PhaseSpaceMapping

class PhaseSpaceMapping : public madspace::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

Public Types

enum TChannelMode

How the space-like (t-channel) part of the phase space is generated.

Values:

enumerator propagator

A chain of 2->2 blocks (TPropagatorMapping).

enumerator rambo

FastRamboMapping on the t-channel legs.

enumerator chili

Collider coordinates (ChiliMapping).

enumerator color_ordered

A color-ordered chain (ColorOrderedMapping).

Public Functions

PhaseSpaceMapping(const Topology &topology, double cm_energy, bool leptonic = false, double invariant_power = 0.8, TChannelMode t_channel_mode = propagator, const std::optional<Cuts> &cuts = std::nullopt, const std::vector<std::vector<std::size_t>> &permutations = {}, const std::optional<std::vector<std::size_t>> &color_order = std::nullopt, double beam_rapidity = 0., bool mirror_beams = false)
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.

PhaseSpaceMapping(const std::vector<double> &external_masses, double cm_energy, bool leptonic = false, double invariant_power = 0.8, TChannelMode mode = rambo, const std::optional<Cuts> &cuts = std::nullopt, const std::optional<std::vector<std::size_t>> &color_order = std::nullopt, double beam_rapidity = 0., bool mirror_beams = false)
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.

inline std::size_t random_dim() const

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

inline virtual std::size_t discrete_dim() const override

Number of discrete channel choices.

inline std::size_t particle_count() const

Total number of particles, incoming and outgoing.

inline std::size_t channel_count() const

Number of permutation channels.

inline double beam_rapidity() const

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

inline bool mirror_beams() const

Whether the mapping takes the mirror_index condition.

inline const Cuts &cuts() const

The cuts, applied to the lab-frame momenta.

inline bool empty() const

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.

Public Static Functions

static inline std::size_t random_dim_for(const Topology &topology, bool leptonic)

Number of continuous unit-hypercube inputs a forward map over topology consumes.

A 1 -> n decay and a leptonic (fixed-s) 2 -> n collision both have 3n-4 degrees of freedom. A hadronic 2 -> n adds the beam momentum fractions, i.e. one further sampled invariant on top of s_hat, giving 3n-2. A hadronic 2 -> 1 collision keeps a single random number, the rapidity of the produced particle, since s_hat is fixed at its mass.

Parameters:

  • topology – The decay topology.

  • leptonic – If true, skip the PDF convolution.

Throws:

std::invalid_argument – for a 2 -> 1 topology without PDFs.