DoubleT

class madspace.DoubleT(self: madspace._madspace_py.DoubleT, t1_invariant_power: SupportsFloat = 0.0, t1_mass: SupportsFloat = 0.0, t1_width: SupportsFloat = 0.0, t2_invariant_power: SupportsFloat = 0.0, t2_mass: SupportsFloat = 0.0, t2_width: SupportsFloat = 0.0, has_cut: bool = False, y_max1: SupportsFloat = -1.0, y_max2: SupportsFloat = -1.0, beam_sign: SupportsFloat = 1.0)

Bases: Mapping

Central two-particle block with both legs sampled in a momentum transfer.

A variant of the \((\phi, t)\) two-particle block (Sec. 2.2.4 of [1]) in which both outgoing legs are attached to a t-channel propagator, so two momentum transfers \(t_1, t_2\) are drawn (each with its own Invariant) in addition to the shared azimuth. It is used as the central block of the ColorOrderedMapping chain.

batch is the leading batch dimension.

Inputs

  • random_phi – float, shape (batch,) – azimuthal-angle random number.

  • random_t1 – float, shape (batch,) – random number for \(|t_1|\).

  • random_t2 – float, shape (batch,) – random number for \(|t_2|\).

Conditions

  • momentum_in1 – float, shape (batch, 4) – first incoming momentum.

  • momentum_in2 – float, shape (batch, 4) – second incoming momentum.

  • mass1 – float, shape (batch,) – mass of the first outgoing particle.

  • mass_rest_min – float, shape (batch,) – minimum invariant mass of the remaining system.

  • etmin_i – float, shape (batch,) – transverse-energy cut on the outgoing particle. Present only when has_cut is true.

  • etmin_ir – float, shape (batch,) – transverse-energy cut on the recoil system. Present only when has_cut is true.

  • x1, x2 – float, shape (batch,) – beam momentum fractions. Present only when a rapidity bound is given (see the constructor).

Outputs

  • momentum1 – float, shape (batch, 4) – first outgoing momentum.

  • momentum2 – float, shape (batch, 4) – recoil momentum.

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

References

Parameters:

  • t1_invariant_power – Exponent of the \(1/|t_1|^{\,p}\) sampling; see Invariant.

  • t1_mass – First t-channel propagator mass; see Invariant.

  • t1_width – First t-channel propagator width; see Invariant.

  • t2_invariant_power – Exponent of the \(1/|t_2|^{\,p}\) sampling; see Invariant.

  • t2_mass – Second t-channel propagator mass; see Invariant.

  • t2_width – Second t-channel propagator width; see Invariant.

  • has_cut – If true, the etmin_* conditions restrict the momentum transfers to the region passing the transverse cuts; see Cuts.

  • y_max1 – Bound on the absolute lab rapidity of momentum1 (the single particle); negative, or 100 and above, for none.

  • y_max2 – The same for momentum2 (the recoil).

  • beam_sign – +1 if momentum_in1 is beam 1 (along +z), -1 if it is beam 2.

The incoming momenta are the beams, so pa.p1 and pb.p1 are fixed by \(|t_1|\) and \(|t_2|\): the rapidity bounds narrow \(|t_1|\) to the values that leave some \(|t_2|\), and then \(|t_2|\) at fixed \(|t_1|\), both exactly. With a bound set, the mapping takes the beam momentum fractions x1, x2 (float, shape (batch,)) as two further conditions.