Processes list

Processes list#

Natively, CepGen provides a collection of predefined, historical processes that can be extended or modified by the user. This page lists and describes them.

As derivatives of a base cepgen::proc::Process object, a few common members and steering parameters are characterising all processes.

For instance, in the description of all process parameters, one may notice the following parameters are systematically steered from the user:

  • alphaEM (cepgen::ParametersList): one of the interpolation modules for the \(Q\)-dependent electromagnetic coupling evolution (see the list) ;

  • alphaS (cepgen::ParametersList): one of the interpolation modules for the \(Q\)-dependent strong coupling evolution (see the list) ;

  • hasEvent (bool): does the process also define an event content that can be generated?

  • kinematics (cepgen::ParametersList): the definition of the phase space to be integrated and for which events will be generated. It is defined in the subsection below ;

  • randomGenerator (cepgen::ParametersList): the modelling for a (potential) random number generator to be used by the process.

Note

List of user-steerable parameters for the definition of event kinematics

The kinematics parameters block contains the usual parameters to be steered:

  • formFactors (2-component vector of cepgen::ParametersList, for positive-z and negative-z beams respectively): one of the electromagnetic/DIS beam form factors modellings (see the list)

  • structureFunctions (cepgen::ParametersList): one of the inelastic beam structure functions modellings (see the list)

  • mode (integer): kinematic regime to generate and the size of the phase space to perform the integration. It can take the following values:

Kinematic cuts are characterised by three parameters collections to be steered:

Additionally, a few parameters are steered to define the beams and their kinematics:

  • pdgIds (vector<int>) for the specification of positive-z and negative-z beam PDG, or HI identifiers. For historical/backward-compatibility reasons, one may also use the following parameters:

    • beam1id and beam2id for the PDG identifier of positive-z and negative-z (resp.) incoming beams

    • beam1A/beam1Z, and beam2A/beam2Z may be used for the atomic/mass numbers of HI beams

  • energies (vector<double>) for the specification of positive-z and negative-z beam energies (in GeV)

  • pz (vector<double>) for the specification of positive-z and negative-z longitudinal beam momenta (in GeV/c)

In the case of symmetric beam particles, the sqrtS (double) parameter may also be used to directly specify the two-beam centre-of-mass energy (in GeV).

LPAIR’s \(\ggll\)#

The \(pp \rightarrow p^{(\ast)}(\ggll)p^{(\ast)}\) process was first described and implemented in the early 1990s as a Fortran code: LPAIR [BDSV91]. In CepGen, it can be reached through the lpair process. It allows to compute the cross-section and generate events for the \(\ggll\) process for ee, ep, and pp collisions.

A phenomenological review of both this process and its first implementation in LPAIR may be found in [Ver83].

The object is implemented as LPAIR, and a list of process-specific steering parameters can be found here.

Factorised processes#

This page describes the different techniques used to simplify the computation of a central exclusive process through the factorisation of its total matrix element into sub-blocks:

  • a parton-from-beam particle flux, encompassing all kinematic features of a “physical” emission, possibly leaving the beam particle on-shell (i.e. surviving the emission), or in a diffractive state (possibly dissociating into a hadronic jet) ;

  • a parton-parton matrix element, e.g. a \(\gamma\gamma\to X\) process, much easier to compute than the full beam-beam interaction \(S\)-matrix.

CepGen gives the user a relative freedom in its implementation of factorised, two-parton level processes. As of version 1.2.0, two main parton emission types (and central matrix element definitions) are indeed handled:

  • a standard, collinear parton emission, with a \(x\) (inelasticity) and \(Q^2\) squared momentum transfer dependence, implying a full momentum transfer along the beam direction (conventionally, the \(z\)-axis) ; this technique is used in many other Monte Carlo generators for the simulation of CEPs ;

  • a parton \(\kt\)-dependent emission, also involving a dependence in the transverse parton virtuality, \(\kt\), involving a broader definition of the phase space (i.e. more time-consuming, but more precise).

To be considered as a valid factorised process implementation in CepGen, the user class is required to derivate from a cepgen::proc::FactorisedProcess base class, with a few required user-overriden methods. See this page for a detailed description of these methods.

Collinear parton emission#

Warning

Under construction

\(\kt\)-factorised processes#

The \(\kt\) factorisation, described in detail in [GdSFP+15] through the \(\ggff\) process listed above, allows to provide a “physical” modelling of this \(\kt\) dependence, commonly introduced as a simple gaussian smearing, e.g. in Pythia 8 (see the BeamRemnants:primordialKT flag).

