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3<title>Fourth-Generation Processes</title>
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29
30<h2>Fourth-Generation Processes</h2>
31
32A fourth generation can be accommodated within the Standard Model,
33without the introduction of any new concepts. Many experimental
34constraints exist, but it has not been fully excluded. Therefore
35we offer a simple implementation, along the lines of the top.
36It could also be useful as a template for studies of other
37new particles with similar characteristics.
38
39<p/>
40The fourth generation are given names as in the third, but with a prime,
41i.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.
43Most important for you is to assign a mass hierarchy, to decide which
44fermions can decay into which. The current implementation assumes that
45mass splittings are big enough that fourth-generation fermions can
46decay to third-generation ones by the emission of an on-shell <i>W</i>.
47To this end, the standard three-generation CKM mixing matrix has been
48extended to include a fourth generation, see below. Since no mixing has
49been implemented in the neutrino sector it would be assumed that the
50lighter of <i>tau'</i> and <i>nu'_tau</i> is stable. No decay modes
51have been implemented that go beyond the Standard Model, so
52modifications would be needed if e.g. also SUSY is included in the game.
53
54<h3>Production processes</h3>
55
56<h4>1) <i>b'</i> processes</h4>
57
58Different ways to produce <i>b'</i> quarks, singly or in pairs.
59For a <i>b' t'</i> pair see section 3 below.
60
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 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
64Common switch for the group of <i>b'</i> production.
65Also includes the process <i>f fbar' -> t' b'bar</i> in section 3 below.
66 
67
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 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
71Scatterings <i>g g -> b' b'bar</i>.
72Code 801.
73 
74
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 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
78Scatterings <i>q qbar -> b' b'bar</i> by gluon exchange.
79Code 802.
80 
81
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 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
85Scatterings <i>q q' -> b' q''</i> by <i>t</i>-channel exchange
86of a <i>W^+-</i> boson.
87Code 803.
88 
89
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 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
93Scatterings <i>f fbar -> b' b'bar</i> by <i>s</i>-channel exchange
94of a <i>gamma^*/Z^0</i> boson.
95Code 804.
96 
97
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 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
101Scatterings <i>f fbar' -> b' qbar''</i> by <i>s</i>-channel exchange
102of a <i>W^+-</i> boson. Here <i>q''</i> is either <i>u</i> or
103<i>c</i>.
104Code 805.
105 
106
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 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
110Scatterings <i>f fbar' -> b' tbar</i> by <i>s</i>-channel exchange
111of a <i>W^+-</i> boson.
112Code 806.
113 
114
115<h4>2) <i>t'</i> processes</h4>
116
117Different ways to produce <i>t'</i> quarks, singly or in pairs.
118For a <i>b' t'</i> pair see section 3 below.
119
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 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
123Common switch for the group of <i>t'</i> production.
124Also includes the process <i>f fbar' -> t' b'bar</i> in section 3 below.
125 
126
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 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
130Scatterings <i>g g -> t' t'bar</i>.
131Code 821.
132 
133
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 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
137Scatterings <i>q qbar -> t' t'bar</i> by gluon exchange.
138Code 822.
139 
140
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 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
144Scatterings <i>q q' -> t' q''</i> by <i>t</i>-channel exchange
145of a <i>W^+-</i> boson.
146Code 823.
147 
148
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 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
152Scatterings <i>f fbar -> t' t'bar</i> by <i>s</i>-channel exchange
153of a <i>gamma^*/Z^0</i> boson.
154Code 824.
155 
156
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 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
160Scatterings <i>f fbar' -> t' qbar''</i> by <i>s</i>-channel exchange
161of a <i>W^+-</i> boson.
162Code 825.
163 
164
165<h4>3) Pair-processes with different flavours</h4>
166 
167Different ways to produce two different fourth-generation fermions.
168
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 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
172Scatterings <i>f fbar' -> t' b'bar</i> by <i>s</i>-channel exchange
173of a <i>W^+-</i> boson.
174Code 841.
175 
176
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 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
180Scatterings <i>f fbar' -> tau' nu'_taubar</i> by <i>s</i>-channel
181exchange of a <i>W^+-</i> boson.
182Code 842.
183 
184
185<p/>
186Missing 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
188the matrix element for such processes have not been implemented for
189two massive particles in the final state. Since this process would
190involve two CKM-suppressed vertices it ought to be small.
191
192<h3>Parameters</h3>
193
194The Cabibbo-Kobayashi-Maskawa matrix is extended by seven further values.
195So as not to mess up the Standard Model, the normal 3 * 3 matrix is
196kept unitary, and so the new off-diagonal elements lead to a slight
197breaking of this. For exploratory studies this should be good enough;
198more detailed 4 * 4 tunes to data would only make sense the day there
199are evidence for the existence of a fourth generation.
200
201<br/><br/><table><tr><td><strong>FourthGeneration:VubPrime </td><td></td><td> <input type="text" name="16" value="0.001" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>0.001</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)</td></tr></table>
202The <i>V_ub'</i> matrix element in the 4 * 4 CKM matrix.
203 
204
205<br/><br/><table><tr><td><strong>FourthGeneration:VcbPrime </td><td></td><td> <input type="text" name="17" value="0.01" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>0.01</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)</td></tr></table>
206The <i>V_cb'</i> matrix element in the 4 * 4 CKM matrix.
207 
208
209<br/><br/><table><tr><td><strong>FourthGeneration:VtbPrime </td><td></td><td> <input type="text" name="18" value="0.1" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>0.1</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)</td></tr></table>
210The <i>V_tb'</i> matrix element in the 4 * 4 CKM matrix.
211 
212
213<br/><br/><table><tr><td><strong>FourthGeneration:VtPrimed </td><td></td><td> <input type="text" name="19" value="0.001" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>0.001</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)</td></tr></table>
214The <i>V_t'd</i> matrix element in the 4 * 4 CKM matrix.
215 
216
217<br/><br/><table><tr><td><strong>FourthGeneration:VtPrimes </td><td></td><td> <input type="text" name="20" value="0.01" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>0.01</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)</td></tr></table>
218The <i>V_t's</i> matrix element in the 4 * 4 CKM matrix.
219 
220
221<br/><br/><table><tr><td><strong>FourthGeneration:VtPrimeb </td><td></td><td> <input type="text" name="21" value="0.1" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>0.1</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)</td></tr></table>
222The <i>V_t'b</i> matrix element in the 4 * 4 CKM matrix.
223 
224
225<br/><br/><table><tr><td><strong>FourthGeneration:VtPrimebPrime </td><td></td><td> <input type="text" name="22" value="0.99" size="20"/>  &nbsp;&nbsp;(<code>default = <strong>0.99</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)</td></tr></table>
226The <i>V_t'b'</i> matrix element in the 4 * 4 CKM matrix.
227   
228
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356
357?>
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360
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