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<title>New-Gauge-Boson Processes</title>
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<h2>New-Gauge-Boson Processes</h2>
This page contains the production of new <i>Z'^0</i> and
<i>W'^+-</i> gauge bosons, e.g. within the context of a new
<i>U(1)</i> or <i>SU(2)</i> gauge group, and also a
(rather speculative) horizontal gauge boson <i>R^0</i>.
Left-right-symmetry scenarios also contain new gauge bosons,
but are described
<a href="LeftRightSymmetryProcesses.html" target="page">separately</a>.
<h3><i>Z'^0</i></h3>
This group only contains one subprocess, with the full
<i>gamma^*/Z^0/Z'^0</i> interference structure for couplings
to fermion pairs. It is possible to pick only a subset, e.g, only
the pure <i>Z'^0</i> piece. No higher-order processes are
available explicitly, but the ISR showers contain automatic
matching to the <i>Z'^0</i> + 1 jet matrix elements, as for
the corresponding <i>gamma^*/Z^0</i> process.
<p/><code>flag </code><strong> NewGaugeBoson:ffbar2gmZZprime </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scattering <i>f fbar →Z'^0</i>.
Code 3001.
<p/><code>mode </code><strong> Zprime:gmZmode </strong>
(<code>default = <strong>0</strong></code>; <code>minimum = 0</code>; <code>maximum = 6</code>)<br/>
Choice of full <i>gamma^*/Z^0/Z'^0</i> structure or not in
the above process. Note that, with the <i>Z'^0</i> part switched
off, this process is reduced to what already exists among
<a href="ElectroweakProcesses.html" target="page">electroweak processes</a>,
so those options are here only for crosschecks.
<br/><code>option </code><strong> 0</strong> : full <i>gamma^*/Z^0/Z'^0</i> structure,
with interference included.
<br/><code>option </code><strong> 1</strong> : only pure <i>gamma^*</i> contribution.
<br/><code>option </code><strong> 2</strong> : only pure <i>Z^0</i> contribution.
<br/><code>option </code><strong> 3</strong> : only pure <i>Z'^0</i> contribution.
<br/><code>option </code><strong> 4</strong> : only the <i>gamma^*/Z^0</i> contribution,
including interference.
<br/><code>option </code><strong> 5</strong> : only the <i>gamma^*/Z'^0</i> contribution,
including interference.
<br/><code>option </code><strong> 6</strong> : only the <i>Z^0/Z'^0</i> contribution,
including interference.
<br/><b>Note</b>: irrespective of the option used, the particle produced
will always be assigned code 32 for <i>Z'^0</i>, and open decay channels
is purely dictated by what is set for the <i>Z'^0</i>.
<p/>
The couplings of the <i>Z'^0</i> to quarks and leptons can
either be assumed universal, i.e. generation-independent, or not.
In the former case eight numbers parametrize the vector and axial
couplings of down-type quarks, up-type quarks, leptons and neutrinos,
respectively. Depending on your assumed neutrino nature you may
want to restrict your freedom in that sector, but no limitations
are enforced by the program. The default corresponds to the same
couplings as that of the Standard Model <i>Z^0</i>, with axial
couplings <i>a_f = +-1</i> and vector couplings
<i>v_f = a_f - 4 e_f sin^2(theta_W)</i>, with
<i>sin^2(theta_W) = 0.23</i>. Without universality
the same eight numbers have to be set separately also for the
second and the third generation. The choice of fixed axial and
vector couplings implies a resonance width that increases linearly
with the <i>Z'^0</i> mass.
<p/>
By a suitable choice of the parameters, it is possible to simulate
just about any imaginable <i>Z'^0</i> scenario, with full
interference effects in cross sections and decay angular
distributions and generation-dependent couplings; the default values
should mainly be viewed as placeholders. The conversion
from the coupling conventions in a set of different <i>Z'^0</i>
models in the literature to those used in PYTHIA is described in
[<a href="Bibliography.html" target="page">Cio08</a>].
<p/><code>flag </code><strong> Zprime:universality </strong>
(<code>default = <strong>on</strong></code>)<br/>
If on then you need only set the first-generation couplings
below, and these are automatically also used for the second and
third generation. If off, then couplings can be chosen separately
for each generation.
