<chapter name="Onia Processes">
<h2>Onia Processes</h2>
Production of any <ei>3S1</ei>, <ei>3PJ</ei>, and <ei>3DJ</ei> charmonium
and bottomonium states via the colour-singlet and colour-octet
mechanisms. This includes by default, but is not limited to, production of
the <ei>3S1</ei> <ei>J/psi</ei> and <ei>Upsilon</ei> and their
radially excited states, as well as the <ei>3PJ</ei> <ei>chi</ei>
states and the <ei>3D1</ei> <ei>psi(3770)</ei>. In each process the
heavy quark content, either <ei>ccbar</ei> or <ei>bbbar</ei>, is
followed by a round-bracketed expression which specifies the physical
state in spectroscopic notation, <ei>(2S+1) L J</ei>. Proceding this
is a square-bracketed expression, also in spectroscopic notation,
which specifies the Fock state through which the process occurs,
where <ei>(1)</ei> indicates a colour-singlet state and <ei>(8)</ei> a
colour-octet state.
<p> The unphysical colour-octet states follow the <code>id</code>
scheme of <ei>99 n_q n_s n_r n_L n_J</ei> where <ei>n_q</ei> is the
quark flavour of the state and <ei>n_s</ei> is the colour-octet state
type. Here <ei>0</ei> is <ei>3S1</ei>, <ei>1</ei> is <ei>1S0</ei>,
and <ei>2</ei> is <ei>3PJ</ei>. All remaining numbers follow the
standard PDG numbering scheme. If a physical state is requested
without a corresponding colour-octet state, a colour-octet state is
automatically added to the <code>ParticleData</code>
when a colour-octet process is selected. The colour-octet state is
created with a mass given by the mass of the physical state plus the
singlet-octet mass splitting parameter <code>Onia:massSplit</code>,
which is by default set at 200 MeV, and decays exclusively
to a gluon and the physical state. If the user wishes to manually
set the mass splitting for each colour-octet state individually
then <code>Onia:forceMassSplit</code> can be set to <ei>off</ei>.
By default the widths of the octet states are set to vanish.
This is not realistic, given their presumably rather rapid decay,
but a nonvanishing width is not likely to have any measurable
consequences that go beyond what comes from viewing the singlet-octet
mass splitting as an effective parameter.
<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by Stefan Wolf [unpublished].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. The expressions for the colour-singlet production of
the <ei>3S1</ei> and <ei>3PJ</ei> states can be found
in <ref>Bai83</ref> and <ref>Gas87</ref>. Colour-octet expressions can
be found in <ref>Cho96</ref> for the <ei>1S0</ei>, <ei>3S1</ei>,
and <ei>3PJ</ei> states, and the matrix elements for the <ei>3DJ</ei>
states are taken from <ref>Yua98</ref>.
<p/>
The implementation of charmonium and bottomonium production, including
the colour-octet production mechanism, requires information on
long-distance NRQCD matrix elements for the various wavefunctions
involved. Default values for these are encoded in the <ei>O</ei>
parameters and are taken from <ref>Nas00</ref>; see
also <ref>Bar07</ref>. The <ei>3DJ</ei> long-distance matrix elements
are extracted from <ref>Yua98</ref>.
<p/>
Note that states that differ only by the radial excitation number
<ei>n_r</ei> share the same short-dinstence matrix elements. The
program has therefore been written such that further radial excitations
can be easily added by editing this file, without requiring a recompilation
of the code. All related arrays must be expanded in exactly the same way,
however, i.e. the code of the colour singlet state, the long-distance
matrix elements and the individual process on/off switches.
<p/>
The description of
<aloc href="TimelikeShowers">final-state radiation</aloc>
is in this case based on some further model assumptions.
<p/>
Most of the processes below are divergent in the limit <ei>pT → 0</ei>,
and therefore a <ei>pTmin</ei> scale should be set. Comparisons with
data indicate that this divergence can be tamed the same way as for
the normal QCD <ei>2 → 2</ei> cross sections <ref>Bar07,Kra08</ref>,
which makes sense, since they are all dominated by the same kind of
<ei>t</ei>-channel gluon exchange. It is therefore possible to use the
<aloc href="UserHooks">SuppressSmallPT</aloc> user hook to impose a
reweighting that cancels the low-<ei>pT</ei> divergence.
