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2<head>
3<title>New-Gauge-Boson Processes</title>
4<link rel="stylesheet" type="text/css" href="pythia.css"/>
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6</head>
7<body>
8
9<h2>New-Gauge-Boson Processes</h2>
10
11This page contains the production of new <i>Z'^0</i> and
12<i>W'^+-</i> gauge bosons, e.g. within the context of a new
13<i>U(1)</i> or <i>SU(2)</i> gauge group, and also a
14(rather speculative) horizontal gauge boson <i>R^0</i>.
15Left-right-symmetry scenarios also contain new gauge bosons,
16but are described
17<a href="LeftRightSymmetryProcesses.html" target="page">separately</a>.
18 
19<h3><i>Z'^0</i></h3>
20 
21This group only contains one subprocess, with the full
22<i>gamma^*/Z^0/Z'^0</i> interference structure for couplings
23to fermion pairs. It is possible to pick only a subset, e.g, only
24the pure <i>Z'^0</i> piece. No higher-order processes are
25available explicitly, but the ISR showers contain automatic
26matching to the <i>Z'^0</i> + 1 jet matrix elements, as for
27the corresponding <i>gamma^*/Z^0</i> process.
28 
29<p/><code>flag&nbsp; </code><strong> NewGaugeBoson:ffbar2gmZZprime &nbsp;</strong> 
30 (<code>default = <strong>off</strong></code>)<br/>
31Scattering <i>f fbar ->Z'^0</i>.
32Code 3001.
33 
34
35<p/><code>mode&nbsp; </code><strong> Zprime:gmZmode &nbsp;</strong> 
36 (<code>default = <strong>0</strong></code>; <code>minimum = 0</code>; <code>maximum = 6</code>)<br/>
37Choice of full <i>gamma^*/Z^0/Z'^0</i> structure or not in
38the above process. Note that, with the <i>Z'^0</i> part switched
39off, this process is reduced to what already exists among
40<a href="ElectroweakProcesses.html" target="page">electroweak processes</a>,
41so those options are here only for crosschecks.
42<br/><code>option </code><strong> 0</strong> : full <i>gamma^*/Z^0/Z'^0</i> structure,
43with interference included. 
44<br/><code>option </code><strong> 1</strong> : only pure <i>gamma^*</i> contribution. 
45<br/><code>option </code><strong> 2</strong> : only pure <i>Z^0</i> contribution. 
46<br/><code>option </code><strong> 3</strong> : only pure <i>Z'^0</i> contribution. 
47<br/><code>option </code><strong> 4</strong> : only the <i>gamma^*/Z^0</i> contribution,
48including interference. 
49<br/><code>option </code><strong> 5</strong> : only the <i>gamma^*/Z'^0</i> contribution,
50including interference. 
51<br/><code>option </code><strong> 6</strong> : only the <i>Z^0/Z'^0</i> contribution,
52including interference. 
53<br/><b>Note</b>: irrespective of the option used, the particle produced
54will always be assigned code 32 for <i>Z'^0</i>, and open decay channels
55is purely dictated by what is set for the <i>Z'^0</i>.
56 
57
58<p/>
59The couplings of the <i>Z'^0</i> to quarks and leptons can
60either be assumed universal, i.e. generation-independent, or not.
61In the former case eight numbers parametrize the vector and axial
62couplings of down-type quarks, up-type quarks, leptons and neutrinos,
63respectively. Depending on your assumed neutrino nature you may
64want to restrict your freedom in that sector, but no limitations
65are enforced by the program. The default corresponds to the same
66couplings as that of the Standard Model <i>Z^0</i>, with axial
67couplings <i>a_f = +-1</i> and vector couplings
68<i>v_f = a_f - 4 e_f sin^2(theta_W)</i>, with
69<i>sin^2(theta_W) = 0.23</i>. Without universality
70the same eight numbers have to be set separately also for the
71second and the third generation. The choice of fixed axial and
72vector couplings implies a resonance width that increases linearly
73with the <i>Z'^0</i> mass.
