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-<title>Beam Remnants</title>
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-
-<h2>Beam Remnants</h2>
-
-<h3>Introduction</h3>
-
-The <code>BeamParticle</code> class contains information on all partons
-extracted from a beam (so far). As each consecutive multiparton interaction
-defines its respective incoming parton to the hard scattering a
-new slot is added to the list. This information is modified when
-the backwards evolution of the spacelike shower defines a new
-initiator parton. It is used, both for the multiparton interactions
-and the spacelike showers, to define rescaled parton densities based
-on the <i>x</i> and flavours already extracted, and to distinguish
-between valence, sea and companion quarks. Once the perturbative
-evolution is finished, further beam remnants are added to obtain a
-consistent set of flavours. The current physics framework is further
-described in [<a href="Bibliography.php" target="page">Sjo04</a>].
-
-<p/>
-The introduction of <?php $filepath = $_GET["filepath"];
-echo "<a href='MultipartonInteractions.php?filepath=".$filepath."' target='page'>";?>rescattering</a>
-in the multiparton interactions framework further complicates the
-processing of events. Specifically, when combined with showers,
-the momentum of an individual parton is no longer uniquely associated
-with one single subcollision. Nevertheless the parton is classified
-with one system, owing to the technical and administrative complications
-of more complete classifications. Therefore the addition of primordial
-<i>kT</i> to the subsystem initiator partons does not automatically
-guarantee overall <i>pT</i> conservation. Various tricks are used to
-minimize the mismatch, with a brute force shift of all parton
-<i>pT</i>'s as a final step.
-
-<p/>
-Much of the above information is stored in a vector of
-<code>ResolvedParton</code> objects, which each contains flavour and
-momentum information, as well as valence/companion information and more.
-The <code>BeamParticle</code> method <code>list()</code> shows the
-contents of this vector, mainly for debug purposes.
-
-<p/>
-The <code>BeamRemnants</code> class takes over for the final step
-of adding primordial <i>kT</i> to the initiators and remnants,
-assigning the relative longitudinal momentum sharing among the
-remnants, and constructing the overall kinematics and colour flow.
-This step couples the two sides of an event, and could therefore
-not be covered in the <code>BeamParticle</code> class, which only
-considers one beam at a time.
-
-<p/>
-The methods of these classes are not intended for general use,
-and so are not described here.
-
-<p/>
-In addition to the parameters described on this page, note that the
-choice of <?php $filepath = $_GET["filepath"];
-echo "<a href='PDFSelection.php?filepath=".$filepath."' target='page'>";?>parton densities</a> is made
-in the <code>Pythia</code> class. Then pointers to the pdf's are handed
-on to <code>BeamParticle</code> at initialization, for all subsequent
-usage.
-
-<h3>Primordial <i>kT</i></h3>
-
-The primordial <i>kT</i> of initiators of hard-scattering subsystems
-are selected according to Gaussian distributions in <i>p_x</i> and
-<i>p_y</i> separately. The widths of these distributions are chosen
-to be dependent on the hard scale of the central process and on the mass
-of the whole subsystem defined by the two initiators:
-<br/><i>
-sigma = (sigma_soft * Q_half + sigma_hard * Q) / (Q_half + Q)
- * m / (m_half + m)
-</i><br/>
-Here <i>Q</i> is the hard-process renormalization scale for the
-hardest process and the <i>pT</i> scale for subsequent multiparton
-interactions, <i>m</i> the mass of the system, and
-<i>sigma_soft</i>, <i>sigma_hard</i>, <i>Q_half</i> and
-<i>m_half</i> parameters defined below. Furthermore each separately
-defined beam remnant has a distribution of width <i>sigma_remn</i>,
-independently of kinematical variables.
-
-<br/><br/><strong>BeamRemnants:primordialKT</strong> <input type="radio" name="1" value="on" checked="checked"><strong>On</strong>
-<input type="radio" name="1" value="off"><strong>Off</strong>
- (<code>default = <strong>on</strong></code>)<br/>
-Allow or not selection of primordial <i>kT</i> according to the
-parameter values below.
-
-
-<br/><br/><table><tr><td><strong>BeamRemnants:primordialKTsoft </td><td></td><td> <input type="text" name="2" value="0.5" size="20"/> (<code>default = <strong>0.5</strong></code>; <code>minimum = 0.</code>)</td></tr></table>
-The width <i>sigma_soft</i> in the above equation, assigned as a
-primordial <i>kT</i> to initiators in the soft-interaction limit.
