3 <title>Fourth-Generation Processes</title>
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30 <h2>Fourth-Generation Processes</h2>
32 A fourth generation can be accommodated within the Standard Model,
33 without the introduction of any new concepts. Many experimental
34 constraints exist, but it has not been fully excluded. Therefore
35 we offer a simple implementation, along the lines of the top.
36 It could also be useful as a template for studies of other
37 new particles with similar characteristics.
40 The fourth generation are given names as in the third, but with a prime,
41 i.e. <i>b'</i> with PDG code 7, <i>t'</i> with code 8,
42 <i>tau'</i> with code 17, and <i>nu'_tau</i> with code 18.
43 Most important for you is to assign a mass hierarchy, to decide which
44 fermions can decay into which. The current implementation assumes that
45 mass splittings are big enough that fourth-generation fermions can
46 decay to third-generation ones by the emission of an on-shell <i>W</i>.
47 To this end, the standard three-generation CKM mixing matrix has been
48 extended to include a fourth generation, see below. Since no mixing has
49 been implemented in the neutrino sector it would be assumed that the
50 lighter of <i>tau'</i> and <i>nu'_tau</i> is stable. No decay modes
51 have been implemented that go beyond the Standard Model, so
52 modifications would be needed if e.g. also SUSY is included in the game.
54 <h3>Production processes</h3>
56 <h4>1) <i>b'</i> processes</h4>
58 Different ways to produce <i>b'</i> quarks, singly or in pairs.
59 For a <i>b' t'</i> pair see section 3 below.
61 <br/><br/><strong>FourthBottom:all</strong> <input type="radio" name="1" value="on"><strong>On</strong>
62 <input type="radio" name="1" value="off" checked="checked"><strong>Off</strong>
63 (<code>default = <strong>off</strong></code>)<br/>
64 Common switch for the group of <i>b'</i> production.
65 Also includes the process <i>f fbar' -> t' b'bar</i> in section 3 below.
68 <br/><br/><strong>FourthBottom:gg2bPrimebPrimebar</strong> <input type="radio" name="2" value="on"><strong>On</strong>
69 <input type="radio" name="2" value="off" checked="checked"><strong>Off</strong>
70 (<code>default = <strong>off</strong></code>)<br/>
71 Scatterings <i>g g -> b' b'bar</i>.
75 <br/><br/><strong>FourthBottom:qqbar2bPrimebPrimebar</strong> <input type="radio" name="3" value="on"><strong>On</strong>
76 <input type="radio" name="3" value="off" checked="checked"><strong>Off</strong>
77 (<code>default = <strong>off</strong></code>)<br/>
78 Scatterings <i>q qbar -> b' b'bar</i> by gluon exchange.
82 <br/><br/><strong>FourthBottom:qq2bPrimeq(t:W)</strong> <input type="radio" name="4" value="on"><strong>On</strong>
83 <input type="radio" name="4" value="off" checked="checked"><strong>Off</strong>
84 (<code>default = <strong>off</strong></code>)<br/>
85 Scatterings <i>q q' -> b' q''</i> by <i>t</i>-channel exchange
86 of a <i>W^+-</i> boson.
90 <br/><br/><strong>FourthBottom:ffbar2bPrimebPrimebar(s:gmZ)</strong> <input type="radio" name="5" value="on"><strong>On</strong>
91 <input type="radio" name="5" value="off" checked="checked"><strong>Off</strong>
92 (<code>default = <strong>off</strong></code>)<br/>
93 Scatterings <i>f fbar -> b' b'bar</i> by <i>s</i>-channel exchange
94 of a <i>gamma^*/Z^0</i> boson.
98 <br/><br/><strong>FourthBottom:ffbar2bPrimeqbar(s:W)</strong> <input type="radio" name="6" value="on"><strong>On</strong>
99 <input type="radio" name="6" value="off" checked="checked"><strong>Off</strong>
100 (<code>default = <strong>off</strong></code>)<br/>
101 Scatterings <i>f fbar' -> b' qbar''</i> by <i>s</i>-channel exchange
102 of a <i>W^+-</i> boson. Here <i>q''</i> is either <i>u</i> or
107 <br/><br/><strong>FourthBottom:ffbar2bPrimetbar(s:W)</strong> <input type="radio" name="7" value="on"><strong>On</strong>
108 <input type="radio" name="7" value="off" checked="checked"><strong>Off</strong>
109 (<code>default = <strong>off</strong></code>)<br/>
110 Scatterings <i>f fbar' -> b' tbar</i> by <i>s</i>-channel exchange
111 of a <i>W^+-</i> boson.
115 <h4>2) <i>t'</i> processes</h4>
117 Different ways to produce <i>t'</i> quarks, singly or in pairs.
118 For a <i>b' t'</i> pair see section 3 below.
120 <br/><br/><strong>FourthTop:all</strong> <input type="radio" name="8" value="on"><strong>On</strong>
121 <input type="radio" name="8" value="off" checked="checked"><strong>Off</strong>
122 (<code>default = <strong>off</strong></code>)<br/>
123 Common switch for the group of <i>t'</i> production.
124 Also includes the process <i>f fbar' -> t' b'bar</i> in section 3 below.
127 <br/><br/><strong>FourthTop:gg2tPrimetPrimebar</strong> <input type="radio" name="9" value="on"><strong>On</strong>
128 <input type="radio" name="9" value="off" checked="checked"><strong>Off</strong>
129 (<code>default = <strong>off</strong></code>)<br/>
130 Scatterings <i>g g -> t' t'bar</i>.
134 <br/><br/><strong>FourthTop:qqbar2tPrimetPrimebar</strong> <input type="radio" name="10" value="on"><strong>On</strong>
135 <input type="radio" name="10" value="off" checked="checked"><strong>Off</strong>
136 (<code>default = <strong>off</strong></code>)<br/>
137 Scatterings <i>q qbar -> t' t'bar</i> by gluon exchange.
141 <br/><br/><strong>FourthTop:qq2tPrimeq(t:W)</strong> <input type="radio" name="11" value="on"><strong>On</strong>
142 <input type="radio" name="11" value="off" checked="checked"><strong>Off</strong>
143 (<code>default = <strong>off</strong></code>)<br/>
144 Scatterings <i>q q' -> t' q''</i> by <i>t</i>-channel exchange
145 of a <i>W^+-</i> boson.
