Classes
struct	SampledEvent
	One sampled linear Breit-Wheeler event. More...

struct	SamplingKernel
	Host-only cached data for repeated linear Breit-Wheeler event sampling. More...

Functions
double	photonEnergyFromWavelengthGeV (double wavelength_m)
	Convert a laser wavelength to a single-photon energy.

double	invariantSGeV2 (double photon1EnergyGeV, double photon2EnergyGeV, const Vector_t< double, 3 > &photon1Direction, const Vector_t< double, 3 > &photon2Direction)
	Two-photon invariant \(s\) for Breit-Wheeler pair production.

double	thresholdInvariantSGeV2 ()
	Threshold invariant for \(\gamma + \gamma \to e^- + e^+\).

bool	isAboveThreshold (double invariantSGeV2)
	Check whether pair creation is kinematically allowed.

double	pairBetaCM (double invariantSGeV2)
	Outgoing lepton speed in the pair center-of-momentum frame.

double	totalCrossSection (double invariantSGeV2)
	Total unpolarized linear Breit-Wheeler cross section.

double	proposalZToScatteringCosineCM (double invariantSGeV2, double proposalZ)
	Map CAIN's proposal parameter \(z \in [-1,1]\) to the CM scattering cosine.

double	unpolarizedAngularWeight (double invariantSGeV2, double proposalZ)
	Evaluate the unpolarized CAIN-aligned angular kernel in proposal coordinates.

SamplingKernel	makeSamplingKernel (double highEnergyPhotonEnergyGeV, double laserPhotonEnergyGeV, const Vector_t< double, 3 > &highEnergyDirection, const Vector_t< double, 3 > &laserDirection)
	Build a cached sampling kernel for repeated sampled events.

std::mt19937_64	makeHostRandomEngine (std::uint64_t streamIndex=0)
	Build a deterministic host RNG from `Options::seed`.

SampledEvent	sampleEvent (const SamplingKernel &kernel, std::mt19937_64 &engine)
	Sample one unpolarized linear Breit-Wheeler event.

Class Documentation

◆ Physics::LinearBreitWheeler::SampledEvent

struct Physics::LinearBreitWheeler::SampledEvent

One sampled linear Breit-Wheeler event.

The first benchmark path keeps only the unpolarized kinematics. The event is represented by the center-of-momentum scattering variables and by the final laboratory-frame electron and positron four-momenta.

Definition at line 59 of file LinearBreitWheeler.h.

Collaboration diagram for Physics::LinearBreitWheeler::SampledEvent:

Class Members
double	azimuthCM = 0.0	Center-of-momentum azimuth \(\phi\) in rad.
double	electronEnergyLabGeV	Outgoing electron energy in the lab frame [GeV].
Vector_t< double, 3 >	electronMomentumLabGeV	Outgoing electron three-momentum in the lab frame [GeV/c].
double	positronEnergyLabGeV	Outgoing positron energy in the lab frame [GeV].
Vector_t< double, 3 >	positronMomentumLabGeV	Outgoing positron three-momentum in the lab frame [GeV/c].
double	scatteringCosineCM	Center-of-momentum scattering cosine \(\cos\theta\).

◆ Physics::LinearBreitWheeler::SamplingKernel

struct Physics::LinearBreitWheeler::SamplingKernel

Host-only cached data for repeated linear Breit-Wheeler event sampling.

This structure stores the fixed two-photon geometry used in the first OPALX Breit-Wheeler validation path. It is intentionally scalar and host-side, matching the staged approach already used for linear Compton benchmarking.

The incoming state consists of two photons:

a high-energy photon with energy \(E_\gamma\) and direction \(\hat n_\gamma\),
a laser photon with energy \(\omega_L\) and direction \(\hat n_L\).

The corresponding two-photon invariant is

\[ s = 2 E_\gamma \omega_L (1 - \hat n_\gamma \cdot \hat n_L). \]

Pair creation is kinematically allowed only for \(s \ge 4 m_e^2\).

