Phase Space Layout

AbstractPhaseSpaceLayout

The AbstractPhaseSpaceLayout is an abstract type that represents the general concept of a phase space layout in a scattering process.

Interface Functions to Implement:

• phase_space_dimension(proc, model, layout::AbstractPhaseSpaceLayout): Defines the number of independent phase space coordinates needed to build the momenta.

AbstractInPhaseSpaceLayout <: AbstractPhaseSpaceLayout

The AbstractInPhaseSpaceLayout represents the phase space layout for the incoming particles in a scattering process. It defines the way in which the momenta of incoming particles are constructed from phase space coordinates.

Interface Functions to Implement:

• phase_space_dimension(proc, model, layout::AbstractInPhaseSpaceLayout): Defines the number of independent phase space coordinates for the incoming particles.
• _build_momenta(proc, model, in_psl::AbstractInPhaseSpaceLayout, in_coords::Tuple): Constructs the momenta for the incoming particles using the phase space coordinates.

AbstractOutPhaseSpaceLayout{IN_PSL<:AbstractInPhaseSpaceLayout} <: AbstractPhaseSpaceLayout

The AbstractOutPhaseSpaceLayout represents the phase space layout for the outgoing particles in a scattering process. It typically depends on the phase space layout of the incoming particles and specifies how the momenta of the outgoing particles are constructed from the respective coordinates.

The generic parameter IN_PSL links the outgoing phase space layout to the incoming layout, allowing consistency between the two configurations in the process.

Interface Functions to Implement:

• phase_space_dimension(proc, model, layout::AbstractOutPhaseSpaceLayout): Defines the number of independent phase space coordinates for the outgoing particles.
• in_phase_space_layout(out_psl::AbstractOutPhaseSpaceLayout): Provides the associated incoming phase space layout to ensure consistency between incoming and outgoing configurations.
• _build_momenta(proc, model, Ptot::AbstractFourMomentum, out_psl::AbstractOutPhaseSpaceLayout, out_coords::Tuple): Constructs the momenta for the outgoing particles, ensuring they comply with energy and momentum conservation based on the total incoming four-momentum.

_build_momenta(proc, model, in_psl::AbstractInPhaseSpaceLayout, in_coords::Tuple)
_build_momenta(proc, model, Ptot::AbstractFourMomentum, out_psl::AbstractOutPhaseSpaceLayout, out_coords::Tuple)

These functions need to be implemented as part of the phase space layout interface for both incoming and outgoing particle momenta construction. They serve as internal, low-level interfaces for constructing the four-momenta of particles during a scattering process, and are typically wrapped by the user-facing build_momenta function.

Incoming Phase Space Layout

The first function, _build_momenta(proc, model, in_psl, in_coords), constructs the four-momenta for the incoming particles based on the specified phase space coordinates (in_coords).

• Arguments:

  • proc: The scattering process definition, subtype of AbstractProcessDefinition.
  • model: The physics model, subtype of AbstractModelDefinition.
  • in_psl: The incoming phase space layout, subtype of AbstractInPhaseSpaceLayout, that defines how to map the coordinates to momenta.
  • in_coords: A tuple of phase space coordinates that parametrize the momenta of the incoming particles.

• Returns:

  • A collection of four-momenta representing the incoming particles. For performance reasons, it is recommended to return a Tuple of four-momenta.

Outgoing Phase Space Layout

The second function, _build_momenta(proc, model, Ptot, out_psl, out_coords), constructs the four-momenta for the outgoing particles. It uses the incoming four-momenta (in_moms) from the incoming state and applies the phase space coordinates (out_coords) to compute the outgoing momenta, ensuring they adhere to energy and momentum conservation laws.

• Arguments:

  • proc: The scattering process definition, subtype of AbstractProcessDefinition.
  • model: The physics model, subtype of AbstractModelDefinition.
  • in_moms: The incoming four-momenta, which is used to compute the momenta of the outgoing particles.
  • out_psl: The outgoing phase space layout, subtype of AbstractOutPhaseSpaceLayout, that maps the coordinates to momenta.
  • out_coords: A tuple of phase space coordinates that parametrize the outgoing particle momenta.

• Returns:

  • A collection of four-momenta representing the outgoing particles. For performance reasons, it is recommended to return a Tuple of four-momenta.

