PhaseSpaceMapping

class madspace.PhaseSpaceMapping(*args, **kwargs)

Bases: Mapping

Full \(2 \to n\) phase-space mapping for one diagram topology.

Assembles a complete mapping from the elementary building blocks along the recursive decomposition of the tree-level phase space (Sec. 2.2 of [1]),

\[\int \mathrm{d}\Phi_n = \Big[\textstyle\prod_i \int \mathrm{d}s_i\Big] \Big[\textstyle\prod_j \int \mathrm{d}\Phi^{(\phi,t)}_{2,j}\Big] \Big[\textstyle\prod_k \int \mathrm{d}\Phi^{(\tilde s,t)}_{2,k}\Big] \Big[\textstyle\prod_l \int \mathrm{d}\Phi_{3,l}\Big] \Big[\textstyle\prod_m \int \mathrm{d}\Phi^{(\phi,\theta)}_{2,m}\Big].\]

The time-like invariants are sampled with Invariant, the s-channel decays with TwoBodyDecay / ThreeBodyDecay, and the PDF convolution with Luminosity. TChannelMode selects the t-channel strategy. The second constructor takes a flat list of external masses instead of a Topology and is used for the topology-free TChannelMode::rambo and TChannelMode::chili modes.

batch is the leading batch dimension. n_out is the number of outgoing particles.

Inputs

  • random – float, shape (batch, random_dim()) – the unit-hypercube coordinates.

  • discrete – int, shape (batch, discrete_dim()) – the discrete channel choices. Present only when discrete_dim() is nonzero.

Conditions

  • permutation_index – int, shape (batch,) – which permutation channel to use. Present only when more than one permutation is given.

  • mirror_index – int, shape (batch,) – 1 to take leg 1 from beam 2 and leg 2 from beam 1. Present only when mirror_beams is set; it follows permutation_index.

Outputs

  • momenta – float, shape (batch, n_out + 2, 4) – all momenta (incoming beams first, then outgoing).

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

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

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

References

Overloaded function.

  1. __init__(self: madspace._madspace_py.PhaseSpaceMapping, topology: madspace._madspace_py.Topology, cm_energy: typing.SupportsFloat, leptonic: bool = False, invariant_power: typing.SupportsFloat = 0.8, t_channel_mode: madspace._madspace_py.PhaseSpaceMapping.TChannelMode = <TChannelMode.propagator: 0>, cuts: madspace._madspace_py.Cuts | None = None, permutations: collections.abc.Sequence[collections.abc.Sequence[typing.SupportsInt]] = [], color_order: collections.abc.Sequence[typing.SupportsInt] | None = None, beam_rapidity: typing.SupportsFloat = 0.0, mirror_beams: bool = False) -> None

Parameters:

  • topology – The diagram topology to follow. See Topology.

  • cm_energy – Total collision energy.

  • leptonic – If true, skip the PDF convolution (no x1/x2 sampling).

  • invariant_power – Exponent of the 1/s^p sampling of every time-like invariant. See Invariant.

  • t_channel_mode – The TChannelMode strategy.

  • cuts – Fiducial cuts to fold into the sampling. See Cuts.

  • permutations – One outgoing-particle permutation per channel. More than one enables the permutation_index condition.

  • color_order – Color ordering for TChannelMode::color_ordered.

  • beam_rapidity – Rapidity of the beams’ centre-of-mass frame in the lab frame the momenta are returned in: 0.5 ln(E1 / E2) for beam energies E1 (along +z) and E2, with cm_energy = 2 sqrt(E1 E2). The phase space is generated in the beams’ frame and boosted into the lab before the cuts, so rapidity cuts act in the lab.

  • mirror_beams – Add the mirror_index condition: for index 1 the event is rotated by pi about the x axis in the beams’ frame (leg 1 from beam 2, leg 2 from beam 1) before the lab boost and the cuts. With identical beams that is a rotation of the lab event too.

  1. __init__(self: madspace._madspace_py.PhaseSpaceMapping, external_masses: collections.abc.Sequence[typing.SupportsFloat], cm_energy: typing.SupportsFloat, leptonic: bool = False, invariant_power: typing.SupportsFloat = 0.8, mode: madspace._madspace_py.PhaseSpaceMapping.TChannelMode = <TChannelMode.rambo: 1>, cuts: madspace._madspace_py.Cuts | None = None, color_order: collections.abc.Sequence[typing.SupportsInt] | None = None, beam_rapidity: typing.SupportsFloat = 0.0, mirror_beams: bool = False) -> None

Parameters:

  • external_masses – Masses of all external particles, the two beams first. A trivial topology is built from them.

  • cm_energy – Total collision energy.

  • leptonic – If true, skip the PDF convolution.

  • invariant_power – Exponent of the 1/s^p invariant sampling. See Invariant.

  • mode – The TChannelMode strategy (default TChannelMode::rambo).

  • cuts – Fiducial cuts. See Cuts.

  • color_order – Color ordering for TChannelMode::color_ordered.

  • beam_rapidity – Rapidity of the beams’ centre-of-mass frame in the lab frame the momenta are returned in: 0.5 ln(E1 / E2) for beam energies E1 (along +z) and E2, with cm_energy = 2 sqrt(E1 E2). The phase space is generated in the beams’ frame and boosted into the lab before the cuts, so rapidity cuts act in the lab.

  • mirror_beams – Add the mirror_index condition: for index 1 the event is rotated by pi about the x axis in the beams’ frame (leg 1 from beam 2, leg 2 from beam 1) before the lab boost and the cuts. With identical beams that is a rotation of the lab event too.

class TChannelMode(*args, **kwargs)

Bases: pybind11_object

Members:

propagator

rambo

chili

color_ordered

Overloaded function.

  1. __init__(self: madspace._madspace_py.PhaseSpaceMapping.TChannelMode, value: typing.SupportsInt) -> None

  2. __init__(self: madspace._madspace_py.PhaseSpaceMapping.TChannelMode, name: str) -> None

chili = <TChannelMode.chili: 2>
color_ordered = <TChannelMode.color_ordered: 3>
PhaseSpaceMapping.TChannelMode.name -> str
propagator = <TChannelMode.propagator: 0>
rambo = <TChannelMode.rambo: 1>
property value
beam_rapidity(self: madspace._madspace_py.PhaseSpaceMapping) → float

Rapidity of the beams’ centre-of-mass frame in the lab frame.

channel_count(self: madspace._madspace_py.PhaseSpaceMapping) → int

Number of permutation channels.

chili = <TChannelMode.chili: 2>
color_ordered = <TChannelMode.color_ordered: 3>
cuts(self: madspace._madspace_py.PhaseSpaceMapping) → madspace._madspace_py.Cuts

The cuts, applied to the lab-frame momenta.

discrete_dim(self: madspace._madspace_py.PhaseSpaceMapping) → int

Number of discrete channel choices.

empty(self: madspace._madspace_py.PhaseSpaceMapping) → bool

True when the cuts exclude the whole region this mapping samples: a pair mass cut puts a propagator’s floor at or above the upper end of its on-shell window.

Every point then fails the cuts, so the channel contributes nothing and should be dropped rather than sampled.

mirror_beams(self: madspace._madspace_py.PhaseSpaceMapping) → bool

Whether the mapping takes the mirror_index condition.

particle_count(self: madspace._madspace_py.PhaseSpaceMapping) → int

Total number of particles, incoming and outgoing.

propagator = <TChannelMode.propagator: 0>
rambo = <TChannelMode.rambo: 1>
random_dim(self: madspace._madspace_py.PhaseSpaceMapping) → int

Number of continuous unit-hypercube inputs consumed by the forward map.