src.diff_cross_section module#

Sample Mandelstam t from binned dsigma/dt tables stored in ROOT files.

Provide functionality to:

  • Load dsigma/dt data from ROOT TGraphAsymmErrors.

  • Build a piecewise-constant PDF and CDF for tau = -t.

  • Sample t values according to the PDF.

  • Convert sampled t to cos(theta*) in the CM frame for pi^- p -> X n

class src.diff_cross_section.DtPdf[source]#

Bases: object

Piecewise-constant PDF built from a binned dsigma/dt table.

__init__(tau_lo, tau_hi, cdf)[source]#

Class constructor.

Parameters:

  • tau_lo – Bin edges for tau = -t in GeV^2.

  • tau_hi – Bin edges for tau = -t in GeV^2.

  • cdf – Cumulative distribution normalized to 1, same length as bins.

src.diff_cross_section.load_graph(root_path)[source]#

Load Table dsigma/dt stored as TGraphAsymmErrors Graph1D_y1.

Parameters:

root_path – Path to the ROOT file.

Returns:

ROOT.TGraphAsymmErrors – The graph object.

src.diff_cross_section.build_pdf_from_graph(g)[source]#

Build a CDF from a TGraphAsymmErrors containing binned dsigma/dt.

For each point i in the graph:

  • Get x_i, y_i, and bin width from asymmetric errors.

  • Compute weight w_i = max(0, y_i) * width_i for central value generation.

  • Build CDF from normalized weights.

Parameters:

g (ROOT.TGraphAsymmErrors) – Graph containing binned dsigma/dt.

Returns:

DtPdf – Precomputed bin edges + CDF.

src.diff_cross_section.sample_t(pdf, rng, size)[source]#

Sample Mandelstam t (negative) from the dsigma/dt CDF table.

Parameters:

  • pdf (DtPdf) – Precomputed PDF and CDF.

  • rng (numpy.random.Generator) – Random number generator (same instance used everywhere).

  • size (int) – Number of samples

Returns:

t (float) – Sampled Mandelstam t value.

src.diff_cross_section.plot_binned_pdf_cdf(pdf, rng, n_samples, plot_name='pi0')[source]#

Plot the binned PDF and CDF from the provided DtPdf object.

Plot:

  • Top: piecewise-constant PDF p(tau) + histogram of sampled tau=-t

  • Bottom: CDF F(tau)

Parameters:

  • pdf (DtPdf) – Precomputed bin edges and CDF.

  • rng (numpy.random.Generator) – Random number generator (same instance used everywhere).

  • n_samples (int) – Number of tau=-t samples for the diagnostic histogram.

  • plot_name (str) – Name of the output plot file (without extension).

src.diff_cross_section.cos_theta_from_t(s, m_a, m_b, m_c, m_d, rng, pdf, n_samples=1000)[source]#

Convert Mandelstam t -> cos(theta*) in the CM frame for a+b -> c+d.

Convention:

  • t = (p_a - p_c)^2, metric (+,-,-,-).

  • theta* is the angle between incoming a and outgoing c in the CM.

Parameters:

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

  • m_a (float) – Particle masses in GeV.

  • m_b (float) – Particle masses in GeV.

  • m_c (float) – Particle masses in GeV.

  • m_d (float) – Particle masses in GeV.

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

  • pdf (DtPdf) – Precomputed PDF and CDF for t sampling.

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

Returns:

cos_theta (float or np.ndarray) – cos(theta*) corresponding to t.