For instance, a \(pp\to p^{(\ast)}(\ggx)p^{(\ast)}\) matrix element can be factorised through the following formalism:

\[\mathrm d\sigma = \int \frac{\mathrm d^2{\mathbf q_{\mathrm T}^2}_1}{\pi {\mathbf q_{\mathrm T}^2}_1} {\cal F}_{\gamma/p}^{\rm el/inel}(x_1,{\mathbf q_{\mathrm T}^2}_1) \int \frac{\mathrm d^2{\mathbf q_{\mathrm T}^2}_2}{\pi {\mathbf q_{\mathrm T}^2}_2} {\cal F}_{\gamma/p}^{\rm el/inel}(x_2,{\mathbf q_{\mathrm T}^2}_2) ~ \mathrm d\sigma^\ast,\]

where \(\mathcal F_{\gamma/p}^{\rm el/inel}(x_i,\vecqt_i)\) are unintegrated parton densities, and \(\mathrm d\sigma^\ast\) the hard process factorised out of the total matrix element.

Elastic unintegrated photon densities are expressed as functions of the proton electric and magnetic form factors \(G_E\) and \(G_M\):

\[\mathcal F_{\gamma/p}^{\rm el}(\xi,\vecqt^2) = \frac{\alpha}{\pi}\left[(1-\xi)\left(\frac{\vecqt^2}{\vecqt^2+\xi^2 m_p^2}\right)^2 F_E(Q^2)+\frac{\xi^2}{4}\left(\frac{\vecqt^2}{\vecqt^2+\xi^2 m_p^2}\right) F_M(Q^2)\right].\]

The inelastic contribution further requires both the diffractive state four-momentum norm \(M_X\) and a proton structure functions parameterisation as an input:

\[\begin{split}\mathcal F_{\gamma/p}^{\rm inel}(\xi,\vecqt^2) = \frac{\alpha}{\pi}\Bigg[(1-\xi)\left(\frac{\vecqt^2}{\vecqt^2+\xi(M_X^2-m_p^2)+\xi^2 m_p^2}\right)^2\frac{F_2(\xbj,Q^2)}{Q^2+M_X^2-m_p^2}+{}\\ {}+\frac{\xi^2}{4}\frac{1}{\xbj^2} \left(\frac{\vecqt^2}{\vecqt^2+\xi(M_X^2-m_p^2)+\xi^2 m_p^2}\right) \frac{2\xbj F_1(\xbj,Q^2)}{Q^2+M_X^2-m_p^2}\Bigg],\end{split}\]

with \(\xbj = {Q^2}/({Q^2+M_X^2-m_p^2})\) the Bjorken scaling variable.

Implementations#

\(\ggff\) process#

The photon transverse momentum-dependant description of this process was previously developed in PPtoLL, and described in [GdSFP+15]. Since it now also supports the quark-antiquark production (thus all charged fermions), it is defined as the PPtoFF process in CepGen.

Process-specific options#

  • method (integer): switch between the two matrix element definitions:

    • 0: on-shell amplitude,

    • 1: off-shell amplitude.

  • pair (integer/PDG): PDG identifier of the fermion pair to be produced in the final state. It can take the following values:

    • PDG.electron := 11: \(e^+e^-\) pair production

    • PDG.muon := 13: \(\mu^+\mu^-\) pair production

    • PDG.tau := 15: \(\tau^+\tau^-\) pair production

    • PDG.down, PDG.up, PDG.strange, PDG.charm, PDG.bottom, PDG.top (or equivalently 1-6): quark pair production.

Full object reference#
class PPtoFF : public FactorisedProcess#

\(\ggww\) process#

The two-photon production of gauge boson pairs process, i.e. \(pp \rightarrow p^{(\ast)}(\ggww)p^{(\ast)}\), is implemented through the PPtoWW process object, featuring the on-shell and off-shell matrix elements reviewed in [LuszczakSchaferS18].

Process-specific options#

  • method (integer): switch between the two matrix element definitions:

  • polarisationStates (int): switch between all combinations of polarisation states to be included in the matrix element. It can take the following values:

    • 0: all contributions,

    • 1: longitudinal-longitudinal,

    • 2: longitudinal-transverse,

    • 3: transverse-longitudinal,

    • 4: transverse-transverse.

Full object reference#
class PPtoWW : public FactorisedProcess#
Contents

By Laurent Forthomme

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