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-
-<h2>Multiparton Interactions</h2>
-
-The starting point for the multiparton interactions physics scenario in
-PYTHIA is provided by [<a href="Bibliography.php" target="page">Sjo87</a>]. Recent developments have
-included a more careful study of flavour and colour correlations,
-junction topologies and the relationship to beam remnants
-[<a href="Bibliography.php" target="page">Sjo04</a>], interleaving with initial-state radiation
-[<a href="Bibliography.php" target="page">Sjo05</a>], making use of transverse-momentum-ordered
-initial- and final-state showers, with the extension to fully
-interleaved evolution covered in [<a href="Bibliography.php" target="page">Cor10a</a>]. A framework to
-handle rescattering is described in [<a href="Bibliography.php" target="page">Cor09</a>].
-
-<p/>
-A big unsolved issue is how the colour of all these subsystems is
-correlated. For sure there is a correlation coming from the colour
-singlet nature of the incoming beams, but in addition final-state
-colour rearrangements may change the picture. Indeed such extra
-effects appear necessary to describe data, e.g. on
-<i><pT>(n_ch)</i>. A simple implementation of colour
-rearrangement is found as part of the
-<?php $filepath = $_GET["filepath"];
-echo "<a href='BeamRemnants.php?filepath=".$filepath."' target='page'>";?>beam remnants</a> description.
-
-<h3>Main variables</h3>
-
-<h4>Matching to hard process</h4>
-
-The maximum <i>pT</i> to be allowed for multiparton interactions is
-related to the nature of the hard process itself. It involves a
-delicate balance between not doublecounting and not leaving any
-gaps in the coverage. The best procedure may depend on information
-only the user has: how the events were generated and mixed (e.g. with
-Les Houches Accord external input), and how they are intended to be
-used. Therefore a few options are available, with a sensible default
-behaviour.
-<br/><br/><table><tr><td><strong>MultipartonInteractions:pTmaxMatch </td><td> (<code>default = <strong>0</strong></code>; <code>minimum = 0</code>; <code>maximum = 2</code>)</td></tr></table>
-Way in which the maximum scale for multiparton interactions is set
-to match the scale of the hard process itself.
-<br/>
-<input type="radio" name="1" value="0" checked="checked"><strong>0 </strong>: <b>(i)</b> if the final state of the hard process (not counting subsequent resonance decays) contains only quarks (<ei>u, d, s, c ,b</ei>), gluons and photons then <ei>pT_max</ei> is chosen to be the factorization scale for internal processes and the <code>scale</code> value for Les Houches input; <b>(ii)</b> if not, interactions are allowed to go all the way up to the kinematical limit. The reasoning is that the former kind of processes are generated by the multiparton-interactions machinery and so would doublecount hard processes if allowed to overlap the same <ei>pT</ei> range, while no such danger exists in the latter case. <br/>
-<input type="radio" name="1" value="1"><strong>1 </strong>: always use the factorization scale for an internal process and the <code>scale</code> value for Les Houches input, i.e. the lower value. This should avoid doublecounting, but may leave out some interactions that ought to have been simulated. <br/>
-<input type="radio" name="1" value="2"><strong>2 </strong>: always allow multiparton interactions up to the kinematical limit. This will simulate all possible event topologies, but may lead to doublecounting. <br/>
-
-<h4>Cross-section parameters</h4>
-
-The rate of interactions is determined by
-<br/><br/><table><tr><td><strong>MultipartonInteractions:alphaSvalue </td><td></td><td> <input type="text" name="2" value="0.127" size="20"/> (<code>default = <strong>0.127</strong></code>; <code>minimum = 0.06</code>; <code>maximum = 0.25</code>)</td></tr></table>
-The value of <i>alpha_strong</i> at <i>m_Z</i>. Default value is
-picked equal to the one used in CTEQ 5L.
-
-
-<p/>
-The actual value is then regulated by the running to the scale
-<i>pT^2</i>, at which it is evaluated
-<br/><br/><table><tr><td><strong>MultipartonInteractions:alphaSorder </td><td> (<code>default = <strong>1</strong></code>; <code>minimum = 0</code>; <code>maximum = 2</code>)</td></tr></table>
-The order at which <ei>alpha_strong</ei> runs at scales away from
-<ei>m_Z</ei>.