74
75<p/>
76By a suitable choice of the parameters, it is possible to simulate
77just about any imaginable <i>Z'^0</i> scenario, with full
78interference effects in cross sections and decay angular
79distributions and generation-dependent couplings; the default values
80should mainly be viewed as placeholders. The conversion
81from the coupling conventions in a set of different <i>Z'^0</i> 
82models in the literature to those used in PYTHIA is described by
83<a href="http://www.hep.uiuc.edu/home/catutza/nota12.ps">C.
84Ciobanu et al.</a>
85
86<p/><code>flag&nbsp; </code><strong> Zprime:universality &nbsp;</strong> 
87 (<code>default = <strong>on</strong></code>)<br/>
88If on then you need only set the first-generation couplings
89below, and these are automatically also used for the second and
90third generation. If off, then couplings can be chosen separately
91for each generation.
92 
93
94<p/>
95Here are the couplings always valid for the first generation,
96and normally also for the second and third by trivial analogy:
97
98<p/><code>parm&nbsp; </code><strong> Zprime:vd &nbsp;</strong> 
99 (<code>default = <strong>-0.693</strong></code>)<br/>
100vector coupling of <i>d</i> quarks.
101 
102
103<p/><code>parm&nbsp; </code><strong> Zprime:ad &nbsp;</strong> 
104 (<code>default = <strong>-1.</strong></code>)<br/>
105axial coupling of <i>d</i> quarks.
106 
107
108<p/><code>parm&nbsp; </code><strong> Zprime:vu &nbsp;</strong> 
109 (<code>default = <strong>0.387</strong></code>)<br/>
110vector coupling of <i>u</i> quarks.
111 
112
113<p/><code>parm&nbsp; </code><strong> Zprime:au &nbsp;</strong> 
114 (<code>default = <strong>1.</strong></code>)<br/>
115axial coupling of <i>u</i> quarks.
116 
117
118<p/><code>parm&nbsp; </code><strong> Zprime:ve &nbsp;</strong> 
119 (<code>default = <strong>-0.08</strong></code>)<br/>
120vector coupling of <i>e</i> leptons.
121 
122
123<p/><code>parm&nbsp; </code><strong> Zprime:ae &nbsp;</strong> 
124 (<code>default = <strong>-1.</strong></code>)<br/>
125axial coupling of <i>e</i> leptons.
126 
127
128<p/><code>parm&nbsp; </code><strong> Zprime:vnue &nbsp;</strong> 
129 (<code>default = <strong>1.</strong></code>)<br/>
130vector coupling of <i>nu_e</i> neutrinos.
131 
132
133<p/><code>parm&nbsp; </code><strong> Zprime:anue &nbsp;</strong> 
134 (<code>default = <strong>1.</strong></code>)<br/>
135axial coupling of <i>nu_e</i> neutrinos.
136 
137
138<p/>
139Here are the further couplings that are specific for
140a scenario with <code>Zprime:universality</code> swiched off:
141
142<p/><code>parm&nbsp; </code><strong> Zprime:vs &nbsp;</strong> 
143 (<code>default = <strong>-0.693</strong></code>)<br/>
144vector coupling of <i>s</i> quarks.
145 
146
147<p/><code>parm&nbsp; </code><strong> Zprime:as &nbsp;</strong> 
148 (<code>default = <strong>-1.</strong></code>)<br/>
149axial coupling of <i>s</i> quarks.
150 
151
152<p/><code>parm&nbsp; </code><strong> Zprime:vc &nbsp;</strong> 
153 (<code>default = <strong>0.387</strong></code>)<br/>
154vector coupling of <i>c</i> quarks.
155 
156
157<p/><code>parm&nbsp; </code><strong> Zprime:ac &nbsp;</strong> 
158 (<code>default = <strong>1.</strong></code>)<br/>
159axial coupling of <i>c</i> quarks.