<p/>
Here are the couplings always valid for the first generation,
and normally also for the second and third by trivial analogy:
<p/><code>parm </code><strong> Zprime:vd </strong>
(<code>default = <strong>-0.693</strong></code>)<br/>
vector coupling of <i>d</i> quarks.
<p/><code>parm </code><strong> Zprime:ad </strong>
(<code>default = <strong>-1.</strong></code>)<br/>
axial coupling of <i>d</i> quarks.
<p/><code>parm </code><strong> Zprime:vu </strong>
(<code>default = <strong>0.387</strong></code>)<br/>
vector coupling of <i>u</i> quarks.
<p/><code>parm </code><strong> Zprime:au </strong>
(<code>default = <strong>1.</strong></code>)<br/>
axial coupling of <i>u</i> quarks.
<p/><code>parm </code><strong> Zprime:ve </strong>
(<code>default = <strong>-0.08</strong></code>)<br/>
vector coupling of <i>e</i> leptons.
<p/><code>parm </code><strong> Zprime:ae </strong>
(<code>default = <strong>-1.</strong></code>)<br/>
axial coupling of <i>e</i> leptons.
<p/><code>parm </code><strong> Zprime:vnue </strong>
(<code>default = <strong>1.</strong></code>)<br/>
vector coupling of <i>nu_e</i> neutrinos.
<p/><code>parm </code><strong> Zprime:anue </strong>
(<code>default = <strong>1.</strong></code>)<br/>
axial coupling of <i>nu_e</i> neutrinos.
<p/>
Here are the further couplings that are specific for
a scenario with <code>Zprime:universality</code> switched off:
<p/><code>parm </code><strong> Zprime:vs </strong>
(<code>default = <strong>-0.693</strong></code>)<br/>
vector coupling of <i>s</i> quarks.
<p/><code>parm </code><strong> Zprime:as </strong>
(<code>default = <strong>-1.</strong></code>)<br/>
axial coupling of <i>s</i> quarks.
<p/><code>parm </code><strong> Zprime:vc </strong>
(<code>default = <strong>0.387</strong></code>)<br/>
vector coupling of <i>c</i> quarks.
<p/><code>parm </code><strong> Zprime:ac </strong>
(<code>default = <strong>1.</strong></code>)<br/>
axial coupling of <i>c</i> quarks.
<p/><code>parm </code><strong> Zprime:vmu </strong>
(<code>default = <strong>-0.08</strong></code>)<br/>
vector coupling of <i>mu</i> leptons.
<p/><code>parm </code><strong> Zprime:amu </strong>
(<code>default = <strong>-1.</strong></code>)<br/>
axial coupling of <i>mu</i> leptons.
<p/><code>parm </code><strong> Zprime:vnumu </strong>
(<code>default = <strong>1.</strong></code>)<br/>
vector coupling of <i>nu_mu</i> neutrinos.
<p/><code>parm </code><strong> Zprime:anumu </strong>
(<code>default = <strong>1.</strong></code>)<br/>
axial coupling of <i>nu_mu</i> neutrinos.
<p/><code>parm </code><strong> Zprime:vb </strong>
(<code>default = <strong>-0.693</strong></code>)<br/>
vector coupling of <i>b</i> quarks.
<p/><code>parm </code><strong> Zprime:ab </strong>
(<code>default = <strong>-1.</strong></code>)<br/>
axial coupling of <i>b</i> quarks.
<p/><code>parm </code><strong> Zprime:vt </strong>
(<code>default = <strong>0.387</strong></code>)<br/>
vector coupling of <i>t</i> quarks.
<p/><code>parm </code><strong> Zprime:at </strong>
(<code>default = <strong>1.</strong></code>)<br/>
axial coupling of <i>t</i> quarks.
<p/><code>parm </code><strong> Zprime:vtau </strong>
(<code>default = <strong>-0.08</strong></code>)<br/>
vector coupling of <i>tau</i> leptons.
<p/><code>parm </code><strong> Zprime:atau </strong>
(<code>default = <strong>-1.</strong></code>)<br/>
axial coupling of <i>tau</i> leptons.