<p/>
An eikonalized description of these processes is included in the
multiparton-interactions framework. Here the low-<ei>pT</ei> 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-<ei>pT</ei> limit.
<flag name="Onia:forceMassSplit" default="on">
Force the mass splitting between the colour-singlet states and their
corresponding colour-octet state to be <code>Onia:massSplit</code>.
</flag>
<parm name="Onia:massSplit" default="0.2" min="0.0" max="1.0">
Mass splitting in GeV between the physical colour-singlet
states and their corresponding colour-octet state.
</parm>
<flag name="Onia:all" default="off">
Common switch for the group of onia production.
</flag>
<flag name="Onia:all(3S1)" default="off">
Common switch for the group of <ei>3S1</ei> onia production,
e.g. <ei>J/psi</ei> and <ei>Upsilon</ei>.
</flag>
<flag name="Onia:all(3PJ)" default="off">
Common switch for the group of <ei>3PJ</ei> onia production,
e.g. <ei>chi_c</ei> and <ei>chi_b</ei>.
</flag>
<flag name="Onia:all(3DJ)" default="off">
Common switch for the group of <ei>3DJ</ei> onia production,
e.g. <ei>psi(3770)</ei>.
</flag>
<flag name="Charmonium:all" default="off">
Common switch for the group of charmonium production,
e.g. <ei>J/psi</ei> and <ei>chi_c</ei>.
</flag>
<flag name="Bottomonium:all" default="off">
Common switch for the group of bottomonium production,
e.g. <ei>Upsilon</ei> and <ei>chi_b</ei>.
</flag>
<h3>Charmonium 3S1 States</h3>
<mvec name="Charmonium:states(3S1)" default="443,100443"
min="0">
The <ei>3S1</ei> charmonium states that can be produced from the following
processes. Note that all vectors within this section,
either of flags or parameters, must be the same length as this
vector.
</mvec>
<pvec name="Charmonium:O(3S1)[3S1(1)]" default="1.16,0.76" min="0.0">
The colour-singlet long-distance matrix
elements <ei><O[3S1(1)]></ei> for the <ei>3S1</ei> charmonium states.
</pvec>
<pvec name="Charmonium:O(3S1)[3S1(8)]" default="0.0119,0.0050"
min="0.0">
The colour-octet long-distance matrix
elements <ei><O[3S1(8)]></ei> for the <ei>3S1</ei> charmonium states.
</pvec>
<pvec name="Charmonium:O(3S1)[1S0(8)]" default="0.01,0.004" min="0.0">
The colour-octet long-distance matrix
elements <ei><O[1S0(8)]></ei> for the <ei>3S1</ei>
charmonium states.
</pvec>
<pvec name="Charmonium:O(3S1)[3P0(8)]" default="0.01,0.004" min="0.0">
The colour-octet long-distance matrix
elements <ei><O[3P0(8)]>/m_Q^2</ei> for the <ei>3S1</ei> charmonium
states. The remaining <ei><O[3PJ(8)]>/m_Q^2</ei>
are calculated from these long-distance matrix elements.
</parm>
<fvec name="Charmonium:gg2ccbar(3S1)[3S1(1)]g" default="off,off">
Colour-singlet production of <ei>3S1</ei> charmonium states via
<ei>g g → ccbar[3S1(1)] g</ei>.
Code 401.
</fvec>
<fvec name="Charmonium:gg2ccbar(3S1)[3S1(8)]g" default="off,off">
Colour-octet production of <ei>3S1</ei> charmonium states via
<ei>g g → ccbar[3S1(8)] g</ei>.
Code 402.
</fvec>
<fvec name="Charmonium:qg2ccbar(3S1)[3S1(8)]q" default="off,off">
Colour-octet production of <ei>3S1</ei> charmonium states via
<ei>q g → ccbar[3S1(8)] q</ei>.
Code 403.
