Photoproduction and $\gamma\gamma$ physics

MSEL = 1, 2, 4, 5, 6, 7, 8
ISUB =

33	$\mathrm{q}_i \gamma \to \mathrm{q}_i \mathrm{g}$
34	$\mathrm{f}_i \gamma \to \mathrm{f}_i \gamma$
54	$\mathrm{g}\gamma \to \mathrm{q}_k \overline{\mathrm{q}}_k$
58	$\gamma \gamma \to \mathrm{f}_k \overline{\mathrm{f}}_k$
80	$\mathrm{q}_i \gamma \to \mathrm{q}_k \pi^{\pm}$
84	$\mathrm{g}\gamma \to \mathrm{Q}_k \overline{\mathrm{Q}}_k$
85	$\gamma \gamma \to \mathrm{F}_k \overline{\mathrm{F}}_k$

An (almost) real photon has both a point-like component and a hadron-like one. This means that several classes of processes may be distinguished, see section .

78.

The processes listed above are possible when the photon interacts as a point-like particle, i.e. couples directly to quarks and leptons.

79.

When the photon acts like a hadron, i.e. is resolved in a partonic substructure, then high-$p_{\perp}$ parton-parton interactions are possible, as described in sections and . These interactions may be further subdivided into VMD and anomalous (GVMD) ones [Sch93,Sch93a].

80.

A hadron-like photon can also produce the equivalent of the minimum bias processes of section . Again, these can be subdivided into VMD and GVMD (anomalous) ones.

For $\gamma\mathrm{p}$ events, we believe that the best description can be obtained when three separate event classes are combined, one for direct, one for VMD and one for GVMD/anomalous events, see the detailed description in [Sch93,Sch93a]. These correspond to MSTP(14) being 0, 2 and 3, respectively. The direct component is high-$p_{\perp}$ only, while VMD and GVMD contain both high-$p_{\perp}$ and low-$p_{\perp}$ events. The option MSTP(14)=1 combines the VMD and GVMD/anomalous parts of the photon into one single resolved photon concept, which therefore is less precise than the full subdivision.

When combining three runs to obtain the totality of $\gamma\mathrm{p}$ interactions, to the best of our knowledge, it is necessary to choose the $p_{\perp}$ cut-offs with some care, so as to represent the expected total cross section.

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The direct processes by themselves only depend on the CKIN(3) cut-off of the generation. In older program versions the preferred value was 0.5 GeV [Sch93,Sch93a]. In the more recent description in [Fri00], also eikonalization of direct with anomalous interactions into the GVMD event class is considered. That is, given a branching $\gamma \to \mathrm{q}\overline{\mathrm{q}}$, direct interactions are viewed as the low-$p_{\perp}$ events and anomalous ones as high-$p_{\perp}$ events that have to merge smoothly. Then the CKIN(3) cut-off is increased to the $p_{\perp\mathrm{min}}$ of multiple interactions processes, see PARP(81) (or PARP(82), depending on minijet unitarization scheme). See MSTP(18) for a possibility to switch back to the older behaviour. However, full backwards compatibility cannot be assured, so the older scenarios are better simulated by using an older PYTHIA version.

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The VMD processes work as ordinary hadron-hadron ones, i.e. one obtains both low- and high-$p_{\perp}$ events by default, with dividing line set by $p_{\perp\mathrm{min}}$ above.

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Also the GVMD processes work like the VMD ones. Again this is a change from previous versions, where the anomalous processes only contained high-$p_{\perp}$ physics and the low-$p_{\perp}$ part was covered in the direct event class. See MSTP(15)=5 for a possibility to switch back to the older behaviour, with comments as above for the direct class. A GVMD state is book-kept as a diffractive state in the event listing, even when it scatters `elastically', since the subsequent hadronization descriptions are very similar.

The processes in points 1 and 2 can be simulated with a photon beam, i.e. when 'gamma' appears as argument in the PYINIT call. It is then necessary to use option MSTP(14) to switch between a point-like and a resolved photon -- it is not possible to simulate the two sets of processes in a single run. This would be the normal mode of operation for beamstrahlung photons, which have $Q^2 = 0$ but with a nontrivial energy spectrum that would be provided by some external routine.

For bremsstrahlung photons, the $x$ and $Q^2$ spectrum can be simulated internally, with the 'gamma/lepton' argument in the PYINIT call. This is the recommended procedure, wherein direct and resolved processes can be mixed. An older -- now not recommended -- alternative is to use a parton-inside-electron structure function concept, obtainable with a simple 'e-' (or other lepton) argument in PYINIT. To access these quark and gluon distributions inside the photon (itself inside the electron), MSTP(12)=1 must then be used. Also the default value MSTP(11)=1 is required for the preceding step, that of finding photons inside the electron. Also here the direct and resolved processes may be generated together. However, this option only works for high-$p_{\perp}$ physics. It is not possible to have also the low-$p_{\perp}$ physics (including multiple interactions in high-$p_{\perp}$ events) for an electron beam. Kindly note that subprocess 34 contains both the scattering of an electron off a photon and the scattering of a quark (inside a photon inside an electron) off a photon; the former can be switched off with the help of the KFIN array.