Definition at line 32 of file LinearBreitWheeler.h.

Collaboration diagram for Physics::LinearBreitWheeler::SamplingKernel:

Class Members
double	cmLorentzGamma	Lorentz factor of the CM frame relative to the laboratory frame.
Vector_t< double, 3 >	cmVelocity	Dimensionless CM boost velocity.
Vector_t< double, 3 >	highEnergyDirection	Normalized incoming high-energy photon direction.
double	highEnergyPhotonEnergyGeV	Incoming high-energy photon energy in the lab frame [GeV].
double	invariantSGeV2 = 0.0	Two-photon invariant \(s\) in GeV^2.
Vector_t< double, 3 >	laserDirection	Normalized incoming laser-photon direction.
double	laserPhotonEnergyGeV	Incoming laser-photon energy in the lab frame [GeV].
double	pairBetaCM = 0.0	Outgoing lepton speed \(\beta = \sqrt{1 - 4m_e^2/s}\) in the pair CM frame.
double	rejectionUpperBound = 0.0	Conservative rejection-sampling envelope for the unpolarized CAIN-aligned angular kernel.

Function Documentation

◆ invariantSGeV2()

double Physics::LinearBreitWheeler::invariantSGeV2	(	double	photon1EnergyGeV,
		double	photon2EnergyGeV,
		const Vector_t< double, 3 > &	photon1Direction,
		const Vector_t< double, 3 > &	photon2Direction
	)

Two-photon invariant \(s\) for Breit-Wheeler pair production.

For two incoming photons with energies \(E_1\) and \(E_2\) and unit directions \(\hat n_1\) and \(\hat n_2\),

\[ s = 2 E_1 E_2 (1 - \hat n_1 \cdot \hat n_2). \]

Parameters

photon1EnergyGeV	First photon energy in GeV.
photon2EnergyGeV	Second photon energy in GeV.
photon1Direction	First photon direction.
photon2Direction	Second photon direction.

Returns: Invariant \(s\) in GeV^2.

Definition at line 152 of file LinearBreitWheeler.cpp.

References dot().

Referenced by makeSamplingKernel(), and TEST().

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◆ isAboveThreshold()

bool Physics::LinearBreitWheeler::isAboveThreshold ( double invariantSGeV2 )

Check whether pair creation is kinematically allowed.

Parameters

invariantSGeV2 Two-photon invariant \(s\) in GeV^2.

Returns: True if \(s \ge 4 m_e^2\).

Definition at line 166 of file LinearBreitWheeler.cpp.

References thresholdInvariantSGeV2().

Referenced by makeSamplingKernel(), pairBetaCM(), proposalZToScatteringCosineCM(), sampleEvent(), TEST(), totalCrossSection(), and unpolarizedAngularWeight().

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◆ makeHostRandomEngine()

std::mt19937_64 Physics::LinearBreitWheeler::makeHostRandomEngine ( std::uint64_t streamIndex = 0 )

Build a deterministic host RNG from Options::seed.

Parameters

streamIndex Optional stream index for reproducible stream splitting.

Returns: Seeded host-side random engine.

Definition at line 248 of file LinearBreitWheeler.cpp.

Referenced by main(), LinearBreitWheelerBenchmark::sampleFinitePhotonBeamHistogram(), LinearBreitWheelerBenchmark::sampleFinitePhotonBeamJointHistogram(), LinearBreitWheelerBenchmark::sampleHistogram(), LinearBreitWheelerBenchmark::sampleJointHistogram(), TEST(), and TEST().

◆ makeSamplingKernel()

SamplingKernel Physics::LinearBreitWheeler::makeSamplingKernel	(	double	highEnergyPhotonEnergyGeV,
		double	laserPhotonEnergyGeV,
		const Vector_t< double, 3 > &	highEnergyDirection,
		const Vector_t< double, 3 > &	laserDirection
	)

Build a cached sampling kernel for repeated sampled events.