-<br/>
-<input type="radio" name="3" value="0"><strong>0 </strong>: zeroth order, i.e. <ei>alpha_strong</ei> is kept fixed.<br/>
-<input type="radio" name="3" value="1" checked="checked"><strong>1 </strong>: first order, which is the normal value.<br/>
-<input type="radio" name="3" value="2"><strong>2 </strong>: second order. Since other parts of the code do not go to second order there is no strong reason to use this option, but there is also nothing wrong with it.<br/>
-
-<p/>
-QED interactions are regulated by the <i>alpha_electromagnetic</i>
-value at the <i>pT^2</i> scale of an interaction.
-
-<br/><br/><table><tr><td><strong>MultipartonInteractions:alphaEMorder </td><td> (<code>default = <strong>1</strong></code>; <code>minimum = -1</code>; <code>maximum = 1</code>)</td></tr></table>
-The running of <ei>alpha_em</ei> used in hard processes.
-<br/>
-<input type="radio" name="4" value="1" checked="checked"><strong>1 </strong>: first-order running, constrained to agree with <code>StandardModel:alphaEMmZ</code> at the <ei>Z^0</ei> mass. <br/>
-<input type="radio" name="4" value="0"><strong>0 </strong>: zeroth order, i.e. <ei>alpha_em</ei> is kept fixed at its value at vanishing momentum transfer.<br/>
-<input type="radio" name="4" value="-1"><strong>-1 </strong>: zeroth order, i.e. <ei>alpha_em</ei> is kept fixed, but at <code>StandardModel:alphaEMmZ</code>, i.e. its value at the <ei>Z^0</ei> mass. <br/>
-
-<p/>
-Note that the choices of <i>alpha_strong</i> and <i>alpha_em</i>
-made here override the ones implemented in the normal process machinery,
-but only for the interactions generated by the
-<code>MultipartonInteractions</code> class.
-
-<p/>
-In addition there is the possibility of a global rescaling of
-cross sections (which could not easily be accommodated by a
-changed <i>alpha_strong</i>, since <i>alpha_strong</i> runs)
-<br/><br/><table><tr><td><strong>MultipartonInteractions:Kfactor </td><td></td><td> <input type="text" name="5" value="1.0" size="20"/> (<code>default = <strong>1.0</strong></code>; <code>minimum = 0.5</code>; <code>maximum = 4.0</code>)</td></tr></table>
-Multiply all cross sections by this fix factor.
-
-
-<p/>
-The processes used to generate multiparton interactions form a subset
-of the standard library of hard processes. The input is slightly
-different from the standard hard-process machinery, however,
-since incoming flavours, the <i>alpha_strong</i> value and most
-of the kinematics are aready fixed when the process is called.
-It is possible to regulate the set of processes that are included in the
-multiparton-interactions framework.
-
-<br/><br/><table><tr><td><strong>MultipartonInteractions:processLevel </td><td> (<code>default = <strong>3</strong></code>; <code>minimum = 0</code>; <code>maximum = 3</code>)</td></tr></table>
-Set of processes included in the machinery.
-<br/>
-<input type="radio" name="6" value="0"><strong>0 </strong>: only the simplest <ei>2 -> 2</ei> QCD processes between quarks and gluons, giving no new flavours, i.e. dominated by <ei>t</ei>-channel gluon exchange.<br/>
-<input type="radio" name="6" value="1"><strong>1 </strong>: also <ei>2 -> 2</ei> QCD processes giving new flavours (including charm and bottom), i.e. proceeding through <ei>s</ei>-channel gluon exchange.<br/>
-<input type="radio" name="6" value="2"><strong>2 </strong>: also <ei>2 -> 2</ei> processes involving one or two photons in the final state, <ei>s</ei>-channel <ei>gamma</ei> boson exchange and <ei>t</ei>-channel <ei>gamma/Z^0/W^+-</ei> boson exchange.<br/>
-<input type="radio" name="6" value="3" checked="checked"><strong>3 </strong>: also charmonium and bottomonium production, via colour singlet and colour octet channels.<br/>
-
-<h4>Cross-section regularization</h4>
-
-There are two complementary ways of regularizing the small-<i>pT</i>
-divergence, a sharp cutoff and a smooth dampening. These can be
-combined as desired, but it makes sense to coordinate with how the
-same issue is handled in <?php $filepath = $_GET["filepath"];
-echo "<a href='SpacelikeShowers.php?filepath=".$filepath."' target='page'>";?>spacelike
-showers</a>. Actually, by default, the parameters defined here are
-used also for the spacelike showers, but this can be overridden.
-
-<p/>
-Regularization of the divergence of the QCD cross section for
-<i>pT -> 0</i> is obtained by a factor <i>pT^4 / (pT0^2 + pT^2)^2</i>,
-and by using an <i>alpha_s(pT0^2 + pT^2)</i>. An energy dependence
-of the <i>pT0</i> choice is introduced by two further parameters,
-so that <i>pT0Ref</i> is the <i>pT0</i> value for the reference
-CM energy, <i>pT0Ref = pT0(ecmRef)</i>.