</fvec>
<fvec name="Charmonium:qqbar2ccbar(3S1)[3S1(8)]g" default="off,off">
Colour-octet production of <ei>3S1</ei> charmonium states via
<ei>q qbar → ccbar[3S1(8)] g</ei>.
Code 404.
</fvec>
<fvec name="Charmonium:gg2ccbar(3S1)[1S0(8)]g" default="off,off">
Colour-octet production of <ei>3S1</ei> charmonium states via
<ei>g g → ccbar[1S0(8)] g</ei>.
Code 405.
</fvec>
<fvec name="Charmonium:qg2ccbar(3S1)[1S0(8)]q" default="off,off">
Colour-octet production of <ei>3S1</ei> charmonium states via
<ei>q g → ccbar[1S0(8)] q</ei>.
Code 406.
</fvec>
<fvec name="Charmonium:qqbar2ccbar(3S1)[1S0(8)]g" default="off,off">
Colour-octet production of <ei>3S1</ei> charmonium states via
<ei>q qbar → ccbar[1S0(8)] g</ei>.
Code 407.
</fvec>
<fvec name="Charmonium:gg2ccbar(3S1)[3PJ(8)]g" default="off,off">
Colour-octet production of <ei>3S1</ei> charmonium states via
<ei>g g → ccbar[3PJ(8)] g</ei>.
Code 408.
</fvec>
<fvec name="Charmonium:qg2ccbar(3S1)[3PJ(8)]q" default="off,off">
Colour-octet production of <ei>3S1</ei> charmonium states via
<ei>q g → ccbar[3PJ(8)] q</ei>.
Code 409.
</fvec>
<fvec name="Charmonium:qqbar2ccbar(3S1)[3PJ(8)]g" default="off,off">
Colour-octet production of <ei>3S1</ei> charmonium states via
<ei>q qbar → ccbar[3SJ(8)] g</ei>.
Code 410.
</fvec>
<h3>Charmonium 3PJ States</h3>
<mvec name="Charmonium:states(3PJ)" default="10441,20443,445">
The <ei>3PJ</ei> charmonium states that can be produced from the following
processes. Note that all vectors within this section,
either of flags or parameters, must be the same length as this
vector.
</mvec>
<pvec name="Charmonium:O(3PJ)[3P0(1)]" default="0.05,0.05,0.05"
min="0.0">
The color-singlet long-distance matrix elements
<ei><O[3P0(1)]>/m_Q^2</ei> for the <ei>3PJ</ei> charmonium
states. The remaining <ei><O[3PJ(1)]>/m_Q^2</ei>
are calculated from these long-distance matrix elements.
</pvec>
<pvec name="Charmonium:O(3PJ)[3S1(8)]" default="0.0031,0.0031,0.0031"
min="0.0">
The color-singlet long-distance matrix elements
<ei><O[3S1(8)]></ei> for the <ei>3PJ</ei> charmonium states.
</pvec>
<fvec name="Charmonium:gg2ccbar(3PJ)[3PJ(1)]g" default="off,off,off">
Colour-singlet production of <ei>3PJ</ei> charmonium states via
<ei>g g → ccbar[3PJ(1)] g</ei>.
Code 411.
</fvec>
<fvec name="Charmonium:qg2ccbar(3PJ)[3PJ(1)]q" default="off,off,off">
Colour-singlet production of <ei>3PJ</ei> charmonium states via
<ei>q g → ccbar[3PJ(1)] q</ei>.
Code 412.
</fvec>
<fvec name="Charmonium:qqbar2ccbar(3PJ)[3PJ(1)]g" default="off,off,off">
Colour-singlet production of <ei>3PJ</ei> charmonium states via
<ei>q qbar → ccbar[3PJ(1)] g</ei>.
Code 413.
</fvec>
<fvec name="Charmonium:gg2ccbar(3PJ)[3S1(8)]g" default="off,off,off">
Colour-octet production of <ei>3PJ</ei> charmonium states via
<ei>g g → ccbar[3S1(8)] g</ei>.
Code 414.
</fvec>
<fvec name="Charmonium:qg2ccbar(3PJ)[3S1(8)]q" default="off,off,off">
Colour-octet production of <ei>3PJ</ei> charmonium states via
<ei>q g → ccbar[3S1(8)] q</ei>.
