## New-Gauge-Boson Processes

This page contains the production of new Z'^0 and W'^+- gauge bosons, e.g. within the context of a new U(1) or SU(2) gauge group, and also a (rather speculative) horizontal gauge boson R^0. Left-right-symmetry scenarios also contain new gauge bosons, but are described separately.

### Z'^0

This group only contains one subprocess, with the full gamma^*/Z^0/Z'^0 interference structure for couplings to fermion pairs. It is possible to pick only a subset, e.g, only the pure Z'^0 piece. No higher-order processes are available explicitly, but the ISR showers contain automatic matching to the Z'^0 + 1 jet matrix elements, as for the corresponding gamma^*/Z^0 process.

`flag` NewGaugeBoson:ffbar2gmZZprime (`default = off`)
Scattering f fbar →Z'^0. Code 3001.

`mode` Zprime:gmZmode (`default = 0`; `minimum = 0`; `maximum = 6`)
Choice of full gamma^*/Z^0/Z'^0 structure or not in the above process. Note that, with the Z'^0 part switched off, this process is reduced to what already exists among electroweak processes, so those options are here only for crosschecks.
`option` 0 : full gamma^*/Z^0/Z'^0 structure, with interference included.
`option` 1 : only pure gamma^* contribution.
`option` 2 : only pure Z^0 contribution.
`option` 3 : only pure Z'^0 contribution.
`option` 4 : only the gamma^*/Z^0 contribution, including interference.
`option` 5 : only the gamma^*/Z'^0 contribution, including interference.
`option` 6 : only the Z^0/Z'^0 contribution, including interference.
Note: irrespective of the option used, the particle produced will always be assigned code 32 for Z'^0, and open decay channels is purely dictated by what is set for the Z'^0.

The couplings of the Z'^0 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 Z^0, with axial couplings a_f = +-1 and vector couplings v_f = a_f - 4 e_f sin^2(theta_W), with sin^2(theta_W) = 0.23. 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 Z'^0 mass.

By a suitable choice of the parameters, it is possible to simulate just about any imaginable Z'^0 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 Z'^0 models in the literature to those used in PYTHIA is described in [Cio08].

`flag` Zprime:universality (`default = on`)
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.

Here are the couplings always valid for the first generation, and normally also for the second and third by trivial analogy:

`parm` Zprime:vd (`default = -0.693`)
vector coupling of d quarks.

`parm` Zprime:ad (`default = -1.`)
axial coupling of d quarks.

`parm` Zprime:vu (`default = 0.387`)
vector coupling of u quarks.

`parm` Zprime:au (`default = 1.`)
axial coupling of u quarks.

`parm` Zprime:ve (`default = -0.08`)
vector coupling of e leptons.

`parm` Zprime:ae (`default = -1.`)
axial coupling of e leptons.

`parm` Zprime:vnue (`default = 1.`)
vector coupling of nu_e neutrinos.

`parm` Zprime:anue (`default = 1.`)
axial coupling of nu_e neutrinos.

Here are the further couplings that are specific for a scenario with `Zprime:universality` switched off:

`parm` Zprime:vs (`default = -0.693`)
vector coupling of s quarks.

`parm` Zprime:as (`default = -1.`)
axial coupling of s quarks.

`parm` Zprime:vc (`default = 0.387`)
vector coupling of c quarks.

`parm` Zprime:ac (`default = 1.`)
axial coupling of c quarks.

`parm` Zprime:vmu (`default = -0.08`)
vector coupling of mu leptons.

`parm` Zprime:amu (`default = -1.`)
axial coupling of mu leptons.

`parm` Zprime:vnumu (`default = 1.`)
vector coupling of nu_mu neutrinos.

`parm` Zprime:anumu (`default = 1.`)
axial coupling of nu_mu neutrinos.

`parm` Zprime:vb (`default = -0.693`)
vector coupling of b quarks.

`parm` Zprime:ab (`default = -1.`)
axial coupling of b quarks.

`parm` Zprime:vt (`default = 0.387`)
vector coupling of t quarks.

`parm` Zprime:at (`default = 1.`)
axial coupling of t quarks.

`parm` Zprime:vtau (`default = -0.08`)
vector coupling of tau leptons.

`parm` Zprime:atau (`default = -1.`)
axial coupling of tau leptons.

`parm` Zprime:vnutau (`default = 1.`)
vector coupling of nu_tau neutrinos.

`parm` Zprime:anutau (`default = 1.`)
axial coupling of nu_tau neutrinos.

The coupling to the decay channel Z'^0 → W^+ W^- is more model-dependent. By default it is therefore off, but can be switched on as follows.

`parm` Zprime:coup2WW (`default = 0.`; `minimum = 0.`)
the coupling Z'^0 → W^+ W^- is taken to be this number times m_W^2 / m_Z'^2 times the Z^0 → W^+ W^- coupling. Thus a unit value corresponds to the Z^0 → W^+ W^- coupling, scaled down by a factor m_W^2 / m_Z'^2, and gives a Z'^0 partial width into this channel that again increases linearly. If you cancel this behaviour, by letting `Zprime:coup2WW` be proportional to m_Z'^2 / m_W^2, you instead obtain a partial width that goes like the fifth power of the Z'^0 mass. These two extremes correspond to the "extended gauge model" and the "reference model", respectively, of [Alt89]. Note that this channel only includes the pure Z' part, while f fbar → gamma^*/Z^*0 → W^+ W^- is available as a separate electroweak process. 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.