-<br/><b>Warning:</b> if a large <i>pT0</i> is picked for multiparton
-interactions, such that the integrated interaction cross section is
-below the nondiffractive inelastic one, this <i>pT0</i> will
-automatically be scaled down to cope.
-
-<p/>
-The actual <i>pT0</i> parameter used at a given CM energy scale,
-<i>ecmNow</i>, is obtained as
-<br/><i>
- pT0 = pT0(ecmNow) = pT0Ref * (ecmNow / ecmRef)^ecmPow
-</i><br/>
-where <i>pT0Ref</i>, <i>ecmRef</i> and <i>ecmPow</i> are the
-three parameters below.
-
-<br/><br/><table><tr><td><strong>MultipartonInteractions:pT0Ref </td><td></td><td> <input type="text" name="7" value="2.15" size="20"/> (<code>default = <strong>2.15</strong></code>; <code>minimum = 0.5</code>; <code>maximum = 10.0</code>)</td></tr></table>
-The <i>pT0Ref</i> scale in the above formula.
-<br/><b>Note:</b> <i>pT0Ref</i> is one of the key parameters in a
-complete PYTHIA tune. Its value is intimately tied to a number of other
-choices, such as that of colour flow description, so unfortunately it is
-difficult to give an independent meaning to <i>pT0Ref</i>.
-
-
-<br/><br/><table><tr><td><strong>MultipartonInteractions:ecmRef </td><td></td><td> <input type="text" name="8" value="1800.0" size="20"/> (<code>default = <strong>1800.0</strong></code>; <code>minimum = 1.</code>)</td></tr></table>
-The <i>ecmRef</i> reference energy scale introduced above.
-
-
-<br/><br/><table><tr><td><strong>MultipartonInteractions:ecmPow </td><td></td><td> <input type="text" name="9" value="0.24" size="20"/> (<code>default = <strong>0.24</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 0.5</code>)</td></tr></table>
-The <i>ecmPow</i> energy rescaling pace introduced above.
-
-
-<p/>
-Alternatively, or in combination, a sharp cut can be used.
-<br/><br/><table><tr><td><strong>MultipartonInteractions:pTmin </td><td></td><td> <input type="text" name="10" value="0.2" size="20"/> (<code>default = <strong>0.2</strong></code>; <code>minimum = 0.1</code>; <code>maximum = 10.0</code>)</td></tr></table>
-Lower cutoff in <i>pT</i>, below which no further interactions
-are allowed. Normally <i>pT0</i> above would be used to provide
-the main regularization of the cross section for <i>pT -> 0</i>,
-in which case <i>pTmin</i> is used mainly for technical reasons.
-It is possible, however, to set <i>pT0Ref = 0</i> and use
-<i>pTmin</i> to provide a step-function regularization, or to
-combine them in intermediate approaches. Currently <i>pTmin</i>
-is taken to be energy-independent.
-
-
-<p/>
-Gösta Gustafson has proposed (private communication, unpublished)
-that the amount of screening, as encapsulated in the <i>pT0</i>
-parameter, fluctuates from one event to the next. Specifically,
-high-activity event are more likely to lead to interactions at large
-<i>pT</i> scales, but the high activity simultaneously leads to a
-larger screening of interactions at smaller <i>pT</i>. Such a scenario
-can approximately be simulated by scaling up the <i>pT0</i> by a
-factor <i>sqrt(n)</i>, where <i>n</i> is the number of interactions
-considered so far, including the current one. That is, for the first
-interaction the dampening factor is <i>pT^4 / (pT0^2 + pT^2)^2</i>,
-for the second <i>pT^4 / (2 pT0^2 + pT^2)^2</i>, for the third
-<i>pT^4 / (3 pT0^2 + pT^2)^2</i>, and so on. Optionally the scheme
-may also be applied to ISR emissions. For simplicity the same
-<i>alpha_s(pT0^2 + pT^2)</i> is used throughout. Note that, in this
-scenario the <i>pT0</i> scale must be lower than in the normal case
-to begin with, since it later is increased back up. Also note that the
-idea with this scenario is to propose an alternative to colour
-reconnection to understand the rise of <i><pT>(n_ch)</i>,
-so that the amount of colour reconnection should be reduced.