The initial OPALX sampled-event path mirrors the linear CAIN event generator: it keeps the fixed two-photon geometry, computes the corresponding CM boost, and precomputes a rejection-sampling envelope for the unpolarized CAIN-style angular weight.

Definition at line 213 of file LinearBreitWheeler.cpp.

Referenced by main(), LinearBreitWheelerBenchmark::sampleFinitePhotonBeamHistogram(), LinearBreitWheelerBenchmark::sampleFinitePhotonBeamJointHistogram(), LinearBreitWheelerBenchmark::sampleHistogram(), LinearBreitWheelerBenchmark::sampleJointHistogram(), TEST(), and TEST().

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◆ pairBetaCM()

double Physics::LinearBreitWheeler::pairBetaCM ( double invariantSGeV2 )

Outgoing lepton speed in the pair center-of-momentum frame.

Above threshold,

\[ \beta = \sqrt{1 - \frac{4m_e^2}{s}}. \]

Parameters

invariantSGeV2 Two-photon invariant \(s\) in GeV^2.

Returns: Dimensionless center-of-momentum lepton speed.

Definition at line 168 of file LinearBreitWheeler.cpp.

References isAboveThreshold(), and thresholdInvariantSGeV2().

Referenced by makeSamplingKernel(), and totalCrossSection().

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◆ photonEnergyFromWavelengthGeV()

double Physics::LinearBreitWheeler::photonEnergyFromWavelengthGeV ( double wavelength_m )

Convert a laser wavelength to a single-photon energy.

The conversion uses

\[ \omega_L = \frac{2 \pi \hbar c}{\lambda_L}. \]

Parameters

wavelength_m Laser wavelength in m.

Returns: Laser photon energy in GeV.

Definition at line 145 of file LinearBreitWheeler.cpp.

References Physics::c, Physics::h_bar, and Physics::two_pi.

Referenced by main(), LinearBreitWheelerBenchmark::sampleFinitePhotonBeamHistogram(), LinearBreitWheelerBenchmark::sampleFinitePhotonBeamJointHistogram(), LinearBreitWheelerBenchmark::sampleHistogram(), LinearBreitWheelerBenchmark::sampleJointHistogram(), TEST(), TEST(), and TEST().

◆ proposalZToScatteringCosineCM()

double Physics::LinearBreitWheeler::proposalZToScatteringCosineCM	(	double	invariantSGeV2,
		double	proposalZ
	)

Map CAIN's proposal parameter \(z \in [-1,1]\) to the CM scattering cosine.

The linear CAIN generator samples a proposal variable \(z\), transforms it to an auxiliary variable \(Y(z)\), and then sets

\[ \cos\theta = 1 - 2Y. \]

This helper exposes that mapping directly so the local angular kernel can be tested pointwise in the same parameterization used by the rejection sampler.

Parameters

invariantSGeV2	Two-photon invariant \(s\) in GeV^2.
proposalZ	CAIN proposal variable \(z\) in [-1,1].

Returns: Center-of-momentum scattering cosine corresponding to proposalZ.

Definition at line 191 of file LinearBreitWheeler.cpp.

References isAboveThreshold().

Referenced by TEST().

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◆ sampleEvent()

SampledEvent Physics::LinearBreitWheeler::sampleEvent	(	const SamplingKernel &	kernel,
		std::mt19937_64 &	engine
	)

Sample one unpolarized linear Breit-Wheeler event.

The angular proposal and acceptance rule are aligned with the linear CAIN event generator LNBWGN, but restricted here to the unpolarized case. The sampled outgoing electron and positron momenta are returned in the lab frame.

Parameters

kernel	Cached sampling kernel created by makeSamplingKernel.
engine	Host-side random engine.

Returns: Sampled event.

Definition at line 252 of file LinearBreitWheeler.cpp.

