<chapter name="Fourth-Generation Processes"> 
 
<h2>Fourth-Generation Processes</h2> 
 
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. <ei>b'</ei> with PDG code 7, <ei>t'</ei> with code 8, 
<ei>tau'</ei> with code 17, and <ei>nu'_tau</ei> 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 <ei>W</ei>. 
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 <ei>tau'</ei> and <ei>nu'_tau</ei> 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. 
 
<h3>Production processes</h3> 
 
<h4>1) <ei>b'</ei> processes</h4> 
 
Different ways to produce <ei>b'</ei> quarks, singly or in pairs. 
For a <ei>b' t'</ei> pair see section 3 below. 
 
<flag name="FourthBottom:all" default="off"> 
Common switch for the group of <ei>b'</ei> production. 
Also includes the process <ei>f fbar' &rarr; t' b'bar</ei> in section 3 below. 
</flag> 
 
<flag name="FourthBottom:gg2bPrimebPrimebar" default="off"> 
Scatterings <ei>g g &rarr; b' b'bar</ei>. 
Code 801. 
</flag> 
 
<flag name="FourthBottom:qqbar2bPrimebPrimebar" default="off"> 
Scatterings <ei>q qbar &rarr; b' b'bar</ei> by gluon exchange. 
Code 802. 
</flag> 
 
<flag name="FourthBottom:qq2bPrimeq(t:W)" default="off"> 
Scatterings <ei>q q' &rarr; b' q''</ei> by <ei>t</ei>-channel exchange 
of a <ei>W^+-</ei> boson. 
Code 803. 
</flag> 
 
<flag name="FourthBottom:ffbar2bPrimebPrimebar(s:gmZ)" default="off"> 
Scatterings <ei>f fbar &rarr; b' b'bar</ei> by <ei>s</ei>-channel exchange 
of a <ei>gamma^*/Z^0</ei> boson. 
Code 804. 
</flag> 
 
<flag name="FourthBottom:ffbar2bPrimeqbar(s:W)" default="off"> 
Scatterings <ei>f fbar' &rarr; b' qbar''</ei> by <ei>s</ei>-channel exchange 
of a <ei>W^+-</ei> boson. Here <ei>q''</ei> is either <ei>u</ei> or 
<ei>c</ei>. 
Code 805. 
</flag> 
 
<flag name="FourthBottom:ffbar2bPrimetbar(s:W)" default="off"> 
Scatterings <ei>f fbar' &rarr; b' tbar</ei> by <ei>s</ei>-channel exchange 
of a <ei>W^+-</ei> boson. 
Code 806. 
</flag> 
 
<h4>2) <ei>t'</ei> processes</h4> 
 
Different ways to produce <ei>t'</ei> quarks, singly or in pairs. 
For a <ei>b' t'</ei> pair see section 3 below. 
 
<flag name="FourthTop:all" default="off"> 
Common switch for the group of <ei>t'</ei> production. 
Also includes the process <ei>f fbar' &rarr; t' b'bar</ei> in section 3 below. 
</flag> 
 
<flag name="FourthTop:gg2tPrimetPrimebar" default="off"> 
Scatterings <ei>g g &rarr; t' t'bar</ei>. 
Code 821. 
</flag> 
 
<flag name="FourthTop:qqbar2tPrimetPrimebar" default="off"> 
Scatterings <ei>q qbar &rarr; t' t'bar</ei> by gluon exchange. 
Code 822. 
</flag> 
 
<flag name="FourthTop:qq2tPrimeq(t:W)" default="off"> 
Scatterings <ei>q q' &rarr; t' q''</ei> by <ei>t</ei>-channel exchange 
of a <ei>W^+-</ei> boson. 
Code 823. 
</flag> 
 
<flag name="FourthTop:ffbar2tPrimetPrimebar(s:gmZ)" default="off"> 
Scatterings <ei>f fbar &rarr; t' t'bar</ei> by <ei>s</ei>-channel exchange 
of a <ei>gamma^*/Z^0</ei> boson. 
Code 824. 
</flag> 
 
<flag name="FourthTop:ffbar2tPrimeqbar(s:W)" default="off"> 
Scatterings <ei>f fbar' &rarr; t' qbar''</ei> by <ei>s</ei>-channel exchange 
of a <ei>W^+-</ei> boson. 
Code 825. 
</flag> 
 
<h4>3) Pair-processes with different flavours</h4> 
  
Different ways to produce two different fourth-generation fermions. 
 
<flag name="FourthPair:ffbar2tPrimebPrimebar(s:W)" default="off"> 
Scatterings <ei>f fbar' &rarr; t' b'bar</ei> by <ei>s</ei>-channel exchange 
of a <ei>W^+-</ei> boson. 
Code 841. 
</flag> 
 
<flag name="FourthPair:ffbar2tauPrimenuPrimebar(s:W)" default="off"> 
Scatterings <ei>f fbar' &rarr; tau' nu'_taubar</ei> by <ei>s</ei>-channel 
exchange of a <ei>W^+-</ei> boson. 
Code 842. 
</flag> 
 
<p/> 
Missing in this list is scatterings <ei>q q' &rarr; t' b'</ei> by 
<ei>t</ei>-channel exchange of a <ei>W^+-</ei> 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. 
 
<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. 
 
<parm name="FourthGeneration:VubPrime" default="0.001" min="0.0" max="1.0"> 
The <ei>V_ub'</ei> matrix element in the 4 * 4 CKM matrix. 
</parm> 
 
<parm name="FourthGeneration:VcbPrime" default="0.01" min="0.0" max="1.0"> 
The <ei>V_cb'</ei> matrix element in the 4 * 4 CKM matrix. 
</parm> 
 
<parm name="FourthGeneration:VtbPrime" default="0.1" min="0.0" max="1.0"> 
The <ei>V_tb'</ei> matrix element in the 4 * 4 CKM matrix. 
</parm> 
 
<parm name="FourthGeneration:VtPrimed" default="0.001" min="0.0" max="1.0"> 
The <ei>V_t'd</ei> matrix element in the 4 * 4 CKM matrix. 
</parm> 
 
<parm name="FourthGeneration:VtPrimes" default="0.01" min="0.0" max="1.0"> 
The <ei>V_t's</ei> matrix element in the 4 * 4 CKM matrix. 
</parm> 
 
<parm name="FourthGeneration:VtPrimeb" default="0.1" min="0.0" max="1.0"> 
The <ei>V_t'b</ei> matrix element in the 4 * 4 CKM matrix. 
</parm> 
 
<parm name="FourthGeneration:VtPrimebPrime" default="0.99" min="0.0" 
max="1.0"> 
The <ei>V_t'b'</ei> matrix element in the 4 * 4 CKM matrix. 
</parm> 
 
</chapter> 
 
<!-- Copyright (C) 2014 Torbjorn Sjostrand --> 
 