<p/><code>parm </code><strong> Zprime:vnutau </strong>
(<code>default = <strong>1.</strong></code>)<br/>
vector coupling of <i>nu_tau</i> neutrinos.
<p/><code>parm </code><strong> Zprime:anutau </strong>
(<code>default = <strong>1.</strong></code>)<br/>
axial coupling of <i>nu_tau</i> neutrinos.
<p/>
The coupling to the decay channel <i>Z'^0 → W^+ W^-</i> is
more model-dependent. By default it is therefore off, but can be
switched on as follows. Furthermore, we have left some amount of
freedom in the choice of decay angular correlations in this
channel, but obviously alternative shapes could be imagined.
<p/><code>parm </code><strong> Zprime:coup2WW </strong>
(<code>default = <strong>0.</strong></code>; <code>minimum = 0.</code>)<br/>
the coupling <i>Z'^0 → W^+ W^-</i> is taken to be this number
times <i>m_W^2 / m_Z'^2</i> times the <i>Z^0 → W^+ W^-</i>
coupling. Thus a unit value corresponds to the
<i>Z^0 → W^+ W^-</i> coupling, scaled down by a factor
<i>m_W^2 / m_Z'^2</i>, and gives a <i>Z'^0</i> partial
width into this channel that again increases linearly. If you
cancel this behaviour, by letting <code>Zprime:coup2WW</code> be
proportional to <i>m_Z'^2 / m_W^2</i>, you instead obtain a
partial width that goes like the fifth power of the <i>Z'^0</i>
mass. These two extremes correspond to the "extended gauge model"
and the "reference model", respectively, of [<a href="Bibliography.html" target="page">Alt89</a>].
Note that this channel only includes the pure <i>Z'</i> part,
while <i>f fbar → gamma^*/Z^*0 → W^+ W^-</i> is available
as a separate electroweak process.
<p/><code>parm </code><strong> Zprime:anglesWW </strong>
(<code>default = <strong>0.</strong></code>; <code>minimum = 0.</code>; <code>maximum = 1.</code>)<br/>
in the decay chain <i>Z'^0 → W^+ W^- →f_1 fbar_2 f_3 fbar_4</i>
the decay angular distributions is taken to be a mixture of two
possible shapes. This parameter gives the fraction that is distributed
as in Higgs <i>h^0 → W^+ W^-</i> (longitudinal bosons),
with the remainder (by default all) is taken to be the same as for
<i>Z^0 → W^+ W^-</i> (a mixture of transverse and longitudinal
bosons).
<p/>
A massive <i>Z'^0</i> is also likely to decay into Higgs bosons
and potentially into other now unknown particles. Such possibilities
clearly are quite model-dependent, and have not been included
for now.
<h3><i>W'^+-</i></h3>
The <i>W'^+-</i> implementation is less ambitious than the
<i>Z'^0</i>. Specifically, while indirect detection of a
<i>Z'^0</i> through its interference contribution is
a possible discovery channel in lepton colliders, there is no
equally compelling case for <i>W^+-/W'^+-</i> interference
effects being of importance for discovery, and such interference
has therefore not been implemented for now. Related to this, a
<i>Z'^0</i> could appear on its own in a new <i>U(1)</i> group,
while <i>W'^+-</i> would have to sit in a <i>SU(2)</i> group
and thus have a <i>Z'^0</i> partner that is likely to be found
first. Only one process is implemented but, like for the
<i>W^+-</i>, the ISR showers contain automatic matching to the
<i>W'^+-</i> + 1 jet matrix elements.
<p/><code>flag </code><strong> NewGaugeBoson:ffbar2Wprime </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scattering <i>f fbar' → W'^+-</i>.
Code 3021.
<p/>
The couplings of the <i>W'^+-</i> are here assumed universal,
i.e. the same for all generations. One may set vector and axial
couplings freely, separately for the <i>q qbar'</i> and the
<i>l nu_l</i> decay channels. The defaults correspond to the
<i>V - A</i> structure and normalization of the Standard Model
<i>W^+-</i>, but can be changed to simulate a wide selection
of models. One limitation is that, for simplicity, the same
Cabibbo--Kobayashi--Maskawa quark mixing matrix is assumed as for
the standard <i>W^+-</i>. Depending on your assumed neutrino
nature you may want to restrict your freedom in the lepton sector,
but no limitations are enforced by the program.
