Photon-photon Interactions

From version 8.214 on, also resolved photon-photon interactions can be simulated. Currently quark and gluon initiated hard-processes with parton showers and hadronization can be generated, but MPIs and soft interactions are not included. Only new parameter is the selection of the PDF set for photons. This page describes some of the special features related to these collisions.

Resolved photon

Photons can either interact directly as an unresolved particle or they can form a hadronic state. In the latter case the hard process can be simulated using PDFs to describe the partonic structure of the resolved photon. The evolution equations for photons include an additional term that corresponds to gamma → q qbar splittings. Due to this, the PDFs are somewhat different for photons than for hadrons and some parts of event generation need special attention.

Process-level generation

Due to the additional term in the evolution equations the quarks in a resolved photon may carry a very large fraction (x~1) of the photon momentum. In these cases it may happen that, after the hard process, there is no energy left to construct the beam remnants. This is true especially if a heavy quark is taken out from the beam and a corresponding massive antiquark needs to be added to the remnant system to conserve flavour. Even though these events are allowed based on the PDFs, they are not physical and should be rejected. Therefore some amount of errors can be expected when generating events close to the edge of phase space, e.g. when collision energy is low.

Spacelike showers

The parton showers are generated according to the DGLAP evolution equations. Due to the gamma → q qbar splitting in the photon evolution, a few modifications are needed for the ISR algorithm.

The additional term corresponds to a possibility to find the original beam photon during the backwards evolution, which is added to QED part of the spacelike shower evolution. If this splitting happens there is no need to construct the beam remnants for the given beam.
The heavy quark production threshold with photon beams is handled in a similar manner as for hadrons, but now the splitting that is forced to happen is gamma → Q Qbar.
As the splittings in backwards evolution increases the x of the parton taken from the beam, the splittings can lead to a situation where there is no room left for massive beam remnants. To make sure that the required remnants can be constructed, splittings that would not leave room for the beam remnants are not allowed.

Beam Remnants

To construct the beam remnants, one should know whether the parton taken from the beam is a valence parton or not. The valence partons of a photon includes the partons that originate from gamma → q qbar splittings of the original beam photon and the valence partons from the hadron-like part of the PDF. In either case, the flavour of the valence quarks can fluctuate. Unfortunately the decomposition to the different components are typically not provided in the PDF sets and some further assumptions are needed to decide for the valence content.

When ISR is applied for photon beams it is possible to end up to the original beam photon during the evolution. Therefore there are three possibilities for the remnants:

Remnants need to be constructed for both beams.
Remnants are constructed only for one side.
No need for remnants on either side.

The last case is the simplest as all the partons in the event are already generated by the parton showers. In the first case the remnants and primordial kT are constructed similarly as for normal hadronic interactions [Sjo04]. For the second case the momenta of the remnant partons can not be balanced between the two beams as the kinematics of the other side are already fixed. In these cases the momenta are balanced between the scattered system and the remnants.

As the primordial kT increases the invariant mass of the remnants and the scattered system, it may again happen that there is no room for the remnant partons after kT is added, so the kinematics can not be constructed. In this case new values for kT are sampled. If this does not work, a new shower is generated and in some rare cases the parton-level generation fails and the hard process is rejected.