References Physics::LinearBreitWheeler::SamplingKernel::cmLorentzGamma, Physics::LinearBreitWheeler::SamplingKernel::cmVelocity, dot(), Physics::LinearBreitWheeler::SamplingKernel::highEnergyDirection, Physics::LinearBreitWheeler::SamplingKernel::invariantSGeV2, isAboveThreshold(), Physics::m_e, Physics::LinearBreitWheeler::SamplingKernel::rejectionUpperBound, Physics::LinearBreitWheeler::SampledEvent::scatteringCosineCM, and Physics::two_pi.

Referenced by main(), LinearBreitWheelerBenchmark::sampleFinitePhotonBeamHistogram(), LinearBreitWheelerBenchmark::sampleFinitePhotonBeamJointHistogram(), LinearBreitWheelerBenchmark::sampleHistogram(), LinearBreitWheelerBenchmark::sampleJointHistogram(), TEST(), and TEST().

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◆ thresholdInvariantSGeV2()

double Physics::LinearBreitWheeler::thresholdInvariantSGeV2 ( )

Threshold invariant for \(\gamma + \gamma \to e^- + e^+\).

The exact kinematic threshold is

\[ s_\text{thr} = 4 m_e^2. \]

Definition at line 164 of file LinearBreitWheeler.cpp.

References Physics::m_e.

Referenced by isAboveThreshold(), pairBetaCM(), TEST(), TEST(), TEST(), and TEST().

◆ totalCrossSection()

double Physics::LinearBreitWheeler::totalCrossSection ( double invariantSGeV2 )

Total unpolarized linear Breit-Wheeler cross section.

The first OPALX implementation uses the standard unpolarized Breit-Wheeler total cross section in terms of the center-of-momentum lepton speed \(\beta = \sqrt{1 - 4m_e^2/s}\):

\[ \sigma_{\gamma\gamma\to e^+e^-} = \frac{\pi r_e^2}{2}(1-\beta^2) \left[ (3-\beta^4) \ln\!\left(\frac{1+\beta}{1-\beta}\right) - 2\beta(2-\beta^2) \right]. \]

Parameters

invariantSGeV2 Two-photon invariant \(s\) in GeV^2.

Returns: Total cross section in m^2.

Definition at line 177 of file LinearBreitWheeler.cpp.

References isAboveThreshold(), pairBetaCM(), Physics::pi, and Physics::r_e.

Referenced by TEST(), and TEST().

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◆ unpolarizedAngularWeight()

double Physics::LinearBreitWheeler::unpolarizedAngularWeight	(	double	invariantSGeV2,
		double	proposalZ
	)

Evaluate the unpolarized CAIN-aligned angular kernel in proposal coordinates.

This is the dimensionless angular weight used by the current OPALX rejection sampler after the CAIN change of variables from the proposal parameter \(z\) to the center-of-momentum scattering angle. It is not the physical cross section in SI units; it is the local kernel shape that controls accepted event sampling.

Parameters

invariantSGeV2	Two-photon invariant \(s\) in GeV^2.
proposalZ	CAIN proposal variable \(z\) in [-1,1].

Returns: Non-negative unpolarized angular weight.

Definition at line 203 of file LinearBreitWheeler.cpp.

References isAboveThreshold().

Referenced by TEST().

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Classes

Functions

Class Documentation

◆ Physics::LinearBreitWheeler::SampledEvent

◆ Physics::LinearBreitWheeler::SamplingKernel

Function Documentation

◆ invariantSGeV2()

◆ isAboveThreshold()

◆ makeHostRandomEngine()

◆ makeSamplingKernel()

◆ pairBetaCM()

◆ photonEnergyFromWavelengthGeV()

◆ proposalZToScatteringCosineCM()

◆ sampleEvent()

◆ thresholdInvariantSGeV2()

◆ totalCrossSection()

◆ unpolarizedAngularWeight()