Code 415.
</fvec>
<fvec name="Charmonium:qqbar2ccbar(3PJ)[3S1(8)]g" default="off,off,off">
Colour-octet production of <ei>3PJ</ei> charmonium states via
<ei>q qbar → ccbar[3S1(8)] g</ei>.
Code 416.
</fvec>
<h3>Charmonium 3DJ States</h3>
<mvec name="Charmonium:states(3DJ)" default="30443">
The <ei>3DJ</ei> charmonium states that can be produced from the following
processes. Note that all vectors within this section,
either of flags or parameters, must be the same length as this
vector.
</mvec>
<pvec name="Charmonium:O(3DJ)[3D1(1)]" default="0.161" min="0.0">
The color-singlet long-distance matrix elements
<ei><O[3D1(1)]></ei> for the <ei>3PJ</ei> charmonium
states. For a <ei>3DJ</ei> charmonium state where <ei>J</ei> is
not <ei>1</ei> the long distance matrix
element <ei><O[3DJ(1)]></ei> is calculated
by <ei>(2J+1)<O[3D1(1)]/3></ei> using leading order spin symmetry
relations.
</pvec>
<pvec name="Charmonium:O(3DJ)[3P0(8)]" default="0.01" min="0.0">
The colour-octet long-distance matrix
elements <ei><O[3P0(8)]>/m_Q^2</ei> for the 3DJ charmonium
states. The remaining <ei><O[3PJ(8)]>/m_Q^2</ei>
are calculated from these long-distance matrix elements.
</parm>
<fvec name="Charmonium:gg2ccbar(3DJ)[3DJ(1)]g" default="off">
Colour-singlet production of <ei>3PJ</ei> charmonium states via
<ei>g g → ccbar[3DJ(1)] g</ei>.
Code 417.
</fvec>
<fvec name="Charmonium:gg2ccbar(3DJ)[3PJ(8)]g" default="off">
Colour-octet production of <ei>3DJ</ei> charmonium states via
<ei>g g → ccbar[3PJ(8)] g</ei>.
Code 418.
</fvec>
<fvec name="Charmonium:qg2ccbar(3DJ)[3PJ(8)]q" default="off">
Colour-octet production of <ei>3DJ</ei> charmonium states via
<ei>q g → ccbar[3PJ(8)] q</ei>.
Code 419.
</fvec>
<fvec name="Charmonium:qqbar2ccbar(3DJ)[3PJ(8)]g" default="off">
Colour-octet production of <ei>3DJ</ei> charmonium states via
<ei>q qbar → ccbar[3PJ(8)] g</ei>.
Code 420.
</fvec>
<h3>Bottomonium 3S1 States</h3>
<mvec name="Bottomonium:states(3S1)" default="553,100553,200553"
min="0">
The <ei>3S1</ei> bottomonium states that can be produced from the following
processes. Note that all vectors within this section,
either of flags or parameters, must be the same length as this
vector.
</mvec>
<pvec name="Bottomonium:O(3S1)[3S1(1)]" default="9.28,4.63,3.54" min="0.0">
The colour-singlet long-distance matrix
elements <ei><O[3S1(1)]></ei> for the <ei>3S1</ei> bottomonium states.
</pvec>
<pvec name="Bottomonium:O(3S1)[3S1(8)]" default="0.15,0.045,0.075"
min="0.0">
The colour-octet long-distance matrix
elements <ei><O[3S1(8)]></ei> for the <ei>3S1</ei> bottomonium states.
</pvec>
<pvec name="Bottomonium:O(3S1)[1S0(8)]" default="0.02,0.06,0.1" min="0.0">
The colour-octet long-distance matrix
elements <ei><O[1S0(8)]></ei> for the <ei>3S1</ei>
bottomonium states.
</pvec>
<pvec name="Bottomonium:O(3S1)[3P0(8)]" default="0.02,0.06,0.1" min="0.0">
The colour-octet long-distance matrix
elements <ei><O[3P0(8)]>/m_Q^2</ei> for the <ei>3S1</ei> bottomonium
states. The remaining <ei><O[3PJ(8)]>/m_Q^2</ei>
are calculated from these long-distance matrix elements.