160 
161
162<p/><code>parm&nbsp; </code><strong> Zprime:vmu &nbsp;</strong> 
163 (<code>default = <strong>-0.08</strong></code>)<br/>
164vector coupling of <i>mu</i> leptons.
165 
166
167<p/><code>parm&nbsp; </code><strong> Zprime:amu &nbsp;</strong> 
168 (<code>default = <strong>-1.</strong></code>)<br/>
169axial coupling of <i>mu</i> leptons.
170 
171
172<p/><code>parm&nbsp; </code><strong> Zprime:vnumu &nbsp;</strong> 
173 (<code>default = <strong>1.</strong></code>)<br/>
174vector coupling of <i>nu_mu</i> neutrinos.
175 
176
177<p/><code>parm&nbsp; </code><strong> Zprime:anumu &nbsp;</strong> 
178 (<code>default = <strong>1.</strong></code>)<br/>
179axial coupling of <i>nu_mu</i> neutrinos.
180 
181
182<p/><code>parm&nbsp; </code><strong> Zprime:vb &nbsp;</strong> 
183 (<code>default = <strong>-0.693</strong></code>)<br/>
184vector coupling of <i>b</i> quarks.
185 
186
187<p/><code>parm&nbsp; </code><strong> Zprime:ab &nbsp;</strong> 
188 (<code>default = <strong>-1.</strong></code>)<br/>
189axial coupling of <i>b</i> quarks.
190 
191
192<p/><code>parm&nbsp; </code><strong> Zprime:vt &nbsp;</strong> 
193 (<code>default = <strong>0.387</strong></code>)<br/>
194vector coupling of <i>t</i> quarks.
195 
196
197<p/><code>parm&nbsp; </code><strong> Zprime:at &nbsp;</strong> 
198 (<code>default = <strong>1.</strong></code>)<br/>
199axial coupling of <i>t</i> quarks.
200 
201
202<p/><code>parm&nbsp; </code><strong> Zprime:vtau &nbsp;</strong> 
203 (<code>default = <strong>-0.08</strong></code>)<br/>
204vector coupling of <i>tau</i> leptons.
205 
206
207<p/><code>parm&nbsp; </code><strong> Zprime:atau &nbsp;</strong> 
208 (<code>default = <strong>-1.</strong></code>)<br/>
209axial coupling of <i>tau</i> leptons.
210 
211
212<p/><code>parm&nbsp; </code><strong> Zprime:vnutau &nbsp;</strong> 
213 (<code>default = <strong>1.</strong></code>)<br/>
214vector coupling of <i>nu_tau</i> neutrinos.
215 
216
217<p/><code>parm&nbsp; </code><strong> Zprime:anutau &nbsp;</strong> 
218 (<code>default = <strong>1.</strong></code>)<br/>
219axial coupling of <i>nu_tau</i> neutrinos.
220 
221
222<p/>
223The coupling to the decay channel <i>Z'^0 -> W^+ W^-</i> is
224more model-dependent. By default it is therefore off, but can be
225switched on as follows. Furthermore, we have left some amount of
226freedom in the choice of decay angular correlations in this
227channel, but obviously alternative shapes could be imagined.
228
229<p/><code>parm&nbsp; </code><strong> Zprime:coup2WW &nbsp;</strong> 
230 (<code>default = <strong>0.</strong></code>; <code>minimum = 0.</code>)<br/>
231the coupling <i>Z'^0 -> W^+ W^-</i> is taken to be this number
232times <i>m_W^2 / m_Z'^2</i> times the <i>Z^0 -> W^+ W^-</i> 
233coupling. Thus a unit value corresponds to the
234<i>Z^0 -> W^+ W^-</i> coupling, scaled down by a factor
235<i>m_W^2 / m_Z'^2</i>, and gives a <i>Z'^0</i> partial
236width into this channel that again increases linearly. If you
237cancel this behaviour, by letting <code>Zprime:coup2WW</code> be
238proportional to <i>m_Z'^2 / m_W^2</i>, you instead obtain a
239partial width that goes like the fifth power of the <i>Z'^0</i> 
240mass. These two extremes correspond to the "extended gauge model"
241and the "reference model", respectively, of [<a href="Bibliography.html" target="page">Alt89</a>].
