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Refactoring of differential cross section functionality (#38)
# Problem statement
The current implementation only allows implementing
`differential_cross_section` directly for given processes. Furthermore,
the interface does not allow the implementation of different phase-space
coordinate systems, e.g. to model $d\sigma/dE$ **and**
$d\sigma/d\cos\theta$ for the same process.
# Suggested solution
## Advanced process interface
I suggest to disassemble the differential cross-sections interface into
a more flexible interface:
```mermaid
flowchart TD
_differential_cross_section --> _differential_probability
_differential_cross_section --> _incident_flux*
_differential_probability --> _avg_matrix_element_square
_differential_probability --> _phase_space_factor*
_differential_probability -.-> _is_in_phasespace*
_avg_matrix_element_square --> _matrix_element*
_avg_matrix_element_square --> _avg_normalization*
```
where the functions with the asterisk give the new interface for the
calculation of differential cross-sections:
* `_matrix_element`: the matrix element of the process
* `_phase_space_factor`: the value of the pre-differential factor of the
phase-space measure
* `_is_in_phasespace`: checks if a given input is physical, see below
* `_incident_flux`: the incident particle flux, used to normalize the
probability
* `_avg_normalization`: normalization for averaging of squared matrix
elements
The underscore of those functions implies, that they are not exported,
and no input validation check is performed. For the functions
`_differential_cross_section` and `_differential_probability` there are
versions `differential_cross_section` and `differential_probability`,
where input validation is performed.
## Phase space definition
To attack the original problem using different coordinate systems for
the same process, this PR adds a simple system for coordinate systems
and frames of reference. Those are propagated through a composite type:
```Julia
PhasespaceDefinition{
CS<:AbstractCoordinateSystem,
F<: AbstractFrameOfReference
}
```
Currently, the given example implementations are very limited, but this
deserves an interface in the future. A dedicated issue will be opened
during the review process of this PR (see todos below).
## Phase space check
**Not included** in the input validation is the check if given incoming
and outgoing phase-spaces are physical, i.e. if all momenta are on-shell
and fulfill some sort of energy-momentum conservation. Therefore, I
suggest to add another interface function
```Julia
_is_in_phasespace(
in_ps_def::AbstractPhasespaceDefinition,
in_ps::AbstractVector{T},
out_ps_def::AbstractPhasespaceDefinition,
out_ps::AbstractVector{T},
) where {T<:QEDbase.AbstractFourMomentum}
```
which returns `true` if the input is physical, and `false` otherwise.
Consequently, there are unsafe versions of cross-sections and
probabilities, which don't perform the check given by the function
above, and safe versions, which return null if the condition given by
`_is_in_phasespace` is not met.
# Final remarks
To conclude, the different versions of cross-section and probability
functions, derived from the interface above, are
```Julia
_unsafe_differential_cross_section # without input validation, without phase-space check
_differential_cross_section # without input validation, with phase-space check
unsafe_differential_cross_section # with input validation, without phase-space check
differential_cross_section # with input validation, with phase-space check
_unsafe_differential_probability # without input validation, without phase-space check
_differential_probability # without input validation, with phase-space check
unsafe_differential_probability # with input validation, without phase-space check
differential_probability # with input validation, with phase-space check
```
where only the functions without an underscore are exported, for all of
those functions, there are implementations for all combinations of
vectors and matrices for the incoming and outgoing phase space.
## Todos:
- [x] write tests for `(_(unsafe_))probability`
- [x] make total cross-section an interface function
- [x] make energy-momentum check for *safe implementations* an interface
function
- [ ] Write a gist about the broadcasted implementations
- [x] rename `_[unsafe_]probability` to
`_[unsafe]differential_probability`
- [x] cleanup in Project.toml
- [x] open issue on `PhasespaceDefinition`
---------
Co-authored-by: Uwe Hernandez Acosta <u.hernandez@hzdr.de>
Co-authored-by: Tom Jungnickel <140055258+tjungni@users.noreply.github.com>- Loading branch information
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Mar 7, 2024
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