<p/><code>parm </code><strong> Wprime:vq </strong>
(<code>default = <strong>1.</strong></code>)<br/>
vector coupling of quarks.
<p/><code>parm </code><strong> Wprime:aq </strong>
(<code>default = <strong>-1.</strong></code>)<br/>
axial coupling of quarks.
<p/><code>parm </code><strong> Wprime:vl </strong>
(<code>default = <strong>1.</strong></code>)<br/>
vector coupling of leptons.
<p/><code>parm </code><strong> Wprime:al </strong>
(<code>default = <strong>-1.</strong></code>)<br/>
axial coupling of leptons.
<p/>
The coupling to the decay channel <i>W'^+- → W^+- Z^0</i> is
more model-dependent, like for <i>Z'^0 → W^+ W^-</i> described
above. By default it is therefore off, but can be
switched on as follows. Furthermore, we have left some amount of
freedom in the choice of decay angular correlations in this
channel, but obviously alternative shapes could be imagined.
<p/><code>parm </code><strong> Wprime:coup2WZ </strong>
(<code>default = <strong>0.</strong></code>; <code>minimum = 0.</code>)<br/>
the coupling <i>W'^0 → W^+- Z^0</i> is taken to be this number
times <i>m_W^2 / m_W'^2</i> times the <i>W^+- → W^+- Z^0</i>
coupling. Thus a unit value corresponds to the
<i>W^+- → W^+- Z^0</i> coupling, scaled down by a factor
<i>m_W^2 / m_W'^2</i>, and gives a <i>W'^+-</i> partial
width into this channel that increases linearly with the
<i>W'^+-</i> mass. If you cancel this behaviour, by letting
<code>Wprime:coup2WZ</code> be proportional to <i>m_W'^2 / m_W^2</i>,
you instead obtain a partial width that goes like the fifth power
of the <i>W'^+-</i> mass. These two extremes correspond to the
"extended gauge model" and the "reference model", respectively,
of [<a href="Bibliography.html" target="page">Alt89</a>].
<p/><code>parm </code><strong> Wprime:anglesWZ </strong>
(<code>default = <strong>0.</strong></code>; <code>minimum = 0.</code>; <code>maximum = 1.</code>)<br/>
in the decay chain <i>W'^+- → W^+- Z^0 →f_1 fbar_2 f_3 fbar_4</i>
the decay angular distributions is taken to be a mixture of two
possible shapes. This parameter gives the fraction that is distributed
as in Higgs <i>H^+- → W^+- Z^0</i> (longitudinal bosons),
with the remainder (by default all) is taken to be the same as for
<i>W^+- → W^+- Z^0</i> (a mixture of transverse and longitudinal
bosons).
<p/>
A massive <i>W'^+-</i> is also likely to decay into Higgs bosons
and potentially into other now unknown particles. Such possibilities
clearly are quite model-dependent, and have not been included
for now.
<h3><i>R^0</i></h3>
The <i>R^0</i> boson (particle code 41) represents one possible
scenario for a horizontal gauge boson, i.e. a gauge boson
that couples between the generations, inducing processes like
<i>s dbar → R^0 → mu^- e^+</i>. Experimental limits on
flavour-changing neutral currents forces such a boson to be fairly
heavy. In spite of being neutral the antiparticle is distinct from
the particle: one carries a net positive generation number and
the other a negative one. This particular model has no new
parameters beyond the <i>R^0</i> mass. Decays are assumed isotropic.
For further details see [<a href="Bibliography.html" target="page">Ben85</a>].
<p/><code>flag </code><strong> NewGaugeBoson:ffbar2R0 </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scattering <i>f_1 fbar_2 → R^0 → f_3 fbar_4</i>, where
<i>f_1</i> and <i>fbar_2</i> are separated by <i>+-</i> one
generation and similarly for <i>f_3</i> and <i>fbar_4</i>.
Thus possible final states are e.g. <i>d sbar</i>, <i>u cbar</i>
<i>s bbar</i>, <i>c tbar</i>, <i>e- mu+</i> and
<i>mu- tau+</i>.
Code 3041.
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