-<br/><br/><table><tr><td><strong>MultipartonInteractions:enhanceScreening </td><td> (<code>default = <strong>0</strong></code>; <code>minimum = 0</code>; <code>maximum = 2</code>)</td></tr></table>
-Choice to activate the above screening scenario, i.e. an increasing
-effective <ei>pT0</ei> for consecutive interactions.
-<br/>
-<input type="radio" name="11" value="0" checked="checked"><strong>0 </strong>: No activity-dependent screening, i.e. <ei>pT0</ei> is fixed.<br/>
-<input type="radio" name="11" value="1"><strong>1 </strong>: The <ei>pT0</ei> scale is increased as a function of the number of MPI's, as explained above. ISR is not affected, but note that, if <code>SpaceShower:samePTasMPI</code> is on, then <code>MultipartonInteractions:pT0Ref</code> is used also for ISR, which may or may not be desirable. <br/>
-<input type="radio" name="11" value="2"><strong>2 </strong>: Both MPI and ISR influence and are influenced by the screening. That is, the dampening is reduced based on the total number of MPI and ISR steps considered so far, including the current one. This dampening is implemented both for MPI and for ISR emissions, for the latter provided that <code>SpaceShower:samePTasMPI</code> is on (default). <br/>
-
-<h4>Impact-parameter dependence</h4>
-
-The choice of impact-parameter dependence is regulated by several
-parameters. The ones listed here refer to nondiffractive topologies
-only, while their equivalents for diffractive events are put in the
-<?php $filepath = $_GET["filepath"];
-echo "<a href='Diffraction.php?filepath=".$filepath."' target='page'>";?>Diffraction</a> description. Note that
-there is currently no <code>bProfile = 4</code> option for diffraction.
-Other parameters are assumed to agree between diffractive and
-nondiffractive topologies.
-
-<br/><br/><table><tr><td><strong>MultipartonInteractions:bProfile </td><td> (<code>default = <strong>1</strong></code>; <code>minimum = 0</code>; <code>maximum = 4</code>)</td></tr></table>
-Choice of impact parameter profile for the incoming hadron beams.
-<br/>
-<input type="radio" name="12" value="0"><strong>0 </strong>: no impact parameter dependence at all.<br/>
-<input type="radio" name="12" value="1" checked="checked"><strong>1 </strong>: a simple Gaussian matter distribution; no free parameters.<br/>
-<input type="radio" name="12" value="2"><strong>2 </strong>: a double Gaussian matter distribution, with the two free parameters <ei>coreRadius</ei> and <ei>coreFraction</ei>.<br/>
-<input type="radio" name="12" value="3"><strong>3 </strong>: an overlap function, i.e. the convolution of the matter distributions of the two incoming hadrons, of the form <ei>exp(- b^expPow)</ei>, where <ei>expPow</ei> is a free parameter.<br/>
-<input type="radio" name="12" value="4"><strong>4 </strong>: a Gaussian matter distribution with a width that varies according to the selected <ei>x</ei> value of an interaction, <ei>1. + a1 log (1 / x)</ei>, where <ei>a1</ei> is a free parameter. Note that once <ei>b</ei> has been selected for the hard process, it remains fixed for the remainder of the evolution. <br/>
-
-<br/><br/><table><tr><td><strong>MultipartonInteractions:coreRadius </td><td></td><td> <input type="text" name="13" value="0.4" size="20"/> (<code>default = <strong>0.4</strong></code>; <code>minimum = 0.1</code>; <code>maximum = 1.</code>)</td></tr></table>
-When assuming a double Gaussian matter profile, <i>bProfile = 2</i>,
-the inner core is assumed to have a radius that is a factor
-<i>coreRadius</i> smaller than the rest.
-
-
-<br/><br/><table><tr><td><strong>MultipartonInteractions:coreFraction </td><td></td><td> <input type="text" name="14" value="0.5" size="20"/> (<code>default = <strong>0.5</strong></code>; <code>minimum = 0.</code>; <code>maximum = 1.</code>)</td></tr></table>
-When assuming a double Gaussian matter profile, <i>bProfile = 2</i>,
-the inner core is assumed to have a fraction <i>coreFraction</i>
-of the matter content of the hadron.
-
-
-<br/><br/><table><tr><td><strong>MultipartonInteractions:expPow </td><td></td><td> <input type="text" name="15" value="1." size="20"/> (<code>default = <strong>1.</strong></code>; <code>minimum = 0.4</code>; <code>maximum = 10.</code>)</td></tr></table>
-When <i>bProfile = 3</i> it gives the power of the assumed overlap
-shape <i>exp(- b^expPow)</i>. Default corresponds to a simple
-exponential drop, which is not too dissimilar from the overlap
-obtained with the standard double Gaussian parameters. For
-<i>expPow = 2</i> we reduce to the simple Gaussian, <i>bProfile = 1</i>,
-and for <i>expPow -> infinity</i> to no impact parameter dependence
-at all, <i>bProfile = 0</i>. For small <i>expPow</i> the program
-becomes slow and unstable, so the min limit must be respected.
