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<html>
<head>
<title>Onia Processes</title>
<link rel="stylesheet" type="text/css" href="pythia.css"/>
<link rel="shortcut icon" href="pythia32.gif"/>
</head>
<body>

<h2>Onia Processes</h2>

Production of J/psi or Upsilon, directly and via chi states and the 
colour-octet mechanism. 
In each process the square-bracketed expression specifies the state 
in spectroscopic notation, <i>(2S+1) L J</i>, followed by 
<i>(1)</i> for colour-singlet states and <i>(8)</i> for 
colour-octet ditto. 

<p/>
The original Fortran code for these processes has been contributed 
by Stefan Wolf [unpublished]. For the C++ version only the unpolarized
expressions are retained, since the theoretical predictions of the 
colour-octet model anyway do not agree with the experimental 
observations. Furthermore, the polarization effects are modest,
so isotropic decay is not a bad starting point. Such an event sample
can afterwards be reweighted at will by the user, to test various
assumptions.

<p/>
The description of  
<a href="TimelikeShowers.html" target="page">final-state radiation</a>
is in this case based on some further model assumptions.

<p/>
Most of the processes below are divergent in the limit <i>pT -> 0</i>, 
and therefore a <i>pTmin</i> scale should be set. Comparisons with 
data indicate that this divergence can be tamed the same way as for 
the normal QCD <i>2 -> 2</i> cross sections [<a href="Bibliography.html" target="page">Bar06,Kra08</a>], 
which makes sense, since they are all dominated by the same kind of 
<i>t</i>-channel gluon exchange. It is therefore possible to use the 
<a href="UserHooks.html" target="page">SuppressSmallPT</a> user hook to impose a 
reweighting that cancels the low-<i>pT</i> divergence.

<p/>
An eikonalized description of these processes is included in the 
multiparton-interactions framework. Here the low-<i>pT</i> dampening
is automatic, and additionally the framework is more consistent
(e.g. with respect to energy-momentum constraints and the 
impact-parameter description) for events where the onium production 
is not the hardest subprocess, as would often be the case in the 
low-<i>pT</i> limit.

<h3>Charmonium</h3>

<p/><code>flag&nbsp; </code><strong> Charmonium:all &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
Common switch for the group of charmonium production.
  

<p/><code>flag&nbsp; </code><strong> Charmonium:gg2QQbar[3S1(1)]g &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>g g -> ccbar[3S1(1)] g</i>.
Code 401.
  

<p/><code>flag&nbsp; </code><strong> Charmonium:gg2QQbar[3P0(1)]g &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>g g -> ccbar[3P0(1)] g</i>.
Code 402.
  

<p/><code>flag&nbsp; </code><strong> Charmonium:gg2QQbar[3P1(1)]g &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>g g -> ccbar[3P1(1)] g</i>.
Code 403.
  

<p/><code>flag&nbsp; </code><strong> Charmonium:gg2QQbar[3P2(1)]g &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>g g -> ccbar[3P2(1)] g</i>.
Code 404.
  

<p/><code>flag&nbsp; </code><strong> Charmonium:qg2QQbar[3P0(1)]q &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>q g -> ccbar[3P0(1)] q</i>.
Code 405.
  

<p/><code>flag&nbsp; </code><strong> Charmonium:qg2QQbar[3P1(1)]q &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>q g -> ccbar[3P1(1)] q</i>.
Code 406.
  

<p/><code>flag&nbsp; </code><strong> Charmonium:qg2QQbar[3P2(1)]q &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>q g -> ccbar[3P2(1)] q</i>.
Code 407.
  

<p/><code>flag&nbsp; </code><strong> Charmonium:qqbar2QQbar[3P0(1)]g &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>q qbar -> ccbar[3P0(1)] g</i>.
Code 408.
  

<p/><code>flag&nbsp; </code><strong> Charmonium:qqbar2QQbar[3P1(1)]g &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>q qbar -> ccbar[3P1(1)] g</i>.
Code 409.
  

<p/><code>flag&nbsp; </code><strong> Charmonium:qqbar2QQbar[3P2(1)]g &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>q qbar -> ccbar[3P2(1)] g</i>.
Code 410.
  

<p/><code>flag&nbsp; </code><strong> Charmonium:gg2QQbar[3S1(8)]g &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>g g -> ccbar[3S1(8)] g</i>.
Code 411.
  