242Note that this channel only includes the pure <i>Z'</i> part,
243while <i>f fbar -> gamma^*/Z^*0 -> W^+ W^-</i> is available
244as a separate electroweak process.
245 
246
247<p/><code>parm&nbsp; </code><strong> Zprime:anglesWW &nbsp;</strong> 
248 (<code>default = <strong>0.</strong></code>; <code>minimum = 0.</code>; <code>maximum = 1.</code>)<br/>
249in the decay chain <i>Z'^0 -> W^+ W^- ->f_1 fbar_2 f_3 fbar_4</i>
250the decay angular distributions is taken to be a mixture of two
251possible shapes. This parameter gives the fraction that is distributed
252as in Higgs <i>h^0 -> W^+ W^-</i> (longitudinal bosons),
253with the remainder (by default all) is taken to be the same as for
254<i>Z^0 -> W^+ W^-</i> (a mixture of transverse and longitudinal
255bosons).   
256 
257
258<p/>
259A massive <i>Z'^0</i> is also likely to decay into Higgses
260and potentially into other now unknown particles. Such possibilities
261clearly are quite model-dependent, and have not been included
262for now.
263
264<h3><i>W'^+-</i></h3>
265 
266The <i>W'^+-</i> implementation is less ambitious than the
267<i>Z'^0</i>. Specifically, while indirect detection of a
268<i>Z'^0</i> through its interference contribution is
269a possible discovery channel in lepton colliders, there is no
270equally compelling case for <i>W^+-/W'^+-</i> interference
271effects being of importance for discovery, and such interference
272has therefore not been implemented for now. Related to this, a
273<i>Z'^0</i> could appear on its own in a new <i>U(1)</i> group,
274while <i>W'^+-</i> would have to sit in a <i>SU(2)</i> group
275and thus have a <i>Z'^0</i> partner that is likely to be found
276first. Only one process is implemented but, like for the
277<i>W^+-</i>, the ISR showers contain automatic matching to the
278<i>W'^+-</i> + 1 jet matrix elements.
279
280<p/><code>flag&nbsp; </code><strong> NewGaugeBoson:ffbar2Wprime &nbsp;</strong> 
281 (<code>default = <strong>off</strong></code>)<br/>
282Scattering <i>f fbar' -> W'^+-</i>.
283Code 3021.
284 
285
286<p/>
287The couplings of the <i>W'^+-</i> are here assumed universal,
288i.e. the same for all generations. One may set vector and axial
289couplings freely, separately for the <i>q qbar'</i> and the
290<i>l nu_l</i> decay channels. The defaults correspond to the
291<i>V - A</i> structure and normalization of the Standard Model
292<i>W^+-</i>, but can be changed to simulate a wide selection
293of models. One limitation is that, for simplicity, the same
294Cabibbo--Kobayashi--Maskawa quark mixing matrix is assumed as for
295the standard <i>W^+-</i>. Depending on your assumed neutrino
296nature you may want to restrict your freedom in the lepton sector,
297but no limitations are enforced by the program.
298
299<p/><code>parm&nbsp; </code><strong> Wprime:vq &nbsp;</strong> 
300 (<code>default = <strong>1.</strong></code>)<br/>
301vector coupling of quarks.
302 
303
304<p/><code>parm&nbsp; </code><strong> Wprime:aq &nbsp;</strong> 
305 (<code>default = <strong>-1.</strong></code>)<br/>
306axial coupling of quarks.
307 
308
309<p/><code>parm&nbsp; </code><strong> Wprime:vl &nbsp;</strong> 
310 (<code>default = <strong>1.</strong></code>)<br/>
311vector coupling of leptons.
312 
313
314<p/><code>parm&nbsp; </code><strong> Wprime:al &nbsp;</strong> 
315 (<code>default = <strong>-1.</strong></code>)<br/>
316axial coupling of leptons.