-
-
-<br/><br/><table><tr><td><strong>BeamRemnants:primordialKThard </td><td></td><td> <input type="text" name="3" value="2.0" size="20"/> (<code>default = <strong>2.0</strong></code>; <code>minimum = 0.</code>)</td></tr></table>
-The width <i>sigma_hard</i> in the above equation, assigned as a
-primordial <i>kT</i> to initiators in the hard-interaction limit.
-
-
-<br/><br/><table><tr><td><strong>BeamRemnants:halfScaleForKT </td><td></td><td> <input type="text" name="4" value="1." size="20"/> (<code>default = <strong>1.</strong></code>; <code>minimum = 0.</code>)</td></tr></table>
-The scale <i>Q_half</i> in the equation above, defining the
-half-way point between hard and soft interactions.
-
-
-<br/><br/><table><tr><td><strong>BeamRemnants:halfMassForKT </td><td></td><td> <input type="text" name="5" value="1." size="20"/> (<code>default = <strong>1.</strong></code>; <code>minimum = 0.</code>)</td></tr></table>
-The scale <i>m_half</i> in the equation above, defining the
-half-way point between low-mass and high-mass subsystems.
-(Kinematics construction can easily fail if a system is assigned
-a primordial <i>kT</i> value higher than its mass, so the
-mass-dampening is intended to reduce some troubles later on.)
-
-
-<br/><br/><table><tr><td><strong>BeamRemnants:primordialKTremnant </td><td></td><td> <input type="text" name="6" value="0.4" size="20"/> (<code>default = <strong>0.4</strong></code>; <code>minimum = 0.</code>)</td></tr></table>
-The width <i>sigma_remn</i>, assigned as a primordial <i>kT</i>
-to beam-remnant partons.
-
-
-<p/>
-A net <i>kT</i> imbalance is obtained from the vector sum of the
-primordial <i>kT</i> values of all initiators and all beam remnants.
-This quantity is compensated by a shift shared equally between
-all partons, except that the dampening factor <i>m / (m_half + m)</i>
-is again used to suppress the role of small-mass systems.
-
-<p/>
-Note that the current <i>sigma</i> definition implies that
-<i><pT^2> = <p_x^2>+ <p_y^2> = 2 sigma^2</i>.
-It thus cannot be compared directly with the <i>sigma</i>
-of nonperturbative hadronization, where each quark-antiquark
-breakup corresponds to <i><pT^2> = sigma^2</i> and only
-for hadrons it holds that <i><pT^2> = 2 sigma^2</i>.
-The comparison is further complicated by the reduction of
-primordial <i>kT</i> values by the overall compensation mechanism.
-
-<br/><br/><strong>BeamRemnants:rescatterRestoreY</strong> <input type="radio" name="7" value="on"><strong>On</strong>
-<input type="radio" name="7" value="off" checked="checked"><strong>Off</strong>
- (<code>default = <strong>off</strong></code>)<br/>
-Is only relevant when <?php $filepath = $_GET["filepath"];
-echo "<a href='MultipartonInteractions.php?filepath=".$filepath."' target='page'>";?>rescattering</a>
-is switched on in the multiparton interactions scenario. For a normal
-interaction the rapidity and mass of a system is preserved when
-primordial <i>kT</i> is introduced, by appropriate modification of the
-incoming parton momenta. Kinematics construction is more complicated for
-a rescattering, and two options are offered. Differences between these
-can be used to explore systematic uncertainties in the rescattering
-framework.<br/>
-The default behaviour is to keep the incoming rescattered parton as is,
-but to modify the unrescattered incoming parton so as to preserve the
-invariant mass of the system. Thereby the rapidity of the rescattering
-is modified.<br/>
-The alternative is to retain the rapidity (and mass) of the rescattered
-system when primordial <i>kT</i> is introduced. This is made at the
-expense of a modified longitudinal momentum of the incoming rescattered
-parton, so that it does not agree with the momentum it ought to have had
-by the kinematics of the previous interaction.<br/>
-For a double rescattering, when both incoming partons have already scattered,
-there is no obvious way to retain the invariant mass of the system in the
-first approach, so the second is always used.
-
-
-<h3>Colour flow</h3>
-
-The colour flows in the separate subprocesses defined in the
-multiparton-interactions scenario are tied together via the assignment
-of colour flow in the beam remnant. This is not an unambiguous
-procedure, but currently no parameters are directly associated with it.
-However, a simple "minimal" procedure of colour flow only via the beam
-remnants does not result in a scenario in
-agreement with data, notably not a sufficiently steep rise of
-<i><pT>(n_ch)</i>. The true origin of this behaviour and the
-correct mechanism to reproduce it remains one of the big unsolved issues
-at the borderline between perturbative and nonperturbative QCD.
