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-<title>Bose-Einstein Effects</title>
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-<h2>Bose-Einstein Effects</h2>
-
-The <code>BoseEinstein</code> class performs shifts of momenta
-of identical particles to provide a crude estimate of
-Bose-Einstein effects. The algorithm is the BE_32 one described in
-[<a href="Bibliography.php" target="page">Lon95</a>], with a Gaussian parametrization of the enhancement.
-We emphasize that this approach is not based on any first-principles
-quantum mechanical description of interference phenomena; such
-approaches anyway have many problems to contend with. Instead a cruder
-but more robust approach is adopted, wherein BE effects are introduced
-after the event has already been generated, with the exception of the
-decays of long-lived particles. The trick is that momenta of identical
-particles are shifted relative to each other so as to provide an
-enhancement of pairs closely separated, which is compensated by a
-depletion of pairs in an intermediate region of separation.
-
-<p/>
-More precisely, the intended target form of the BE corrrelations in
-BE_32 is
-<br/><i>
-f_2(Q) = (1 + lambda * exp(-Q^2 R^2))
- * (1 + alpha * lambda * exp(-Q^2 R^2/9) * (1 - exp(-Q^2 R^2/4)))
-</i><br/>
-where <i>Q^2 = (p_1 + p_2)^2 - (m_1 + m_2)^2</i>.
-Here the strength <i>lambda</i> and effective radius <i>R</i>
-are the two main parameters. The first factor of the
-equation is implemented by pulling pairs of identical hadrons closer
-to each other. This is done in such a way that three-monentum is
-conserved, but at the price of a small but non-negligible negative
-shift in the energy of the event. The second factor compensates this
-by pushing particles apart. The negative <i>alpha</i> parameter is
-determined iteratively, separately for each event, so as to restore
-energy conservation. The effective radius parameter is here <i>R/3</i>,
-i.e. effects extend further out in <i>Q</i>. Without the dampening
-<i>(1 - exp(-Q^2 R^2/4))</i> in the second factor the value at the
-origin would become <i>f_2(0) = (1 + lambda) * (1 + alpha * lambda)</i>,
-with it the desired value <i>f_2(0) = (1 + lambda)</i> is restored.
-The end result can be viewed as a poor man's rendering of a rapidly
-dampened oscillatory behaviour in <i>Q</i>.
-
-<p/>
-Further details can be found in [<a href="Bibliography.php" target="page">Lon95</a>]. For instance, the
-target is implemented under the assumption that the initial distribution
-in <i>Q</i> can be well approximated by pure phase space at small
-values, and implicitly generates higher-order effects by the way
-the algorithm is implemented. The algorithm is applied after the decay
-of short-lived resonances such as the <i>rho</i>, but before the decay
-of longer-lived particles.
-
-<p/>
-This algorithm is known to do a reasonable job of describing BE
-phenomena at LEP. It has not been tested against data for hadron
-colliders, to the best of our knowledge, so one should exercise some
-judgement before using it. Therefore by default the master switch
-<?php $filepath = $_GET["filepath"];
-echo "<a href='MasterSwitches.php?filepath=".$filepath."' target='page'>";?>HadronLevel:BoseEinstein</a> is off.
-Furthermore, the implementation found here is not (yet) as
-sophisticated as the one used at LEP2, in that no provision is made
-for particles from separate colour singlet systems, such as
-<i>W</i>'s and <i>Z</i>'s, interfering only at a reduced rate.
-
-<p/>
-<b>Warning:</b> The algorithm will create a new copy of each particle
-with shifted momentum by BE effects, with status code 99, while the
-original particle with the original momentum at the same time will be
-marked as decayed. This means that if you e.g. search for all
-<i>pi+-</i> in an event you will often obtain the same particle twice.
-One way to protect yourself from unwanted doublecounting is to
-use only particles with a positive status code, i.e. ones for which
-<code>event[i].isFinal()</code> is <code>true</code>.
-
-
-<h3>Main parameters</h3>
-
-<br/><br/><strong>BoseEinstein:Pion</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/>
-Include effects or not for identical <i>pi^+</i>, <i>pi^-</i>
-and <i>pi^0</i>.
-
-
-<br/><br/><strong>BoseEinstein:Kaon</strong> <input type="radio" name="2" value="on" checked="checked"><strong>On</strong>
-<input type="radio" name="2" value="off"><strong>Off</strong>
- (<code>default = <strong>on</strong></code>)<br/>
-Include effects or not for identical <i>K^+</i>, <i>K^-</i>,
-<i>K_S^0</i> and <i>K_L^0</i>.
-
-
-<br/><br/><strong>BoseEinstein:Eta</strong> <input type="radio" name="3" value="on" checked="checked"><strong>On</strong>
-<input type="radio" name="3" value="off"><strong>Off</strong>
- (<code>default = <strong>on</strong></code>)<br/>
-Include effects or not for identical <i>eta</i> and <i>eta'</i>.
-
-
-<br/><br/><table><tr><td><strong>BoseEinstein:lambda </td><td></td><td> <input type="text" name="4" value="1." size="20"/> (<code>default = <strong>1.</strong></code>; <code>minimum = 0.</code>; <code>maximum = 2.</code>)</td></tr></table>
-The strength parameter for Bose-Einstein effects. On physical grounds
-it should not be above unity, but imperfections in the formalism
-used may require that nevertheless.
-
-
-<br/><br/><table><tr><td><strong>BoseEinstein:QRef </td><td></td><td> <input type="text" name="5" value="0.2" size="20"/> (<code>default = <strong>0.2</strong></code>; <code>minimum = 0.05</code>; <code>maximum = 1.</code>)</td></tr></table>
-The size parameter of the region in <i>Q</i> space over which
-Bose-Einstein effects are significant. Can be thought of as
-the inverse of an effective distance in normal space,
-<i>R = hbar / QRef</i>, with <i>R</i> as used in the above equation.
-That is, <i>f_2(Q) = (1 + lambda * exp(-(Q/QRef)^2)) * (...)</i>.
-
-
-<br/><br/><table><tr><td><strong>BoseEinstein:widthSep </td><td></td><td> <input type="text" name="6" value="0.02" size="20"/> (<code>default = <strong>0.02</strong></code>; <code>minimum = 0.001</code>; <code>maximum = 1.</code>)</td></tr></table>
-Particle species with a width above this value (in GeV) are assumed
-to be so short-lived that they decay before Bose-Einstein effects
-are considered, while otherwise they do not. In the former case the
-decay products thus can obtain shifted momenta, in the latter not.
-The default has been picked such that both <i>rho</i> and
-<i>K^*</i> decay products would be modified.
-
-
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-
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-
-<!-- Copyright (C) 2012 Torbjorn Sjostrand -->
-
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