<html> <head> <title>New-Gauge-Boson Processes</title> <link rel="stylesheet" type="text/css" href="pythia.css"/> <link rel="shortcut icon" href="pythia32.gif"/> </head> <body> <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. </body> </html> <!-- Copyright (C) 2014 Torbjorn Sjostrand -->
