ChiliMapping

class madspace.ChiliMapping(self: madspace._madspace_py.ChiliMapping, n_particles: SupportsInt, y_max: collections.abc.Sequence[SupportsFloat], pt_min: collections.abc.Sequence[SupportsFloat])

Bases: Mapping

Chili mapping: the final state directly in collider coordinates.

Generates the momenta in transverse momentum, rapidity and azimuth rather than along a diagram topology, reconstructing the incoming momentum fractions from the final-state kinematics [1] (conceptually the ALPGEN construction, [4]). Dropping overall factors, the measure is

\[\mathrm{d}\Phi_n = \delta^{(4)}\!\Big(p_a + p_b - \sum_i p_i\Big) \prod_{i=1}^{n} \frac{\mathrm{d}p_{\mathrm{T},i}^2\,\mathrm{d}y_i\, \mathrm{d}\phi_i}{4}.\]

The first \(n-1\) momenta are generated explicitly. The transverse components of the last are fixed by recoil, and its rapidity is sampled uniformly. Each \(p_\mathrm{T}^2\) is drawn from

\[p_\mathrm{T}^2 = \Big(\tfrac{r}{p_{\mathrm{T},\max}^2} + \tfrac{1-r}{p_{\mathrm{T},\min}^2}\Big)^{-1}\]

when a lower cut applies, and from a small- \(p_\mathrm{T}\)-regulated map otherwise. Azimuths are sampled relative to the running recoil direction, \(\phi = 2\pi r_\phi + \phi_\mathrm{rec}\) (Sec. 2.4 of [1], following [2, 3]). Chili does not guarantee physical configurations, so unphysical points are removed by a technical cut.

batch is the leading batch dimension.

Inputs

• random_i – float, shape (batch,) – the 3 * n_particles - 2 random numbers.

Conditions

• com_energy – float, shape (batch,) – total collision energy.

• mass_i – float, shape (batch,) – the n_particles outgoing masses.

Outputs

• momentum_i – float, shape (batch, 4) – the n_particles + 2 momenta (incoming beams first, then outgoing).

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

References

• [1] T. Heimel, O. Mattelaer, R. Winterhalder, “MadSpace”, https://arxiv.org/abs/2602.06895 (Sec. 2.4)

• [2] E. Bothmann et al., “Efficient phase-space generation for hadron collider event simulation”, https://arxiv.org/abs/2302.10449

• [3] E. Bothmann et al., “A portable parton-level event generator for the high-luminosity LHC”, https://arxiv.org/abs/2311.06198

• [4] M. L. Mangano et al., “ALPGEN, a generator for hard multiparton processes in hadronic collisions”, https://arxiv.org/abs/hep-ph/0206293

Parameters:

• n_particles – Number of outgoing particles.

• y_max – Per-outgoing-particle maximum rapidity; empty disables the rapidity cut. See Cuts.

• pt_min – Per-outgoing-particle minimum transverse momentum; empty disables the cut. See Cuts.

random_dim(self: madspace._madspace_py.ChiliMapping) → int

Number of uniform random inputs consumed by the forward mapping, equal to 3 * n_particles - 2.