<chapter name="Photoproduction"> 
 
<h2>Photoproduction</h2> 
 
<p> 
Interactions involving one or two photons, either in photon-photon or 
photon-hadron collision or photons emitted from lepton beams. 
Includes both direct and resolved contributions and also soft QCD and MPIs 
for events with resolved photons. Only (quasi-)real photons are considered 
so virtuality of the photons is restricted. The PDF set for resolved photons 
is selected in the <aloc href="PDFSelection">PDF selection</aloc>. 
This page describes some of the special features related to these collisions 
and introduces the relevant parameters. 
</p> 
 
<h3>Types of photon processes</h3> 
 
<p> 
Photons can be either resolved or act as point-like particles (direct). 
Therefore for a photon-photon interaction there are four different 
contributions, resolved-resolved, resolved-direct, direct-resolved and 
direct-direct. In case of photon-hadron collisions there are two 
contributions. With the default value of the parameter below, a mix of 
relevant contributions is generated but each process type can also be 
generated individually. Note that for photon-hadron collisions the code 
for direct contribution depends on which of the beams is photon. 
The sample main program <code>main343.cc</code> demonstrates different 
possibilities. 
</p> 
 
<modepick name="Photon:ProcessType" default="0" min="0" max="4"> 
Sets desired contribution for interactions with one or two photons. 
<option value="0"> Mix of relevant contributions below. </option> 
<option value="1"> Resolved-Resolved: Both colliding photons are 
resolved and the partonic content is given by the PDFs. Hard processes 
and non-diffractive events can be generated. </option> 
<option value="2"> Resolved-Direct: Photon A is resolved and photon B 
unresolved, i.e. act as an initiator for the hard process. Hard processes 
with a parton and a photon in the initial state can be generated. 
In case of photon-hadron collision this provides the direct contribution 
when hadron is beam A and photon beam B.</option> 
<option value="3"> Direct-Resolved: As above but now photon A is unresolved 
and photon B resolved. Direct contribution of photon-hadron when photon 
beam A.</option> 
<option value="4"> Direct-Direct: Both photons are unresolved. Hard 
processes with two photon initiators can be generated.</option> 
</modepick> 
 
<p> 
The type of the generated process can be obtained from 
<aloc href="EventInformation">Info class</aloc> with method 
<code>int Info::photonMode()</code> which follows the conventions above. 
</p> 
 
<h3>Resolved photon</h3> 
 
<p> 
Photons can either interact directly as an unresolved particle or as a 
hadronic state ("Vector Meson Dominance"). 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 <ei>gamma &rarr; q qbar</ei> splittings. 
Due to this, the PDFs are somewhat different for photons than for hadrons 
and some parts of event generation need special attention. 
</p> 
 
<h4>Process-level generation</h4> 
 
<p> 
Due to the additional term in the evolution equations the quarks in a 
resolved photon may carry a very large fraction <ei>(x~1)</ei> 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 alone, 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. 
</p> 
 
<h4>Spacelike showers</h4> 
 
<p> 
The parton showers are generated according to the DGLAP evolution equations. 
Due to the <ei>gamma &rarr; q qbar</ei> splitting in the photon evolution, 
a few modifications are needed for the ISR algorithm. 
<ul> 
<li> 
The additional term corresponds to a possibility to find the original beam 
photon during the backwards evolution, which is added to the QED part of the 
spacelike shower evolution. If this splitting happens there is no need to 
construct the beam remnants for the given beam. 
</li> 
<li> 
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 <ei>gamma &rarr; Q Qbar</ei>. 
</li> 
<li> 
As the splittings in backwards evolution increases the <ei>x</ei> 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. 
</li> 
</ul> 
</p> 
 
<h4>MPIs with photon beams</h4> 
 
<p> 
Multiparton interactions with resolved photon beams are generated as with 
hadron beams. The only difference follows again from the additional 
<ei>gamma &rarr; q qbar</ei> splittings where the beam photon becomes 
unresolved. If this splitting happens during the interleaved evolution 
for either of the photon beams no further MPIs below the branching scale 
<ei>pT</ei> are allowed since the photon is not resolved anymore. 
</p> 
 