-As a simple attempt, an additional step is introduced, wherein the gluons
-of a lower-<i>pT</i> system are merged with the ones in a higher-pT one.
-
-<br/><br/><strong>BeamRemnants:reconnectColours</strong> <input type="radio" name="8" value="on" checked="checked"><strong>On</strong>
-<input type="radio" name="8" value="off"><strong>Off</strong>
- (<code>default = <strong>on</strong></code>)<br/>
-Allow or not a system to be merged with another one.
-
-
-<br/><br/><table><tr><td><strong>BeamRemnants:reconnectRange </td><td></td><td> <input type="text" name="9" value="10.0" size="20"/> (<code>default = <strong>10.0</strong></code>; <code>minimum = 0.</code>; <code>maximum = 10.</code>)</td></tr></table>
-A system with a hard scale <i>pT</i> can be merged with one of a
-harder scale with a probability that is
-<i>pT0_Rec^2 / (pT0_Rec^2 + pT^2)</i>, where
-<i>pT0_Rec</i> is <code>reconnectRange</code> times <i>pT0</i>,
-the latter being the same energy-dependent dampening parameter as
-used for multiparton interactions.
-Thus it is easy to merge a low-<i>pT</i> system with any other,
-but difficult to merge two high-<i>pT</i> ones with each other.
-
-
-<p/>
-The procedure is used iteratively. Thus first the reconnection probability
-<i>P = pT0_Rec^2 / (pT0_Rec^2 + pT^2)</i> of the lowest-<i>pT</i>
-system is found, and gives the probability for merger with the
-second-lowest one. If not merged, it is tested with the third-lowest one,
-and so on. For the <i>m</i>'th higher system the reconnection
-probability thus becomes <i>(1 - P)^(m-1) P</i>. That is, there is
-no explicit dependence on the higher <i>pT</i> scale, but implicitly
-there is via the survival probability of not already having been merged
-with a lower-<i>pT</i> system. Also note that the total reconnection
-probability for the lowest-<i>pT</i> system in an event with <i>n</i>
-systems becomes <i>1 - (1 - P)^(n-1)</i>. Once the fate of the
-lowest-<i>pT</i> system has been decided, the second-lowest is considered
-with respect to the ones above it, then the third-lowest, and so on.
-
-<p/>
-Once it has been decided which systems should be joined, the actual merging
-is carried out in the opposite direction. That is, first the hardest
-system is studied, and all colour dipoles in it are found (including to
-the beam remnants, as defined by the holes of the incoming partons).
-Next each softer system to be merged is studied in turn. Its gluons are,
-in decreasing <i>pT</i> order, inserted on the colour dipole <i>i,j</i>
-that gives the smallest <i>(p_g p_i)(p_g p_j)/(p_i p_j)</i>, i.e.
-minimizes the "disturbance" on the existing dipole, in terms of
-<i>pT^2</i> or <i>Lambda</i> measure (string length). The insertion
-of the gluon means that the old dipole is replaced by two new ones.
-Also the (rather few) quark-antiquark pairs that can be traced back to
-a gluon splitting are treated in close analogy with the gluon case.
-Quark lines that attach directly to the beam remnants cannot be merged
-but are left behind.
-
-<p/>
-The joining procedure can be viewed as a more sophisticated variant of
-the one introduced already in [<a href="Bibliography.php" target="page">Sjo87</a>]. Clearly it is ad hoc.
-It hopefully captures some elements of truth. The lower <i>pT</i> scale
-a system has the larger its spatial extent and therefore the larger its
-overlap with other systems. It could be argued that one should classify
-individual initial-state partons by <i>pT</i> rather than the system
-as a whole. However, for final-state radiation, a soft gluon radiated off
-a hard parton is actually produced at late times and therefore probably
-less likely to reconnect. In the balance, a classification by system
-<i>pT</i> scale appears sensible as a first try.
-
-<p/>
-Note that the reconnection is carried out before resonance decays are
-considered. Colour inside a resonance therefore is not reconnected.
-This is a deliberate choice, but certainly open to discussion and
-extensions at a later stage, as is the rest of this procedure.
-
-<h3>Further variables</h3>
-
-<br/><br/><table><tr><td><strong>BeamRemnants:maxValQuark </td><td></td><td> <input type="text" name="10" value="3" size="20"/> (<code>default = <strong>3</strong></code>; <code>minimum = 0</code>; <code>maximum = 5</code>)</td></tr></table>
-The maximum valence quark kind allowed in acceptable incoming beams,
-for which multiparton interactions are simulated. Default is that hadrons
-may contain <i>u</i>, <i>d</i> and <i>s</i> quarks,
-but not <i>c</i> and <i>b</i> ones, since sensible
-kinematics has not really been worked out for the latter.