-
-
-<br/><br/><table><tr><td><strong>MultipartonInteractions:a1 </td><td></td><td> <input type="text" name="16" value="0.15" size="20"/> (<code>default = <strong>0.15</strong></code>; <code>minimum = 0.</code>; <code>maximum = 2.</code>)</td></tr></table>
-When <i>bProfile = 4</i>, this gives the <i>a1</i> constant in the
-Gaussian width. When <i>a1 = 0.</i>, this reduces back to the single
-Gaussian case.
-
-
-<h4>Rescattering</h4>
-
-It is possible that a parton may rescatter, i.e. undergo a further
-interaction subsequent to the first one. The machinery to model this
-kind of physics has only recently become fully operational
-[<a href="Bibliography.php" target="page">Cor09</a>], and is therefore not yet so well explored.
-
-<p/>
-The rescatting framework has ties with other parts of the program,
-notably with the <?php $filepath = $_GET["filepath"];
-echo "<a href='BeamRemnants.php?filepath=".$filepath."' target='page'>";?>beam remnants</a>.
-
-<br/><br/><strong>MultipartonInteractions:allowRescatter</strong> <input type="radio" name="17" value="on"><strong>On</strong>
-<input type="radio" name="17" value="off" checked="checked"><strong>Off</strong>
- (<code>default = <strong>off</strong></code>)<br/>
-Switch to allow rescattering of partons; on/off = true/false.<br/>
-<b>Note:</b> the rescattering framework has not yet been implemented
-for the <code>MultipartonInteractions:bProfile = 4</code> option,
-and can therefore not be switched on in that case.
-<b>Warning:</b> use with caution since machinery is still not
-so well tested.
-
-
-<br/><br/><strong>MultipartonInteractions:allowDoubleRescatter</strong> <input type="radio" name="18" value="on"><strong>On</strong>
-<input type="radio" name="18" value="off" checked="checked"><strong>Off</strong>
- (<code>default = <strong>off</strong></code>)<br/>
-Switch to allow rescattering of partons, where both incoming partons
-have already rescattered; on/off = true/false. Is only used if
-<code>MultipartonInteractions:allowRescatter</code> is switched on.<br/>
-<b>Warning:</b> currently there is no complete implementation that
-combines it with shower evolution, so you must use
-<code>PartonLevel:ISR = off</code> and <code>PartonLevel:FSR = off</code>.
-If not, a warning will be issued and double rescattering will not be
-simulated. The rate also comes out to be much lower than for single
-rescattering, so to first approximation it can be neglected.
-
-
-<br/><br/><table><tr><td><strong>MultipartonInteractions:rescatterMode </td><td> (<code>default = <strong>0</strong></code>; <code>minimum = 0</code>; <code>maximum = 4</code>)</td></tr></table>
-Selection of which partons rescatter against unscattered partons
-from the incoming beams A and B, based on their rapidity value
-<ei>y</ei> in the collision rest frame. Here <ei>ySep</ei> is
-shorthand for <code>MultipartonInteractions:ySepRescatter</code> and
-<ei>deltaY</ei> for <code>MultipartonInteractions:deltaYRescatter</code>,
-defined below. The description is symmetric between the two beams,
-so only one case is described below.
-<br/>
-<input type="radio" name="19" value="0" checked="checked"><strong>0 </strong>: only scattered partons with <ei>y > 0</ei> can collide with unscattered partons from beam B.<br/>
-<input type="radio" name="19" value="1"><strong>1 </strong>: only scattered partons with <ei>y > ySep</ei> can collide with unscattered partons from beam B.<br/>
-<input type="radio" name="19" value="2"><strong>2 </strong>: the probability for a scattered parton to be considered as a potential rescatterer against unscattered partons in beam B increases linearly from zero at <ei>y = ySep - deltaY</ei> to unity at <ei>y = ySep + deltaY</ei>.<br/>
-<input type="radio" name="19" value="3"><strong>3 </strong>: the probability for a scattered parton to be considered as a potential rescatterer against unscattered partons in beam B increases with <ei>y</ei> according to <ei>(1/2) * (1 + tanh( (y - ySep) / deltaY))</ei>.<br/>
-<input type="radio" name="19" value="4"><strong>4 </strong>: all partons are potential rescatterers against both beams.<br/>
-
-<br/><br/><table><tr><td><strong>MultipartonInteractions:ySepRescatter </td><td></td><td> <input type="text" name="20" value="0." size="20"/> (<code>default = <strong>0.</strong></code>)</td></tr></table>
-used for some of the <code>MultipartonInteractions:rescatterMode</code>
-options above, as the rapidity for which a scattered parton has a 50%
-probability to be considered as a potential rescatterer.