<p/><code>flag&nbsp; </code><strong> Charmonium:gg2QQbar[1S0(8)]g &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>g g -> ccbar[3S1(8)] g</i>.
Code 412.
  

<p/><code>flag&nbsp; </code><strong> Charmonium:gg2QQbar[3PJ(8)]g &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>g g -> ccbar[3S1(8)] g</i>.
Code 413.
  

<p/><code>flag&nbsp; </code><strong> Charmonium:qg2QQbar[3S1(8)]q &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>q g -> ccbar[3S1(8)] q</i>.
Code 414.
  

<p/><code>flag&nbsp; </code><strong> Charmonium:qg2QQbar[1S0(8)]q &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>q g -> ccbar[3S1(8)] q</i>.
Code 415.
  

<p/><code>flag&nbsp; </code><strong> Charmonium:qg2QQbar[3PJ(8)]q &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>q g -> ccbar[3S1(8)] q</i>.
Code 416.
  

<p/><code>flag&nbsp; </code><strong> Charmonium:qqbar2QQbar[3S1(8)]g &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>q qbar -> ccbar[3S1(8)] g</i>.
Code 417.
  

<p/><code>flag&nbsp; </code><strong> Charmonium:qqbar2QQbar[1S0(8)]g &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>q qbar -> ccbar[3S1(8)] g</i>.
Code 418.
  

<p/><code>flag&nbsp; </code><strong> Charmonium:qqbar2QQbar[3PJ(8)]g &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>q qbar -> ccbar[3S1(8)] g</i>.
Code 419.
  

<h3>Bottomonium</h3>

<p/><code>flag&nbsp; </code><strong> Bottomonium:all &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
Common switch for the group of charmonium production.
  

<p/><code>flag&nbsp; </code><strong> Bottomonium:gg2QQbar[3S1(1)]g &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>g g -> bbbar[3S1(1)] g</i>.
Code 501.
  

<p/><code>flag&nbsp; </code><strong> Bottomonium:gg2QQbar[3P0(1)]g &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>g g -> bbbar[3P0(1)] g</i>.
Code 502.
  

<p/><code>flag&nbsp; </code><strong> Bottomonium:gg2QQbar[3P1(1)]g &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>g g -> bbbar[3P1(1)] g</i>.
Code 503.
  

<p/><code>flag&nbsp; </code><strong> Bottomonium:gg2QQbar[3P2(1)]g &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>g g -> bbbar[3P2(1)] g</i>.
Code 504.
  

<p/><code>flag&nbsp; </code><strong> Bottomonium:qg2QQbar[3P0(1)]q &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>q g -> bbbar[3P0(1)] q</i>.
Code 505.
  

<p/><code>flag&nbsp; </code><strong> Bottomonium:qg2QQbar[3P1(1)]q &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>q g -> bbbar[3P1(1)] q</i>.
Code 506.
  

<p/><code>flag&nbsp; </code><strong> Bottomonium:qg2QQbar[3P2(1)]q &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>q g -> bbbar[3P2(1)] q</i>.
Code 507.
  

<p/><code>flag&nbsp; </code><strong> Bottomonium:qqbar2QQbar[3P0(1)]g &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>q qbar -> bbbar[3P0(1)] g</i>.
Code 508.
  

<p/><code>flag&nbsp; </code><strong> Bottomonium:qqbar2QQbar[3P1(1)]g &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>q qbar -> bbbar[3P1(1)] g</i>.
Code 509.
  

<p/><code>flag&nbsp; </code><strong> Bottomonium:qqbar2QQbar[3P2(1)]g &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>q qbar -> bbbar[3P2(1)] g</i>.
Code 510.
  

<p/><code>flag&nbsp; </code><strong> Bottomonium:gg2QQbar[3S1(8)]g &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>g g -> bbbar[3S1(8)] g</i>.
Code 511.
  

<p/><code>flag&nbsp; </code><strong> Bottomonium:gg2QQbar[1S0(8)]g &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>g g -> bbbar[3S1(8)] g</i>.
Code 512.
  

<p/><code>flag&nbsp; </code><strong> Bottomonium:gg2QQbar[3PJ(8)]g &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>g g -> bbbar[3S1(8)] g</i>.
Code 513.
  

<p/><code>flag&nbsp; </code><strong> Bottomonium:qg2QQbar[3S1(8)]q &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>q g -> bbbar[3S1(8)] q</i>.
Code 514.
  

