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<h2>Fourth-Generation Processes</h2> 
<ol id="toc">
  <li><a href="#section0">Production processes</a></li>
  <li><a href="#section1">Parameters</a></li>
</ol>

 
A fourth generation can be accommodated within the Standard Model, 
without the introduction of any new concepts. Many experimental 
constraints exist, but it has not been fully excluded. Therefore 
we offer a simple implementation, along the lines of the top. 
It could also be useful as a template for studies of other 
new particles with similar characteristics. 
 
<p/> 
The fourth generation are given names as in the third, but with a prime, 
i.e. <i>b'</i> with PDG code 7, <i>t'</i> with code 8, 
<i>tau'</i> with code 17, and <i>nu'_tau</i> with code 18. 
Most important for you is to assign a mass hierarchy, to decide which 
fermions can decay into which. The current implementation assumes that 
mass splittings are big enough that fourth-generation fermions can 
decay to third-generation ones by the emission of an on-shell <i>W</i>. 
To this end, the standard three-generation CKM mixing matrix has been 
extended to include a fourth generation, see below. Since no mixing has 
been implemented in the neutrino sector it would be assumed that the 
lighter of <i>tau'</i> and <i>nu'_tau</i> is stable. No decay modes 
have been implemented that go beyond the Standard Model, so 
modifications would be needed if e.g. also SUSY is included in the game. 
 
<a name="section0"></a> 
<h3>Production processes</h3> 
 
<h4>1) <i>b'</i> processes</h4> 
 
Different ways to produce <i>b'</i> quarks, singly or in pairs. 
For a <i>b' t'</i> pair see section 3 below. 
 
<br/><br/><strong>FourthBottom:all</strong>  <input type="radio" name="1" value="on"><strong>On</strong>
<input type="radio" name="1" value="off" checked="checked"><strong>Off</strong>
 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
Common switch for the group of <i>b'</i> production. 
Also includes the process <i>f fbar' &rarr; t' b'bar</i> in section 3 below. 
   
 
<br/><br/><strong>FourthBottom:gg2bPrimebPrimebar</strong>  <input type="radio" name="2" value="on"><strong>On</strong>
<input type="radio" name="2" value="off" checked="checked"><strong>Off</strong>
 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>g g &rarr; b' b'bar</i>. 
Code 801. 
   
 
<br/><br/><strong>FourthBottom:qqbar2bPrimebPrimebar</strong>  <input type="radio" name="3" value="on"><strong>On</strong>
<input type="radio" name="3" value="off" checked="checked"><strong>Off</strong>
 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>q qbar &rarr; b' b'bar</i> by gluon exchange. 
Code 802. 
   
 
<br/><br/><strong>FourthBottom:qq2bPrimeq(t:W)</strong>  <input type="radio" name="4" value="on"><strong>On</strong>
<input type="radio" name="4" value="off" checked="checked"><strong>Off</strong>
 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>q q' &rarr; b' q''</i> by <i>t</i>-channel exchange 
of a <i>W^+-</i> boson. 
Code 803. 
   
 
<br/><br/><strong>FourthBottom:ffbar2bPrimebPrimebar(s:gmZ)</strong>  <input type="radio" name="5" value="on"><strong>On</strong>
<input type="radio" name="5" value="off" checked="checked"><strong>Off</strong>
 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>f fbar &rarr; b' b'bar</i> by <i>s</i>-channel exchange 
of a <i>gamma^*/Z^0</i> boson. 
Code 804. 
   
 
<br/><br/><strong>FourthBottom:ffbar2bPrimeqbar(s:W)</strong>  <input type="radio" name="6" value="on"><strong>On</strong>
<input type="radio" name="6" value="off" checked="checked"><strong>Off</strong>
 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>f fbar' &rarr; b' qbar''</i> by <i>s</i>-channel exchange 
of a <i>W^+-</i> boson. Here <i>q''</i> is either <i>u</i> or 
<i>c</i>. 
Code 805. 
   
 
<br/><br/><strong>FourthBottom:ffbar2bPrimetbar(s:W)</strong>  <input type="radio" name="7" value="on"><strong>On</strong>
<input type="radio" name="7" value="off" checked="checked"><strong>Off</strong>
 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>f fbar' &rarr; b' tbar</i> by <i>s</i>-channel exchange 
of a <i>W^+-</i> boson. 
Code 806. 
   
 
<h4>2) <i>t'</i> processes</h4> 
 
Different ways to produce <i>t'</i> quarks, singly or in pairs. 
For a <i>b' t'</i> pair see section 3 below. 
 