-A <i>ySep > 0</i> generally implies that some central partons cannot
-rescatter at all, while a <i>ySep < 0</i> instead allows central
-partons to scatter against either beam.
-
-
-<br/><br/><table><tr><td><strong>MultipartonInteractions:deltaYRescatter </td><td></td><td> <input type="text" name="21" value="1." size="20"/> (<code>default = <strong>1.</strong></code>; <code>minimum = 0.1</code>)</td></tr></table>
-used for some of the <code>MultipartonInteractions:rescatterMode</code>
-options above, as the width of the rapidity transition region, where the
-probability rises from zero to unity that a scattered parton is considered
-as a potential rescatterer.
-
-
-
-<h3>Further variables</h3>
-
-These should normally not be touched. Their only function is for
-cross-checks.
-
-<br/><br/><table><tr><td><strong>MultipartonInteractions:nQuarkIn </td><td></td><td> <input type="text" name="22" value="5" size="20"/> (<code>default = <strong>5</strong></code>; <code>minimum = 0</code>; <code>maximum = 5</code>)</td></tr></table>
-Number of allowed incoming quark flavours in the beams; a change
-to 4 would thus exclude <i>b</i> and <i>bbar</i> as incoming
-partons, etc.
-
-
-<br/><br/><table><tr><td><strong>MultipartonInteractions:nSample </td><td></td><td> <input type="text" name="23" value="1000" size="20"/> (<code>default = <strong>1000</strong></code>; <code>minimum = 100</code>)</td></tr></table>
-The allowed <i>pT</i> range is split (unevenly) into 100 bins,
-and in each of these the interaction cross section is evaluated in
-<i>nSample</i> random phase space points. The full integral is used
-at initialization, and the differential one during the run as a
-"Sudakov form factor" for the choice of the hardest interaction.
-A larger number implies increased accuracy of the calculations.
-
-
-<h3>Technical notes</h3>
-
-Relative to the articles mentioned above, not much has happened.
-The main news is a technical one, that the phase space of the
-<i>2 -> 2</i> (massless) QCD processes is now sampled in
-<i>dy_3 dy_4 dpT^2</i>, where <i>y_3</i> and <i>y_4</i> are
-the rapidities of the two produced partons. One can show that
-<br/><i>
- (dx_1 / x_1) * (dx_2 / x_2) * d(tHat) = dy_3 * dy_4 * dpT^2
-</i><br/>
-Furthermore, since cross sections are dominated by the "Rutherford"
-one of <i>t</i>-channel gluon exchange, which is enhanced by a
-factor of 9/4 for each incoming gluon, effective structure functions
-are defined as
-<br/><i>
- F(x, pT2) = (9/4) * xg(x, pT2) + sum_i xq_i(x, pT2)
-</i><br/>
-With this technical shift of factors 9/4 from cross sections to parton
-densities, a common upper estimate of
-<br/><i>
- d(sigmaHat)/d(pT2) < pi * alpha_strong^2 / pT^4
-</i><br/>
-is obtained.
-
-<p/>
-In fact this estimate can be reduced by a factor of 1/2 for the
-following reason: for any configuration <i>(y_3, y_4, pT2)</i> also
-one with <i>(y_4, y_3, pT2)</i> lies in the phase space. Not both
-of those can enjoy being enhanced by the <i>tHat -> 0</i>
-singularity of
-<br/><i>
- d(sigmaHat) propto 1/tHat^2.
-</i><br/>
-Or if they are, which is possible with identical partons like
-<i>q q -> q q</i> and <i>g g -> g g</i>, each singularity comes
-with half the strength. So, when integrating/averaging over the two
-configurations, the estimated <i>d(sigmaHat)/d(pT2)</i> drops.
-Actually, it drops even further, since the naive estimate above is
-based on
-<br/><i>
- (4 /9) * (1 + (uHat/sHat)^2) < 8/9 < 1
-</i><br/>
-The 8/9 value would be approached for <i>tHat -> 0</i>, which
-implies <i>sHat >> pT2</i> and thus a heavy parton-distribution
-penalty, while parton distributions are largest for
-<i>tHat = uHat = -sHat/2</i>, where the above expression
-evaluates to 5/9. A fudge factor is therefore introduced to go the
-final step, so it can easily be modifed when further non-Rutherford
-processes are added, or should parton distributions change significantly.