Notes

Both versions of _build_momenta handle the construction of particle momenta during different phases of the scattering process:

• The incoming version constructs momenta based on phase space coordinates alone.
• The outgoing version constructs momenta based on both phase space coordinates and the total four-momentum, ensuring conservation laws are respected.

phase_space_dimension(proc, model, layout::AbstractPhaseSpaceLayout)::Int

This function needs to be implemented for the phase-space layout interface. Return the dimensionality of the phase space, i.e., the number of coordinates, for a given process and model within the specified layout.

The phase space dimension is a crucial quantity that determines how many independent coordinates are required to describe the system of particles in the scattering process. It depends on the number of particles involved and the specific interaction model in use.

Arguments

• proc: The scattering process definition, a subtype of AbstractProcessDefinition.
• model: The physics model, a subtype of AbstractModelDefinition.
• layout: A specific phase space layout, either AbstractInPhaseSpaceLayout or AbstractOutPhaseSpaceLayout.

Returns

• The integer representing the number of independent phase space coordinates.

in_phase_space_layout(out_psl::AbstractOutPhaseSpaceLayout)::AbstractInPhaseSpaceLayout

This function needs to be implemented for the AbstractOutPhaseSpaceLayout interface. Given an outgoing phase space layout (out_psl), this function returns the associated incoming phase space layout.

This is useful for ensuring consistency between the incoming and outgoing particle momenta when calculating or sampling phase space points in scattering processes.

Arguments

• out_psl: The outgoing phase space layout, a subtype of AbstractOutPhaseSpaceLayout.

Returns

• The associated incoming phase space layout, a subtype of AbstractInPhaseSpaceLayout.

build_momenta(proc, model, in_psl::AbstractInPhaseSpaceLayout, in_coords::Tuple)

Construct the momenta of the incoming particles using the provided phase space coordinates.

This is the user-facing function that calls _build_momenta internally and validates the number of coordinates against the phase space dimensionality.

Arguments

• proc: The scattering process definition, subtype of AbstractProcessDefinition.
• model: The physics model, subtype of AbstractModelDefinition.
• in_psl: The incoming phase space layout, subtype of AbstractInPhaseSpaceLayout.
• in_coords: A tuple of phase space coordinates that parametrize the incoming particle momenta.

Returns

• A collection of four-momenta representing the incoming particles. Because of performance reasons, it is recommended to return a Tuple of four-momenta.

build_momenta(proc::AbstractProcessDefinition, model::AbstractModelDefinition, in_psl::AbstractInPhaseSpaceLayout, in_coords::Real)

A scalar version of build_momenta for incoming phase space layouts (in_psl), where the phase space coordinates are provided as a single scalar instead of a tuple.

Arguments:

• proc: The scattering process definition, subtype of AbstractProcessDefinition.
• model: The physics model, subtype of AbstractModelDefinition.
• in_psl: The incoming phase space layout, subtype of AbstractInPhaseSpaceLayout.
• in_coords::Real: A single scalar representing the phase space coordinate for the incoming particles.

Returns:

• A collection of four-momenta representing the incoming particles. For performance reasons, it is recommended to return a Tuple of four-momenta.

Notes:

This function is a convenience wrapper around build_momenta, automatically converting the scalar in_coords into a 1-tuple. It is useful when the incoming phase space only requires a single coordinate to define the particle momenta.

build_momenta(proc, model, Ptot::AbstractFourMomentum, out_psl::AbstractOutPhaseSpaceLayout, out_coords::Tuple)

Construct the momenta of the outgoing particles using the provided phase space coordinates (out_coords) and total incoming momentum (Ptot).

This function ensures that the outgoing momenta satisfy energy and momentum conservation, consistent with the physics model in use.

Arguments

• proc: The scattering process definition, subtype of AbstractProcessDefinition.
• model: The physics model, subtype of AbstractModelDefinition.
• in_moms: The incoming four-momenta, used to compute the outgoing momenta.
• out_psl: The outgoing phase space layout, subtype of `AbstractOutPhaseSpaceLayout.
• out_coords: A tuple of phase space coordinates that parametrize the outgoing particle momenta.

Returns

• A collection of four-momenta representing the incoming particles. Because of performance reasons, it is recommened to return a Tuple of four-momenta.