<p> 
If there have been multiple interactions and a <ei>gamma &rarr; q qbar 
</ei> splitting occur, the kinematics of this branching are not constructed 
in the spacelike shower. Instead the <ei>pT</ei> scale of the branching is 
stored and the relevant momenta are then fixed in the beam remnant handling. 
Therefore the status codes for the partons related to this splitting 
actually refer to beam remnants. 
</p> 
 
<p> 
If there are no MPIs before the <ei>gamma &rarr; q qbar</ei> splitting, 
this splitting is constructed in the spacelike shower in the usual way, 
but the mother beam photon is not added to the event record, since a copy 
of it already exists at the top of the event record. This is unlike the 
documentation of other ISR splittings, where the mother of the branching 
is shown, but consistent with the photon not being added (a second time) 
for events that contain several MPIs. Optionally the photon can be shown, 
using the following flag. 
 
<flag name="Photon:showUnres" default="off"> 
Show the evolution steps of the beam photon in the event record, if on. 
</flag> 
</p> 
 
<p> 
Based on comparisons with charged hadron production in photon-photon 
collision data from LEP, the default MPI parametrization tuned to 
proton-(anti)proton collisions produces too much hadrons from the 
additional interactions. Such differences are not surprising, given 
that the photon is less hadron-like than the proton, e.g. with less 
well developed PDFs, leaving less room for MPIs. Therefore a different 
parametrization for <ei>pT0(eCM)</ei> is used in case of photon-photon 
collisions, where the default values are tuned to the LEP data 
(a reference to this study will be added later). By default, 
a logarithmic dependence on <ei>eCM</ei> is used. 
<note>Note:</note> These parameters override the choices made in 
<aloc href="MultipartonInteractions">Multiparton Interactions</aloc> 
when photon-photon collisions are generated. 
</p> 
 
<modepick name="PhotonPhoton:pT0parametrization" default="1" min="0" max="1"> 
Choice of <ei>pT0</ei> parametrization. See 
<aloc href="MultipartonInteractions">Multiparton Interactions</aloc> for 
further details. 
<option value="0">Power law in <ei>eCM</ei>.</option> 
<option value="1">Logarithmic in <ei>eCM</ei>.</option> 
</modepick> 
 
<parm name="PhotonPhoton:ecmRef" default="100.0" min="1."> 
The <ei>ecmRef</ei> reference energy scale. 
</parm> 
 
<parm name="PhotonPhoton:pT0Ref" default="1.52" min="0.5" max="10.0"> 
The value of <ei>pT0</ei> at the reference energy scale. 
</parm> 
 
<parm name="PhotonPhoton:ecmPow" default="0.413" min="0.0" max="0.5"> 
The <ei>ecmPow</ei> energy rescaling pace. 
</parm> 
 
<p/> 
Alternatively, or in combination, a sharp cut can be used. 
<parm name="PhotonPhoton:pTmin" default="0.2" min="0.1" 
max="10.0"> 
More details in 
<aloc href="MultipartonInteractions">Multiparton Interactions</aloc>. 
</parm> 
 
<p> 
A similar study for photon-hadron collisions will follow, current 
recommendation is to use value <ei>pT0Ref = 3.0 GeV</ei> set in 
<aloc href="MultipartonInteractions">Multiparton Interactions</aloc> page. 
</p> 
 
<p> 
The total cross section for photon-photon collisions is paramerized as in 
<ref>Sch97</ref>. Approximate diffractive cross sections have been defined 
according to the assumed VMD contribution. 
</p> 
 
<h4>Beam Remnants</h4> 
 
<p> 
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 <ei>gamma &rarr; q qbar</ei> 
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 the valence content. 
</p> 
 
<p> 
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: 
<ul> 
<li> 
Remnants need to be constructed for both beams. 
</li> 
<li> 
Remnants are constructed only for one side. 
</li> 
<li> 
No need for remnants on either side. 
</li> 
</ul> 
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 <ei>kT</ei> are constructed similarly as for normal hadronic 
interactions <ref>Sjo04</ref>. 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. 
</p> 
 