-
-<p/>
-At initialization, it is assumed that
-<br/><i>
- d(sigma)/d(pT2) < d(sigmaHat)/d(pT2) * F(x_T, pT2) * F(x_T, pT2)
- * (2 y_max(pT))^2
-</i><br/>
-where the first factor is the upper estimate as above, the second two
-the parton density sum evaluated at <i>y_3 = y_ 4 = 0</i> so that
-<i>x_1 = x_2 = x_T = 2 pT / E_cm</i>, where the product is expected
-to be maximal, and the final is the phase space for
-<i>-y_max < y_{3,4} < y_max</i>.
-The right-hand side expression is scanned logarithmically in <i>y</i>,
-and a <i>N</i> is determined such that it always is below
-<i>N/pT^4</i>.
-
-<p/>
-To describe the dampening of the cross section at <i>pT -> 0</i> by
-colour screening, the actual cross section is multiplied by a
-regularization factor <i>(pT^2 / (pT^2 + pT0^2))^2</i>, and the
-<i>alpha_s</i> is evaluated at a scale <i>pT^2 + pT0^2</i>,
-where <i>pT0</i> is a free parameter of the order of 2 - 4 GeV.
-Since <i>pT0</i> can be energy-dependent, an ansatz
-<br/><i>
- pT0(ecm) = pT0Ref * (ecm/ecmRef)^ecmPow
-</i><br/>
-is used, where <i>ecm</i> is the current CM frame energy,
-<i>ecmRef</i> is an arbitrary reference energy where <i>pT0Ref</i>
-is defined, and <i>ecmPow</i> gives the energy rescaling pace. For
-technical reasons, also an absolute lower <i>pT</i> scale <i>pTmin</i>,
-by default 0.2 GeV, is introduced. In principle, it is possible to
-recover older scenarios with a sharp <i>pT</i> cutoff by setting
-<i>pT0 = 0</i> and letting <i>pTmin</i> be a larger number.
-
-<p/>
-The above scanning strategy is then slightly modified: instead of
-an upper estimate <i>N/pT^4</i> one of the form
-<i>N/(pT^2 + r * pT0^2)^2</i> is used. At first glance, <i>r = 1</i>
-would seem to be fixed by the form of the regularization procedure,
-but this does not take into account the nontrivial dependence on
-<i>alpha_s</i>, parton distributions and phase space. A better
-Monte Carlo efficiency is obtained for <i>r</i> somewhat below unity,
-and currently <i>r = 0.25</i> is hardcoded.
-
-In the generation a trial <i>pT2</i> is then selected according to
-<br/><i>
- d(Prob)/d(pT2) = (1/sigma_ND) * N/(pT^2 + r * pT0^2)^2 * ("Sudakov")
-</i><br/>
-For the trial <i>pT2</i>, a <i>y_3</i> and a <i>y_4</i> are then
-selected, and incoming flavours according to the respective
-<i>F(x_i, pT2)</i>, and then the cross section is evaluated for this
-flavour combination. The ratio of trial/upper estimate gives the
-probability of survival.
-
-<p/>
-Actually, to profit from the factor 1/2 mentioned above, the cross
-section for the combination with <i>y_3</i> and <i>y_4</i>
-interchanged is also tried, which corresponds to exchanging <i>tHat</i>
-and <i>uHat</i>, and the average formed, while the final kinematics
-is given by the relative importance of the two.
-
-<p/>
-Furthermore, since large <i>y</i> values are disfavoured by dropping
-PDF's, a factor
-<br/><i>
- WT_y = (1 - (y_3/y_max)^2) * (1 - (y_4/y_max)^2)
-</i><br/>
-is evaluated, and used as a survival probability before the more
-time-consuming PDF+ME evaluation, with surviving events given a
-compensating weight <i>1/WT_y</i>.
-
-<p/>
-An impact-parameter dependencs is also allowed. Based on the hard
-<i>pT</i> scale of the first interaction, and enhancement/depletion
-factor is picked, which multiplies the rate of subsequent interactions.
-
-<p/>
-Parton densities are rescaled and modified to take into account the
-energy-momentum and flavours kicked out by already-considered
-interactions.
