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[u/mrichter/AliRoot.git] / PYTHIA8 / pythia8130 / xmldoc / BoseEinsteinEffects.xml
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5ad4eb21 1<chapter name="Bose-Einstein Effects">
2
3<h2>Bose-Einstein Effects</h2>
4
5The <code>BoseEinstein</code> class performs shifts of momenta
6of identical particles to provide a crude estimate of
7Bose-Einstein effects. The algorithm is the BE_32 one described in
8<ref>Lon95</ref>, with a Gaussian parametrization of the enhancement.
9We emphasize that this approach is not based on any first-principles
10quantum mechanical description of interference phenomena; such
11approaches anyway have many problems to contend with. Instead a cruder
12but more robust approach is adopted, wherein BE effects are introduced
13after the event has already been generated, with the exception of the
14decays of long-lived particles. The trick is that momenta of identical
15particles are shifted relative to each other so as to provide an
16enhancement of pairs closely separated, which is compensated by a
17depletion of pairs in an intermediate region of separation.
18
19<p/>
20More precisely, the intended target form of the BE corrrelations in
21BE_32 is
22<eq>
23f_2(Q) = (1 + lambda * exp(-Q^2 R^2))
24 * (1 + alpha * lambda * exp(-Q^2 R^2/9) * (1 - exp(-Q^2 R^2/4)))
25</eq>
26where <ei>Q^2 = (p_1 + p_2)^2 - (m_1 + m_2)^2</ei>.
27Here the strength <ei>lambda</ei> and effective radius <ei>R</ei>
28are the two main parameters. The first factor of the
29equation is implemented by pulling pairs of identical hadrons closer
30to each other. This is done in such a way that three-monentum is
31conserved, but at the price of a small but non-negligible negative
32shift in the energy of the event. The second factor compensates this
33by pushing particles apart. The negative <ei>alpha</ei> parameter is
34determined iteratively, separately for each event, so as to restore
35energy conservation. The effective radius parameter is here <ei>R/3</ei>,
36i.e. effects extend further out in <ei>Q</ei>. Without the dampening
37<ei>(1 - exp(-Q^2 R^2/4))</ei> in the second factor the value at the
38origin would become <ei>f_2(0) = (1 + lambda) * (1 + alpha * lambda)</ei>,
39with it the desired value <ei>f_2(0) = (1 + lambda)</ei> is restored.
40The end result can be viewed as a poor man's rendering of a rapidly
41dampened oscillatory behaviour in <ei>Q</ei>.
42
43<p/>
44Further details can be found in <ref>Lon95</ref>. For instance, the
45target is implemented under the assumption that the initial distribution
46in <ei>Q</ei> can be well approximated by pure phase space at small
47values, and implicitly generates higher-order effects by the way
48the algorithm is implemented. The algorithm is applied after the decay
49of short-lived resonances such as the <ei>rho</ei>, but before the decay
50of longer-lived particles.
51
52<p/>
53This algorithm is known to do a reasonable job of describing BE
54phenomena at LEP. It has not been tested against data for hadron
55colliders, to the best of our knowledge, so one should exercise some
56judgement before using it. Therefore by default the master switch
57<aloc href="MasterSwitches">HadronLevel:BoseEinstein</aloc> is off.
58Furthermore, the implementation found here is not (yet) as
59sophisticated as the one used at LEP2, in that no provision is made
60for particles from separate colour singlet systems, such as
61<ei>W</ei>'s and <ei>Z</ei>'s, interfering only at a reduced rate.
62
63<p/>
64<b>Warning:</b> The algorithm will create a new copy of each particle
65with shifted momentum by BE effects, with status code 99, while the
66original particle with the original momentum at the same time will be
67marked as decayed. This means that if you e.g. search for all
68<ei>pi+-</ei> in an event you will often obtain the same particle twice.
69One way to protect yourself from unwanted doublecounting is to
70use only particles with a positive status code, i.e. ones for which
71<code>event[i].isFinal()</code> is <code>true</code>.
72
73
74<h3>Main parameters</h3>
75
76<flag name="BoseEinstein:Pion" default="on">
77Include effects or not for identical <ei>pi^+</ei>, <ei>pi^-</ei>
78and <ei>pi^0</ei>.
79</flag>
80
81<flag name="BoseEinstein:Kaon" default="on">
82Include effects or not for identical <ei>K^+</ei>, <ei>K^-</ei>,
83<ei>K_S^0</ei> and <ei>K_L^0</ei>.
84</flag>
85
86<flag name="BoseEinstein:Eta" default="on">
87Include effects or not for identical <ei>eta</ei> and <ei>eta'</ei>.
88</flag>
89
90<parm name="BoseEinstein:lambda" default="1." min="0." max="2.">
91The strength parameter for Bose-Einstein effects. On physical grounds
92it should not be above unity, but imperfections in the formalism
93used may require that nevertheless.
94</parm>
95
96<parm name="BoseEinstein:QRef" default="0.2" min="0.05" max="1.">
97The size parameter of the region in <ei>Q</ei> space over which
98Bose-Einstein effects are significant. Can be thought of as
99the inverse of an effective distance in normal space,
100<ei>R = hbar / QRef</ei>, with <ei>R</ei> as used in the above equation.
101That is, <ei>f_2(Q) = (1 + lambda * exp(-(Q/QRef)^2)) * (...)</ei>.
102</parm>
103
104<parm name="BoseEinstein:widthSep" default="0.02" min="0.001" max="1.">
105Particle species with a width above this value (in GeV) are assumed
106to be so short-lived that they decay before Bose-Einstein effects
107are considered, while otherwise they do not. In the former case the
108decay products thus can obtain shifted momenta, in the latter not.
109The default has been picked such that both <ei>rho</ei> and
110<ei>K^*</ei> decay products would be modified.
111</parm>
112
113</chapter>
114
115<!-- Copyright (C) 2008 Torbjorn Sjostrand -->
116