`parm` Zprime:anglesWW (`default = 0.`; `minimum = 0.`; `maximum = 1.`)
in the decay chain Z'^0 → W^+ W^- →f_1 fbar_2 f_3 fbar_4 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 h^0 → W^+ W^- (longitudinal bosons), with the remainder (by default all) is taken to be the same as for Z^0 → W^+ W^- (a mixture of transverse and longitudinal bosons).

A massive Z'^0 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.

Finally, to allow the exploration of more BSM physics scenarios, we include the possibility of the Z'^0 (and hence the gamma and Z^0) coupling to a fourth generation of fermions. This provides redundancy with and extensions beyond those processes implemented as fourth-generation processes. By default, the decay channels for the fourth-generation and not included. They are enabled using:

`flag` Zprime:coup2gen4 (`default = off`)
Z'^0 couples to 4th generation fermions.

Here are the further couplings that are specific for a scenario with `Zprime:universality` switched off:

`parm` Zprime:vbPrime (`default = -0.693`)
vector coupling of b' quarks.

`parm` Zprime:abPrime (`default = -1.`)
axial coupling of b' quarks.

`parm` Zprime:vtPrime (`default = 0.387`)
vector coupling of t' quarks.

`parm` Zprime:atPrime (`default = 1.`)
axial coupling of t' quarks.

`parm` Zprime:vtauPrime (`default = -0.08`)
vector coupling of tau' leptons.

`parm` Zprime:atauPrime (`default = -1.`)
axial coupling of tau' leptons.

`parm` Zprime:vnutauPrime (`default = 1.`)
vector coupling of nu_tau' neutrinos.

`parm` Zprime:anutauPrime (`default = 1.`)
axial coupling of nu_tau' neutrinos.

### W'^+-

The W'^+- implementation is less ambitious than the Z'^0. Specifically, while indirect detection of a Z'^0 through its interference contribution is a possible discovery channel in lepton colliders, there is no equally compelling case for W^+-/W'^+- interference effects being of importance for discovery, and such interference has therefore not been implemented for now. Related to this, a Z'^0 could appear on its own in a new U(1) group, while W'^+- would have to sit in a SU(2) group and thus have a Z'^0 partner that is likely to be found first. Only one process is implemented but, like for the W^+-, the ISR showers contain automatic matching to the W'^+- + 1 jet matrix elements.

`flag` NewGaugeBoson:ffbar2Wprime (`default = off`)
Scattering f fbar' → W'^+-. Code 3021.

The couplings of the W'^+- are here assumed universal, i.e. the same for all generations. One may set vector and axial couplings freely, separately for the q qbar' and the l nu_l decay channels. The defaults correspond to the V - A structure and normalization of the Standard Model W^+-, 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 W^+-. 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.

`parm` Wprime:vq (`default = 1.`)
vector coupling of quarks.

`parm` Wprime:aq (`default = -1.`)
axial coupling of quarks.

`parm` Wprime:vl (`default = 1.`)
vector coupling of leptons.

`parm` Wprime:al (`default = -1.`)
axial coupling of leptons.

The coupling to the decay channel W'^+- → W^+- Z^0 is model-dependent, like for Z'^0 → W^+ W^- 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.

`parm` Wprime:coup2WZ (`default = 0.`; `minimum = 0.`)
the coupling W'^0 → W^+- Z^0 is taken to be this number times m_W^2 / m_W'^2 times the W^+- → W^+- Z^0 coupling. Thus a unit value corresponds to the W^+- → W^+- Z^0 coupling, scaled down by a factor m_W^2 / m_W'^2, and gives a W'^+- partial width into this channel that increases linearly with the W'^+- mass. If you cancel this behaviour, by letting `Wprime:coup2WZ` be proportional to m_W'^2 / m_W^2, you instead obtain a partial width that goes like the fifth power of the W'^+- mass. These two extremes correspond to the "extended gauge model" and the "reference model", respectively, of [Alt89].

`parm` Wprime:anglesWZ (`default = 0.`; `minimum = 0.`; `maximum = 1.`)
in the decay chain W'^+- → W^+- Z^0 →f_1 fbar_2 f_3 fbar_4 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 H^+- → W^+- Z^0 (longitudinal bosons), with the remainder (by default all) is taken to be the same as for W^+- → W^+- Z^0 (a mixture of transverse and longitudinal bosons).

A massive W'^+- 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.

### R^0

The R^0 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 s dbar → R^0 → mu^- e^+. 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 R^0 mass. Decays are assumed isotropic. For further details see [Ben85].

`flag` NewGaugeBoson:ffbar2R0 (`default = off`)
Scattering f_1 fbar_2 → R^0 → f_3 fbar_4, where f_1 and fbar_2 are separated by +- one generation and similarly for f_3 and fbar_4. Thus possible final states are e.g. d sbar, u cbar s bbar, c tbar, e- mu+ and mu- tau+. Code 3041.