Luminosity

class madspace.Luminosity(self: madspace._madspace_py.Luminosity, s_lab: SupportsFloat, s_hat_min: SupportsFloat, s_hat_max: SupportsFloat = 0.0, invariant_power: SupportsFloat = 1.0, mass: SupportsFloat = 0.0, width: SupportsFloat = 0.0)

Bases: Mapping

PDF-convolution mapping: parton momentum fractions from two random numbers.

Trades the parton momentum fractions \(x_1, x_2\) for the partonic invariant \(\hat s = x_1 x_2 s_\mathrm{lab}\) and one angular variable [1]. \(\hat s\) is drawn in [s_hat_min, s_hat_max] with an Invariant, which forwards invariant_power, mass and width. The momentum fractions then follow from logarithmic sampling,

\[x_1 = \tau^{\,r}, \qquad x_2 = \tau^{\,1-r}, \qquad \tau = \hat s / s_\mathrm{lab},\]

which cancels the \(1/x_1\) of the convolution measure. Choosing invariant_power \(\simeq 1\) (the default) also absorbs the \(1/\hat s\) flux factor. A nonzero width instead resolves an s-channel resonance in \(\hat s\) directly (Sec. 2.2.2 of [1]). This parametrization is specific to hadron collisions.

batch is the leading batch dimension.

Inputs

  • r_s – float, shape (batch,) – random number for \(\hat s\).

  • r_x – float, shape (batch,) – random number for the \(x_1/x_2\) split.

Conditions

  • None.

Outputs

  • x1 – float, shape (batch,) – first parton momentum fraction.

  • x2 – float, shape (batch,) – second parton momentum fraction.

  • s_hat – float, shape (batch,) – partonic invariant \(\hat s = x_1 x_2 s_\mathrm{lab}\).

In addition every mapping returns a weight (float, shape (batch,)), the Jacobian of the transformation.

References

Parameters:

  • s_lab – Hadronic invariant \(s_\mathrm{lab}\) (squared collider energy).

  • s_hat_min – Lower bound on \(\hat s\), set by the final-state masses and analysis cuts.

  • s_hat_max – Upper bound on \(\hat s\); 0 uses \(s_\mathrm{lab}\).

  • invariant_power – Exponent of the \(1/\hat s^{\,p}\) sampling of \(\hat s\); 1 absorbs the flux factor. See Invariant.

  • mass – Resonance mass for \(\hat s\); see Invariant.

  • width – Resonance width; a nonzero value selects Breit-Wigner sampling of \(\hat s\). See Invariant.