<p> 
Since the primordial <ei>kT</ei> 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 <ei>kT</ei> is added, so the kinematics can not be 
constructed. In this case new values for <ei>kT</ei> 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. The inclusion 
of additional MPIs increases the invariant mass of the remnants and takes 
more momentum from the beam particles. Even though the MPIs that would 
not leave enough room for the remnants are rejected, these can still lead 
to a situation where the kinematics cannot be constructed due to the added 
primordial <ei>kT</ei>. This may cause some amount of errors especially when 
the invariant mass of <ei>gamma-gamma</ei> system is small. 
</p> 
 
<h3>Photons from lepton or hadron beams</h3> 
 
<p> 
Interaction of photons from leptons, including photon-photon interactions in 
lepton-lepton collisions and photon-hadron ones in lepton-hadron collisions, 
can be set up as described in 
<aloc href="PDFSelection">PDF selection</aloc>. It is also possible to 
consider photons from proton beams. Since the current 
framework can handle only (quasi-)real photons, an upper limit needs to be set 
for the photon virtuality. This can be done with the parameter 
<code>Photon:Q2max</code>. The upper virtuality limit will also set 
the upper limit for the <ei>k_T</ei> of the photon, which in turn will 
be the same as the <ei>k_T</ei> of the scattered lepton. Also some other 
cuts can be imposed. 
 
<parm name="Photon:Q2max" default="1.0" max="2.0"> 
Upper limit for (quasi-)real photon virtuality in <ei>GeV^2</ei>. Too low a 
value might cause problems, e.g. if the lower <ei>Q^2</ei> limit derived from 
kinematics becomes larger than the upper limit. 
</parm> 
 
<parm name="Photon:Wmin" default="10.0" min="5.0"> 
Lower limit for invariant mass of <ei>gamma-gamma</ei> or 
<ei>photon-hadron</ei> system in <ei>GeV</ei>. 
</parm> 
 
<parm name="Photon:Wmax" default="-1.0"> 
Upper limit for invariant mass of <ei>gamma-gamma</ei> 
(<ei>gamma-hadron</ei>) system in <ei>GeV</ei>. 
A value below <code>Photon:Wmin</code> means that the invariant mass of 
the original system (<ei>lepton+lepton</ei>, <ei>lepton+hadron</ei> or 
<ei>hadron+hadron</ei>) is used as an upper limit. 
</parm> 
 
<parm name="Photon:thetaAMax" default="-1.0" max="3.141593"> 
Upper limit for scattering angle of scattered beam particle on side A 
in <ei>rad</ei>. A negative value means that no cut is applied. Since 
<ei>k_T</ei> depends on the virtuality of the emitted photon, the 
<code>Photon:Q2max</code> cut is usually more restrictive unless a 
very small angle is used. This cut is only applied when the colliding 
beams are defined in their CM frame 
(<code>Beams:frameType=1</code>). Furthermore, in case of <ei>2 &rarr; 
1</ei> processes with unresolved photons, the scattered beam particle 
kinematics is modified later in the event generation, to keep the mass 
of the intermediate particle intact, so an accurate rejection can be 
obtained only based on the final momenta of the scattered beam 
particles in the event record. 
</parm> 
 
<parm name="Photon:thetaBMax" default="-1.0" max="3.141593"> 
As above but for side B. 
</parm> 
 
<flag name="Photon:sampleQ2" default="on"> 
Determines whether the sampling for the photon virtuality is done. This has 
to be used when and <ei>Q^2</ei>-integrated photon flux is used. In this case 
the virtuality and the transverse momentum of the photon (and the recoiling 
particle) is set to zero, which strictly speaking is kinematically impossible. 
The error here is very small for the cases where the virtualities 
are negligible, however (e.g. photons from heavy ions).</flag> 
</p> 
 
<h4>MPIs with photons</h4> 
 
<p> 
The invariant mass of a <ei>gamma-gamma</ei> or <ei>gamma-hadron</ei> system 
from lepton or hadron beams will vary. Therefore, to generate MPIs and 
non-diffractive events in <ei>gamma-gamma</ei> and <ei>gamma-hadron</ei> 
collisions, the MPI framework is initialized with several 
values of <ei>W</ei> from <code>Photon:Wmin</code> to 
<code>Photon:Wmax</code>. The parameter values are then interpolated 
for the sampled <ei>W</ei>. 
</p> 
 
</chapter> 
 
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