<p/><code>flag&nbsp; </code><strong> Bottomonium:qg2QQbar[1S0(8)]q &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>q g -> bbbar[3S1(8)] q</i>.
Code 515.
  

<p/><code>flag&nbsp; </code><strong> Bottomonium:qg2QQbar[3PJ(8)]q &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>q g -> bbbar[3S1(8)] q</i>.
Code 516.
  

<p/><code>flag&nbsp; </code><strong> Bottomonium:qqbar2QQbar[3S1(8)]g &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>q qbar -> bbbar[3S1(8)] g</i>.
Code 517.
  

<p/><code>flag&nbsp; </code><strong> Bottomonium:qqbar2QQbar[1S0(8)]g &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>q qbar -> bbbar[3S1(8)] g</i>.
Code 518.
  

<p/><code>flag&nbsp; </code><strong> Bottomonium:qqbar2QQbar[3PJ(8)]g &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
<i>q qbar -> bbbar[3S1(8)] g</i>.
Code 519.
  

<h3>Onium matrix elements</h3>

The implementation of charmonium and bottomonium production, including
the colour-octet production mechanism, requires information on NRQCD
matrix elements for the various wavefunctions involved. Default values
for these are encoded in the following ten variables. They
are taken from [<a href="Bibliography.html" target="page">Nas00</a>]; see also [<a href="Bibliography.html" target="page">Bar06</a>]. 

<p/><code>parm&nbsp; </code><strong> Charmonium:OJpsi3S11 &nbsp;</strong> 
 (<code>default = <strong>1.16</strong></code>; <code>minimum = 0.0</code>)<br/>
<i>&lt;O(J/psi)[3S1(1)]&gt;</i>.
  

<p/><code>parm&nbsp; </code><strong> Charmonium:OJpsi3S18 &nbsp;</strong> 
 (<code>default = <strong>0.0119</strong></code>; <code>minimum = 0.0</code>)<br/>
<i>&lt;O(J/psi)[3S1(8)]&gt;</i>.
  

<p/><code>parm&nbsp; </code><strong> Charmonium:OJpsi1S08 &nbsp;</strong> 
 (<code>default = <strong>0.01</strong></code>; <code>minimum = 0.0</code>)<br/>
<i>&lt;O(J/psi)[1S0(8)]&gt;</i>.
  

<p/><code>parm&nbsp; </code><strong> Charmonium:OJpsi3P08 &nbsp;</strong> 
 (<code>default = <strong>0.01</strong></code>; <code>minimum = 0.0</code>)<br/>
<i>&lt;O(J/psi)[3P0(8)]&gt;/m_c^2</i>.
  

<p/><code>parm&nbsp; </code><strong> Charmonium:Ochic03P01 &nbsp;</strong> 
 (<code>default = <strong>0.05</strong></code>; <code>minimum = 0.0</code>)<br/>
<i>&lt;O(chi_c0)[3P0(8)]&gt;/m_c^2</i>.
  

<p/><code>parm&nbsp; </code><strong> Bottomonium:OUpsilon3S11 &nbsp;</strong> 
 (<code>default = <strong>9.28</strong></code>; <code>minimum = 0.0</code>)<br/>
<i>&lt;O(Upsilon)[3S1(1)]&gt;</i>.
  

<p/><code>parm&nbsp; </code><strong> Bottomonium:OUpsilon3S18 &nbsp;</strong> 
 (<code>default = <strong>0.15</strong></code>; <code>minimum = 0.0</code>)<br/>
<i>&lt;O(Upsilon)[3S1(8)]&gt;</i>.
  

<p/><code>parm&nbsp; </code><strong> Bottomonium:OUpsilon1S08 &nbsp;</strong> 
 (<code>default = <strong>0.02</strong></code>; <code>minimum = 0.0</code>)<br/>
<i>&lt;O(Upsilon)[1S0(8)]&gt;</i>.
  

<p/><code>parm&nbsp; </code><strong> Bottomonium:OUpsilon3P08 &nbsp;</strong> 
 (<code>default = <strong>0.02</strong></code>; <code>minimum = 0.0</code>)<br/>
<i>&lt;O(Upsilon)[3P0(8)]&gt;/m_b^2</i>.
  

<p/><code>parm&nbsp; </code><strong> Bottomonium:Ochib03P01 &nbsp;</strong> 
 (<code>default = <strong>0.085</strong></code>; <code>minimum = 0.0</code>)<br/>
<i>&lt;O(chi_b0)[3P0(8)]&gt;/m_b^2</i>.
  


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