-
-
-<br/><br/><table><tr><td><strong>BeamRemnants:companionPower </td><td></td><td> <input type="text" name="11" value="4" size="20"/> (<code>default = <strong>4</strong></code>; <code>minimum = 0</code>; <code>maximum = 4</code>)</td></tr></table>
-When a sea quark has been found, a companion antisea quark ought to be
-nearby in <i>x</i>. The shape of this distribution can be derived
-from the gluon mother distribution convoluted with the
-<i>g -> q qbar</i> splitting kernel. In practice, simple solutions
-are only feasible if the gluon shape is assumed to be of the form
-<i>g(x) ~ (1 - x)^p / x</i>, where <i>p</i> is an integer power,
-the parameter above. Allowed values correspond to the cases programmed.
-<br/>
-Since the whole framework is approximate anyway, this should be good
-enough. Note that companions typically are found at small <i>Q^2</i>,
-if at all, so the form is supposed to represent <i>g(x)</i> at small
-<i>Q^2</i> scales, close to the lower cutoff for multiparton interactions.
-
-
-<p/>
-When assigning relative momentum fractions to beam-remnant partons,
-valence quarks are chosen according to a distribution like
-<i>(1 - x)^power / sqrt(x)</i>. This <i>power</i> is given below
-for quarks in mesons, and separately for <i>u</i> and <i>d</i>
-quarks in the proton, based on the approximate shape of low-<i>Q^2</i>
-parton densities. The power for other baryons is derived from the
-proton ones, by an appropriate mixing. The <i>x</i> of a diquark
-is chosen as the sum of its two constituent <i>x</i> values, and can
-thus be above unity. (A common rescaling of all remnant partons and
-particles will fix that.) An additional enhancement of the diquark
-momentum is obtained by its <i>x</i> value being rescaled by the
-<code>valenceDiqEnhance</code> factor.
-
-<br/><br/><table><tr><td><strong>BeamRemnants:valencePowerMeson </td><td></td><td> <input type="text" name="12" value="0.8" size="20"/> (<code>default = <strong>0.8</strong></code>; <code>minimum = 0.</code>)</td></tr></table>
-The abovementioned power for valence quarks in mesons.
-
-
-<br/><br/><table><tr><td><strong>BeamRemnants:valencePowerUinP </td><td></td><td> <input type="text" name="13" value="3.5" size="20"/> (<code>default = <strong>3.5</strong></code>; <code>minimum = 0.</code>)</td></tr></table>
-The abovementioned power for valence <i>u</i> quarks in protons.
-
-
-<br/><br/><table><tr><td><strong>BeamRemnants:valencePowerDinP </td><td></td><td> <input type="text" name="14" value="2.0" size="20"/> (<code>default = <strong>2.0</strong></code>; <code>minimum = 0.</code>)</td></tr></table>
-The abovementioned power for valence <i>d</i> quarks in protons.
-
-
-<br/><br/><table><tr><td><strong>BeamRemnants:valenceDiqEnhance </td><td></td><td> <input type="text" name="15" value="2.0" size="20"/> (<code>default = <strong>2.0</strong></code>; <code>minimum = 0.5</code>; <code>maximum = 10.</code>)</td></tr></table>
-Enhancement factor for valence diqaurks in baryons, relative to the
-simple sum of the two constituent quarks.
-
-
-<br/><br/><strong>BeamRemnants:allowJunction</strong> <input type="radio" name="16" value="on" checked="checked"><strong>On</strong>
-<input type="radio" name="16" value="off"><strong>Off</strong>
- (<code>default = <strong>on</strong></code>)<br/>
-The <code>off</code> option is intended for debug purposes only, as
-follows. When more than one valence quark is kicked out of a baryon
-beam, as part of the multiparton interactions scenario, the subsequent
-hadronization is described in terms of a junction string topology.
-This description involves a number of technical complications that
-may make the program more unstable. As an alternative, by switching
-this option off, junction configurations are rejected (which gives
-an error message that the remnant flavour setup failed), and the
-multiparton interactions and showers are redone until a
-junction-free topology is found.
-
-
-<input type="hidden" name="saved" value="1"/>
-
-<?php
-echo "<input type='hidden' name='filepath' value='".$_GET["filepath"]."'/>"?>
-
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-</form>
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-{
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-fwrite($handle,$data);
-}
-fclose($handle);
-}
-
-?>
-</body>
-</html>
-
-<!-- Copyright (C) 2012 Torbjorn Sjostrand -->
git://git.uio.no / u / mrichter / AliRoot.git / blobdiff