boost_cm_to_lab(p4_cm, beta_cm)[source]#

Boost a 4-vector from CM to LAB.

Parameters:

  • p4_cm (ROOT.TLorentzVector) – 4-vector in the CM frame.

  • beta_cm (ROOT.TVector3) – Boost vector that takes CM -> LAB.

Returns:

p4_lab (ROOT.TLorentzVector) – Boosted 4-vector in the LAB frame.

src.kinematics.decay_to_two_photons_isotropic(p_mother_lab, rng)[source]#

Isotropic two-body decay mother -> gamma gamma.

Parameters:

  • p_mother_lab (ROOT.TLorentzVector) – Mother 4-vector in the LAB frame.

  • rng (np.random.Generator) – Random number generator.

Returns:

g1_lab, g2_lab (ROOT.TLorentzVector) – Photon 4-vectors in the LAB frame.

src.kinematics.generate_event_from_t(rng, n_samples, channel='pi0')[source]#

Generate a single event given a sampled Mandelstam t.

Parameters:

  • rng (np.random.Generator) – Random number generator.

  • n_samples (int) – Number of samples to generate.

  • channel (str) – Either “pi0” or “eta”.

Returns:

event_list (list[dict]) – List of dictionaries with ROOT TLorentzVectors and useful scalars: - cos_theta_star - p_meson_cm, p_meson_lab - g1_lab, g2_lab - m_gg (reconstructed invariant mass from LAB photons) - opening_angle (radians) between LAB photons

src.kinematics.plot_kinematics(n_samples, rng)[source]#

Plot kinematic distributions for generated events.

Plots:

  • Meson pseudorapidity in LAB.

  • Photon pseudorapidity in LAB from meson decay.

  • DeltaR between the two photons from meson decay.

  • Photon energy in LAB from meson decay.

  • Meson energy in LAB.

Parameters:

  • n_samples (int) – Number of samples to generate.

  • rng (np.random.Generator) – Random number generator.