317 
318
319<p/>
320The coupling to the decay channel <i>W'^+- -> W^+- Z^0</i> is
321more model-dependent, like for <i>Z'^0 -> W^+ W^-</i> described
322above. By default it is therefore off, but can be
323switched on as follows. Furthermore, we have left some amount of
324freedom in the choice of decay angular correlations in this
325channel, but obviously alternative shapes could be imagined.
326
327<p/><code>parm&nbsp; </code><strong> Wprime:coup2WZ &nbsp;</strong> 
328 (<code>default = <strong>0.</strong></code>; <code>minimum = 0.</code>)<br/>
329the coupling <i>W'^0 -> W^+- Z^0</i> is taken to be this number
330times <i>m_W^2 / m_W'^2</i> times the <i>W^+- -> W^+- Z^0</i> 
331coupling. Thus a unit value corresponds to the
332<i>W^+- -> W^+- Z^0</i> coupling, scaled down by a factor
333<i>m_W^2 / m_W'^2</i>, and gives a <i>W'^+-</i> partial
334width into this channel that increases linearly with the
335<i>W'^+-</i> mass. If you cancel this behaviour, by letting
336<code>Wprime:coup2WZ</code> be proportional to <i>m_W'^2 / m_W^2</i>,
337you instead obtain a partial width that goes like the fifth power
338of the <i>W'^+-</i> mass. These two extremes correspond to the
339"extended gauge model" and the "reference model", respectively,
340of [<a href="Bibliography.html" target="page">Alt89</a>].
341 
342
343<p/><code>parm&nbsp; </code><strong> Wprime:anglesWZ &nbsp;</strong> 
344 (<code>default = <strong>0.</strong></code>; <code>minimum = 0.</code>; <code>maximum = 1.</code>)<br/>
345in the decay chain <i>W'^+- -> W^+- Z^0 ->f_1 fbar_2 f_3 fbar_4</i>
346the decay angular distributions is taken to be a mixture of two
347possible shapes. This parameter gives the fraction that is distributed
348as in Higgs <i>H^+- -> W^+- Z^0</i> (longitudinal bosons),
349with the remainder (by default all) is taken to be the same as for
350<i>W^+- -> W^+- Z^0</i> (a mixture of transverse and longitudinal
351bosons).   
352 
353
354<p/>
355A massive <i>W'^+-</i> is also likely to decay into Higgses
356and potentially into other now unknown particles. Such possibilities
357clearly are quite model-dependent, and have not been included
358for now.
359
360<h3><i>R^0</i></h3>
361 
362The <i>R^0</i> boson (particle code 41) represents one possible
363scenario for a horizontal gauge boson, i.e. a gauge boson
364that couples between the generations, inducing processes like
365<i>s dbar -> R^0 -> mu^- e^+</i>. Experimental limits on
366flavour-changing neutral currents forces such a boson to be fairly
367heavy. In spite of being neutral the antiparticle is distinct from
368the particle: one carries a net positive generation number and
369the other a negative one. This particular model has no new
370parameters beyond the <i>R^0</i> mass. Decays are assumed isotropic. 
371For further details see [<a href="Bibliography.html" target="page">Ben85</a>].
372 
373<p/><code>flag&nbsp; </code><strong> NewGaugeBoson:ffbar2R0 &nbsp;</strong> 
374 (<code>default = <strong>off</strong></code>)<br/>
375Scattering <i>f_1 fbar_2 -> R^0 -> f_3 fbar_4</i>, where
376<i>f_1</i> and <i>fbar_2</i> are separated by <i>+-</i> one
377generation and similarly for <i>f_3</i> and <i>fbar_4</i>.
378Thus possible final states are e.g. <i>d sbar</i>, <i>u cbar</i>
379<i>s bbar</i>, <i>c tbar</i>, <i>e- mu+</i> and
380<i>mu- tau+</i>.
381Code 3041.
382 
383
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386
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