</parm>
<fvec name="Bottomonium:gg2bbbar(3S1)[3S1(1)]g" default="off,off,off">
Colour-singlet production of <ei>3S1</ei> bottomonium states via
<ei>g g → bbbar[3S1(1)] g</ei>.
Code 501.
</fvec>
<fvec name="Bottomonium:gg2bbbar(3S1)[3S1(8)]g" default="off,off,off">
Colour-octet production of <ei>3S1</ei> bottomonium states via
<ei>g g → bbbar[3S1(8)] g</ei>.
Code 502.
</fvec>
<fvec name="Bottomonium:qg2bbbar(3S1)[3S1(8)]q" default="off,off,off">
Colour-octet production of <ei>3S1</ei> bottomonium states via
<ei>q g → bbbar[3S1(8)] q</ei>.
Code 503.
</fvec>
<fvec name="Bottomonium:qqbar2bbbar(3S1)[3S1(8)]g" default="off,off,off">
Colour-octet production of <ei>3S1</ei> bottomonium states via
<ei>q qbar → bbbar[3S1(8)] g</ei>.
Code 504.
</fvec>
<fvec name="Bottomonium:gg2bbbar(3S1)[1S0(8)]g" default="off,off,off">
Colour-octet production of <ei>3S1</ei> bottomonium states via
<ei>g g → bbbar[1S0(8)] g</ei>.
Code 505.
</fvec>
<fvec name="Bottomonium:qg2bbbar(3S1)[1S0(8)]q" default="off,off,off">
Colour-octet production of <ei>3S1</ei> bottomonium states via
<ei>q g → bbbar[1S0(8)] q</ei>.
Code 506.
</fvec>
<fvec name="Bottomonium:qqbar2bbbar(3S1)[1S0(8)]g" default="off,off,off">
Colour-octet production of <ei>3S1</ei> bottomonium states via
<ei>q qbar → bbbar[1S0(8)] g</ei>.
Code 507.
</fvec>
<fvec name="Bottomonium:gg2bbbar(3S1)[3PJ(8)]g" default="off,off,off">
Colour-octet production of <ei>3S1</ei> bottomonium states via
<ei>g g → bbbar[3PJ(8)] g</ei>.
Code 508.
</fvec>
<fvec name="Bottomonium:qg2bbbar(3S1)[3PJ(8)]q" default="off,off,off">
Colour-octet production of <ei>3S1</ei> bottomonium states via
<ei>q g → bbbar[3PJ(8)] q</ei>.
Code 509.
</fvec>
<fvec name="Bottomonium:qqbar2bbbar(3S1)[3PJ(8)]g" default="off,off,off">
Colour-octet production of <ei>3S1</ei> bottomonium states via
<ei>q qbar → bbbar[3SJ(8)] g</ei>.
Code 510.
</fvec>
<h3>Bottomonium 3PJ States</h3>
<mvec name="Bottomonium:states(3PJ)" default="10551,20553,555">
The <ei>3PJ</ei> bottomonium states that can be produced from the following
processes. Note that all vectors within this section,
either of flags or parameters, must be the same length as this
vector.
</mvec>
<pvec name="Bottomonium:O(3PJ)[3P0(1)]" default="0.085,0.085,0.085"
min="0.0">
The color-singlet long-distance matrix elements
<ei><O[3P0(1)]>/m_Q^2</ei> for the <ei>3PJ</ei> bottomonium
states. The remaining <ei><O[3PJ(1)]>/m_Q^2</ei>
are calculated from these long-distance matrix elements.
</pvec>
<pvec name="Bottomonium:O(3PJ)[3S1(8)]" default="0.04,0.04,0.04"
min="0.0">
The color-singlet long-distance matrix elements
<ei><O[3S1(8)]></ei> for the <ei>3PJ</ei> bottomonium states.
</pvec>
<fvec name="Bottomonium:gg2bbbar(3PJ)[3PJ(1)]g" default="off,off,off">
Colour-singlet production of <ei>3PJ</ei> bottomonium states via
<ei>g g → bbbar[3PJ(1)] g</ei>.