-
-<input type="hidden" name="saved" value="1"/>
-
-<?php
-echo "<input type='hidden' name='filepath' value='".$_GET["filepath"]."'/>"?>
-
-<table width="100%"><tr><td align="right"><input type="submit" value="Save Settings" /></td></tr></table>
-</form>
-
-<?php
-
-if($_POST["saved"] == 1)
-{
-$filepath = $_POST["filepath"];
-$handle = fopen($filepath, 'a');
-
-if($_POST["1"] != "0")
-{
-$data = "MultipartonInteractions:pTmaxMatch = ".$_POST["1"]."\n";
-fwrite($handle,$data);
-}
-if($_POST["2"] != "0.127")
-{
-$data = "MultipartonInteractions:alphaSvalue = ".$_POST["2"]."\n";
-fwrite($handle,$data);
-}
-if($_POST["3"] != "1")
-{
-$data = "MultipartonInteractions:alphaSorder = ".$_POST["3"]."\n";
-fwrite($handle,$data);
-}
-if($_POST["4"] != "1")
-{
-$data = "MultipartonInteractions:alphaEMorder = ".$_POST["4"]."\n";
-fwrite($handle,$data);
-}
-if($_POST["5"] != "1.0")
-{
-$data = "MultipartonInteractions:Kfactor = ".$_POST["5"]."\n";
-fwrite($handle,$data);
-}
-if($_POST["6"] != "3")
-{
-$data = "MultipartonInteractions:processLevel = ".$_POST["6"]."\n";
-fwrite($handle,$data);
-}
-if($_POST["7"] != "2.15")
-{
-$data = "MultipartonInteractions:pT0Ref = ".$_POST["7"]."\n";
-fwrite($handle,$data);
-}
-if($_POST["8"] != "1800.0")
-{
-$data = "MultipartonInteractions:ecmRef = ".$_POST["8"]."\n";
-fwrite($handle,$data);
-}
-if($_POST["9"] != "0.24")
-{
-$data = "MultipartonInteractions:ecmPow = ".$_POST["9"]."\n";
-fwrite($handle,$data);
-}
-if($_POST["10"] != "0.2")
-{
-$data = "MultipartonInteractions:pTmin = ".$_POST["10"]."\n";
-fwrite($handle,$data);
-}
-if($_POST["11"] != "0")
-{
-$data = "MultipartonInteractions:enhanceScreening = ".$_POST["11"]."\n";
-fwrite($handle,$data);
-}
-if($_POST["12"] != "1")
-{
-$data = "MultipartonInteractions:bProfile = ".$_POST["12"]."\n";
-fwrite($handle,$data);
-}
-if($_POST["13"] != "0.4")
-{
-$data = "MultipartonInteractions:coreRadius = ".$_POST["13"]."\n";
-fwrite($handle,$data);
-}
-if($_POST["14"] != "0.5")
-{
-$data = "MultipartonInteractions:coreFraction = ".$_POST["14"]."\n";
-fwrite($handle,$data);
-}
-if($_POST["15"] != "1.")
-{
-$data = "MultipartonInteractions:expPow = ".$_POST["15"]."\n";
-fwrite($handle,$data);
-}
-if($_POST["16"] != "0.15")
-{
-$data = "MultipartonInteractions:a1 = ".$_POST["16"]."\n";
-fwrite($handle,$data);
-}
-if($_POST["17"] != "off")
-{
-$data = "MultipartonInteractions:allowRescatter = ".$_POST["17"]."\n";
-fwrite($handle,$data);
-}
-if($_POST["18"] != "off")
-{
-$data = "MultipartonInteractions:allowDoubleRescatter = ".$_POST["18"]."\n";
-fwrite($handle,$data);
-}
-if($_POST["19"] != "0")
-{
-$data = "MultipartonInteractions:rescatterMode = ".$_POST["19"]."\n";
-fwrite($handle,$data);
-}
-if($_POST["20"] != "0.")
-{
-$data = "MultipartonInteractions:ySepRescatter = ".$_POST["20"]."\n";
-fwrite($handle,$data);
-}
-if($_POST["21"] != "1.")
-{
-$data = "MultipartonInteractions:deltaYRescatter = ".$_POST["21"]."\n";
-fwrite($handle,$data);
-}
-if($_POST["22"] != "5")
-{
-$data = "MultipartonInteractions:nQuarkIn = ".$_POST["22"]."\n";
-fwrite($handle,$data);
-}
-if($_POST["23"] != "1000")
-{
-$data = "MultipartonInteractions:nSample = ".$_POST["23"]."\n";
-fwrite($handle,$data);
-}
-fclose($handle);
-}
-
-?>
-</body>
-</html>
-
-<!-- Copyright (C) 2012 Torbjorn Sjostrand -->
git://git.uio.no / u / mrichter / AliRoot.git / blobdiff