If you are only concerned with standard QCD physics, the option MSTP(14)=10 or the default MSTP(14)=30 gives an automatic mixture of the VMD, direct and GVMD/anomalous event classes. The mixture is properly given according to the relative cross sections. Whenever possible, this option is therefore preferable in terms of user-friendliness. However, it can only work because of a completely new layer of administration, not found anywhere else in PYTHIA. For instance, a subprocess like $\mathrm{q}\mathrm{g}\to \mathrm{q}\mathrm{g}$ is allowed in several of the classes, but appears with different sets of parton distributions and different $p_{\perp}$ cut-offs in each of these, so that it is necessary to switch gears between each event in the generation. It is therefore not possible to avoid a number of restrictions on what you can do in this case:

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The MSTP(14)=10 and =30 options can only be used for incoming photon beams, with or without convolution with the bremsstrahlung spectrum, i.e. when 'gamma' or 'gamma/lepton' is the argument in the PYINIT call.

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The machinery has only been set up to generate standard QCD physics, specifically either `minimum-bias' one or high-$p_{\perp}$ jets. There is thus no automatic mixing of processes only for heavy-flavour production, say, or of some exotic particle. For minimum bias, you are not allowed to use the CKIN variables at all. This is not a major limitation, since it is in the spirit of minimum-bias physics not to impose any constraints on allowed jet production. (If you still do, these cuts will be ineffective for the VMD processes but take effect for the other ones, giving inconsistencies.) The minimum-bias physics option is obtained by default; by switching from MSEL=1 to MSEL=2 also the elastic and diffractive components of the VMD and GVMD parts are included. High-$p_{\perp}$ jet production is obtained by setting the CKIN(3) cut-off larger than the $p_{\perp\mathrm{min}}(W^2)$ of the multiple interactions scenario. For lower input CKIN(3) values the program will automatically switch back to minimum-bias physics.

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Multiple interactions become possible in both the VMD and GVMD sector, with the average number of interactions given by the ratio of the jet to the total cross section. Currently only the simpler default scenario MSTP(82)=1 is implemented, however, i.e. the more sophisticated variable-impact-parameter ones need further physics studies and model development.

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Some variables are internally recalculated and reset, notably CKIN(3). This is because it must have values that depend on the component studied. It can therefore not be modified without changing PYINPR and recompiling the program, which obviously is a major exercise.

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Pileup events are not at all allowed.

Also, a warning about the usage of PDFLIB for photons. So long as MSTP(14)=1, i.e. the photon is not split up, PDFLIB is accessed by MSTP(56)=2 and MSTP(55) as the parton distribution set. However, when the VMD and anomalous pieces are split, the VMD part is based on a rescaling of pion distributions by VMD factors (except for the SaS sets, that already come with a separate VMD piece). Therefore, to access PDFLIB for MSTP(14)=10, it is not correct to set MSTP(56)=2 and a photon distribution in MSTP(55). Instead, one should put MSTP(56)=2, MSTP(54)=2 and a pion distribution code in MSTP(53), while MSTP(55) has no function. The anomalous part is still based on the SaS parameterization, with PARP(15) as main free parameter.

Currently, hadrons are not defined with any photonic content. None of the processes are therefore relevant in hadron-hadron collisions. In $\mathrm{e}\mathrm{p}$ collisions, the electron can emit an almost real photon, which may interact directly or be resolved. In $\mathrm{e}^+\mathrm{e}^-$ collisions, one may have direct, singly-resolved or doubly-resolved processes.

The $\gamma\gamma$ equivalent to the $\gamma\mathrm{p}$ description involves six different event classes, see section . These classes can be obtained by setting MSTP(14) to 0, 2, 3, 5, 6 and 7, respectively. If one combines the VMD and anomalous parts of the parton distributions of the photon, in a more coarse description, it is enough to use the MSTP(14) options 0, 1 and 4. The cut-off procedures follows from the ones used for the $\gamma\mathrm{p}$ ones above.

As with $\gamma\mathrm{p}$ events, the options MSTP(14)=10 or MSTP(14)=30 give a mixture of the six possible $\gamma\gamma$ event classes. The same complications and restrictions exist here as already listed above.

Process 54 generates a mixture of quark flavours; allowed flavours are set by the gluon MDME values. Process 58 can generate both quark and lepton pairs, according to the MDME values of the photon. Processes 84 and 85 are variants of these matrix elements, with fermion masses included in the matrix elements, but where only one flavour can be generated at a time. This flavour is selected as described for processes 81 and 82 in section , with the exception that for process 85 the `heaviest' flavour allowed for photon splitting takes to place of the heaviest flavour allowed for gluon splitting. Since lepton KF codes come after quark ones, they are counted as being `heavier', and thus take precedence if they have been allowed.

Process 80 is a higher twist one. The theory for such processes is rather shaky, so results should not be taken too literally. The messy formulae given in [Bag82] have not been programmed in full, instead the pion form factor has been parameterized as $Q^2 F_{\pi}(Q^2) \approx 0.55 / \ln Q^2$, with $Q$ in GeV.