<br/><br/><strong>FourthTop:all</strong>  <input type="radio" name="8" value="on"><strong>On</strong>
<input type="radio" name="8" value="off" checked="checked"><strong>Off</strong>
 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
Common switch for the group of <i>t'</i> production. 
Also includes the process <i>f fbar' &rarr; t' b'bar</i> in section 3 below. 
   
 
<br/><br/><strong>FourthTop:gg2tPrimetPrimebar</strong>  <input type="radio" name="9" value="on"><strong>On</strong>
<input type="radio" name="9" value="off" checked="checked"><strong>Off</strong>
 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>g g &rarr; t' t'bar</i>. 
Code 821. 
   
 
<br/><br/><strong>FourthTop:qqbar2tPrimetPrimebar</strong>  <input type="radio" name="10" value="on"><strong>On</strong>
<input type="radio" name="10" value="off" checked="checked"><strong>Off</strong>
 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>q qbar &rarr; t' t'bar</i> by gluon exchange. 
Code 822. 
   
 
<br/><br/><strong>FourthTop:qq2tPrimeq(t:W)</strong>  <input type="radio" name="11" value="on"><strong>On</strong>
<input type="radio" name="11" value="off" checked="checked"><strong>Off</strong>
 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>q q' &rarr; t' q''</i> by <i>t</i>-channel exchange 
of a <i>W^+-</i> boson. 
Code 823. 
   
 
<br/><br/><strong>FourthTop:ffbar2tPrimetPrimebar(s:gmZ)</strong>  <input type="radio" name="12" value="on"><strong>On</strong>
<input type="radio" name="12" value="off" checked="checked"><strong>Off</strong>
 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>f fbar &rarr; t' t'bar</i> by <i>s</i>-channel exchange 
of a <i>gamma^*/Z^0</i> boson. 
Code 824. 
   
 
<br/><br/><strong>FourthTop:ffbar2tPrimeqbar(s:W)</strong>  <input type="radio" name="13" value="on"><strong>On</strong>
<input type="radio" name="13" value="off" checked="checked"><strong>Off</strong>
 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>f fbar' &rarr; t' qbar''</i> by <i>s</i>-channel exchange 
of a <i>W^+-</i> boson. 
Code 825. 
   
 
<h4>3) Pair-processes with different flavours</h4> 
 
Different ways to produce two different fourth-generation fermions. 
 
<br/><br/><strong>FourthPair:ffbar2tPrimebPrimebar(s:W)</strong>  <input type="radio" name="14" value="on"><strong>On</strong>
<input type="radio" name="14" value="off" checked="checked"><strong>Off</strong>
 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>f fbar' &rarr; t' b'bar</i> by <i>s</i>-channel exchange 
of a <i>W^+-</i> boson. 
Code 841. 
   
 
<br/><br/><strong>FourthPair:ffbar2tauPrimenuPrimebar(s:W)</strong>  <input type="radio" name="15" value="on"><strong>On</strong>
<input type="radio" name="15" value="off" checked="checked"><strong>Off</strong>
 &nbsp;&nbsp;(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>f fbar' &rarr; tau' nu'_taubar</i> by <i>s</i>-channel 
exchange of a <i>W^+-</i> boson. 
Code 842. 
   
 
<p/> 
Missing in this list is scatterings <i>q q' &rarr; t' b'</i> by 
<i>t</i>-channel exchange of a <i>W^+-</i> boson, since currently 
the matrix element for such processes have not been implemented for 
two massive particles in the final state. Since this process would 
involve two CKM-suppressed vertices it ought to be small. 
 
<a name="section1"></a> 
<h3>Parameters</h3> 
 
The Cabibbo-Kobayashi-Maskawa matrix is extended by seven further values. 
So as not to mess up the Standard Model, the normal 3 * 3 matrix is 
kept unitary, and so the new off-diagonal elements lead to a slight 
breaking of this. For exploratory studies this should be good enough; 
more detailed 4 * 4 tunes to data would only make sense the day there 
are evidence for the existence of a fourth generation. 
 
<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>
The <i>V_ub'</i> matrix element in the 4 * 4 CKM matrix. 
   
 
<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>
The <i>V_cb'</i> matrix element in the 4 * 4 CKM matrix. 
   
 
<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>
The <i>V_tb'</i> matrix element in the 4 * 4 CKM matrix. 
   
 
<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>
The <i>V_t'd</i> matrix element in the 4 * 4 CKM matrix. 
   
 
<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>
The <i>V_t's</i> matrix element in the 4 * 4 CKM matrix. 
   
 
<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>
The <i>V_t'b</i> matrix element in the 4 * 4 CKM matrix. 
   
 
<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>
The <i>V_t'b'</i> matrix element in the 4 * 4 CKM matrix. 
   
 
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