Code 511.
</fvec>
<fvec name="Bottomonium:qg2bbbar(3PJ)[3PJ(1)]q" default="off,off,off">
Colour-singlet production of <ei>3PJ</ei> bottomonium states via
<ei>q g → bbbar[3PJ(1)] q</ei>.
Code 512.
</fvec>
<fvec name="Bottomonium:qqbar2bbbar(3PJ)[3PJ(1)]g" default="off,off,off">
Colour-singlet production of <ei>3PJ</ei> bottomonium states via
<ei>q qbar → bbbar[3PJ(1)] g</ei>.
Code 513.
</fvec>
<fvec name="Bottomonium:gg2bbbar(3PJ)[3S1(8)]g" default="off,off,off">
Colour-octet production of <ei>3PJ</ei> bottomonium states via
<ei>g g → bbbar[3S1(8)] g</ei>.
Code 514.
</fvec>
<fvec name="Bottomonium:qg2bbbar(3PJ)[3S1(8)]q" default="off,off,off">
Colour-octet production of <ei>3PJ</ei> bottomonium states via
<ei>q g → bbbar[3S1(8)] q</ei>.
Code 515.
</fvec>
<fvec name="Bottomonium:qqbar2bbbar(3PJ)[3S1(8)]g" default="off,off,off">
Colour-octet production of <ei>3PJ</ei> bottomonium states via
<ei>q qbar → bbbar[3S1(8)] g</ei>.
Code 516.
</fvec>
<h3>Bottomonium 3DJ States</h3>
<mvec name="Bottomonium:states(3DJ)" default="">
The <ei>3DJ</ei> bottomonium states that can be produced from the following
processes. Currently, no <ei>3DJ</ei> states are included in the
default <code>ParticleData</code> and so none are included here. Note
that all vectors within this section, either of flags or parameters,
must be the same length as this vector.
</mvec>
<pvec name="Bottomonium:O(3DJ)[3D1(1)]" default="" min="0.0">
The color-singlet long-distance matrix elements
<ei><O[3D1(1)]></ei> for the <ei>3PJ</ei> bottomonium
states. For a <ei>3DJ</ei> bottomonium state where <ei>J</ei> is
not <ei>1</ei> the long distance matrix
element <ei><O[3DJ(1)]></ei> is calculated
by <ei>(2J+1)<O[3D1(1)]/3></ei> using leading order spin symmetry
relations.
</pvec>
<pvec name="Bottomonium:O(3DJ)[3P0(8)]" default="" min="0.0">
The colour-octet long-distance matrix
elements <ei><O[3P0(8)]>/m_Q^2</ei> for the 3DJ bottomonium
states. The remaining <ei><O[3PJ(8)]>/m_Q^2</ei>
are calculated from these long-distance matrix elements.
</parm>
<fvec name="Bottomonium:gg2bbbar(3DJ)[3DJ(1)]g" default="">
Colour-singlet production of <ei>3PJ</ei> bottomonium states via
<ei>g g → bbbar[3DJ(1)] g</ei>.
Code 517.
</fvec>
<fvec name="Bottomonium:gg2bbbar(3DJ)[3PJ(8)]g" default="">
Colour-octet production of <ei>3DJ</ei> bottomonium states via
<ei>g g → bbbar[3PJ(8)] g</ei>.
Code 518.
</fvec>
<fvec name="Bottomonium:qg2bbbar(3DJ)[3PJ(8)]q" default="">
Colour-octet production of <ei>3DJ</ei> bottomonium states via
<ei>q g → bbbar[3PJ(8)] q</ei>.
Code 519.
</fvec>
<fvec name="Bottomonium:qqbar2bbbar(3DJ)[3PJ(8)]g" default="">
Colour-octet production of <ei>3DJ</ei> bottomonium states via
<ei>q qbar → bbbar[3PJ(8)] g</ei>.
Code 520.
</fvec>
</chapter>
<!-- Copyright (C) 2014 Torbjorn Sjostrand -->
Marcin Chrzaszcz