149 <br/><br/><strong>FourthTop:ffbar2tPrimetPrimebar(s:gmZ)</strong> <input type="radio" name="12" value="on"><strong>On</strong>
150 <input type="radio" name="12" value="off" checked="checked"><strong>Off</strong>
151 (<code>default = <strong>off</strong></code>)<br/>
152 Scatterings <i>f fbar -> t' t'bar</i> by <i>s</i>-channel exchange
153 of a <i>gamma^*/Z^0</i> boson.
157 <br/><br/><strong>FourthTop:ffbar2tPrimeqbar(s:W)</strong> <input type="radio" name="13" value="on"><strong>On</strong>
158 <input type="radio" name="13" value="off" checked="checked"><strong>Off</strong>
159 (<code>default = <strong>off</strong></code>)<br/>
160 Scatterings <i>f fbar' -> t' qbar''</i> by <i>s</i>-channel exchange
161 of a <i>W^+-</i> boson.
165 <h4>3) Pair-processes with different flavours</h4>
167 Different ways to produce two different fourth-generation fermions.
169 <br/><br/><strong>FourthPair:ffbar2tPrimebPrimebar(s:W)</strong> <input type="radio" name="14" value="on"><strong>On</strong>
170 <input type="radio" name="14" value="off" checked="checked"><strong>Off</strong>
171 (<code>default = <strong>off</strong></code>)<br/>
172 Scatterings <i>f fbar' -> t' b'bar</i> by <i>s</i>-channel exchange
173 of a <i>W^+-</i> boson.
177 <br/><br/><strong>FourthPair:ffbar2tauPrimenuPrimebar(s:W)</strong> <input type="radio" name="15" value="on"><strong>On</strong>
178 <input type="radio" name="15" value="off" checked="checked"><strong>Off</strong>
179 (<code>default = <strong>off</strong></code>)<br/>
180 Scatterings <i>f fbar' -> tau' nu'_taubar</i> by <i>s</i>-channel
181 exchange of a <i>W^+-</i> boson.
186 Missing in this list is scatterings <i>q q' -> t' b'</i> by
187 <i>t</i>-channel exchange of a <i>W^+-</i> boson, since currently
188 the matrix element for such processes have not been implemented for
189 two massive particles in the final state. Since this process would
190 involve two CKM-suppressed vertices it ought to be small.
194 The Cabibbo-Kobayashi-Maskawa matrix is extended by seven further values.
195 So as not to mess up the Standard Model, the normal 3 * 3 matrix is
196 kept unitary, and so the new off-diagonal elements lead to a slight
197 breaking of this. For exploratory studies this should be good enough;
198 more detailed 4 * 4 tunes to data would only make sense the day there
199 are evidence for the existence of a fourth generation.
201 <br/><br/><table><tr><td><strong>FourthGeneration:VubPrime </td><td></td><td> <input type="text" name="16" value="0.001" size="20"/> (<code>default = <strong>0.001</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)</td></tr></table>
202 The <i>V_ub'</i> matrix element in the 4 * 4 CKM matrix.
205 <br/><br/><table><tr><td><strong>FourthGeneration:VcbPrime </td><td></td><td> <input type="text" name="17" value="0.01" size="20"/> (<code>default = <strong>0.01</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)</td></tr></table>
206 The <i>V_cb'</i> matrix element in the 4 * 4 CKM matrix.
209 <br/><br/><table><tr><td><strong>FourthGeneration:VtbPrime </td><td></td><td> <input type="text" name="18" value="0.1" size="20"/> (<code>default = <strong>0.1</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)</td></tr></table>
210 The <i>V_tb'</i> matrix element in the 4 * 4 CKM matrix.
213 <br/><br/><table><tr><td><strong>FourthGeneration:VtPrimed </td><td></td><td> <input type="text" name="19" value="0.001" size="20"/> (<code>default = <strong>0.001</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)</td></tr></table>
214 The <i>V_t'd</i> matrix element in the 4 * 4 CKM matrix.
217 <br/><br/><table><tr><td><strong>FourthGeneration:VtPrimes </td><td></td><td> <input type="text" name="20" value="0.01" size="20"/> (<code>default = <strong>0.01</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)</td></tr></table>
218 The <i>V_t's</i> matrix element in the 4 * 4 CKM matrix.
221 <br/><br/><table><tr><td><strong>FourthGeneration:VtPrimeb </td><td></td><td> <input type="text" name="21" value="0.1" size="20"/> (<code>default = <strong>0.1</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)</td></tr></table>
222 The <i>V_t'b</i> matrix element in the 4 * 4 CKM matrix.
225 <br/><br/><table><tr><td><strong>FourthGeneration:VtPrimebPrime </td><td></td><td> <input type="text" name="22" value="0.99" size="20"/> (<code>default = <strong>0.99</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)</td></tr></table>
226 The <i>V_t'b'</i> matrix element in the 4 * 4 CKM matrix.
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361 <!-- Copyright (C) 2010 Torbjorn Sjostrand -->