<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' → t' b'bar</ei> in section 3 below.
</flag>
<flag name="FourthBottom:gg2bPrimebPrimebar" default="off">
Scatterings <ei>g g → b' b'bar</ei>.
Code 801.
</flag>
<flag name="FourthBottom:qqbar2bPrimebPrimebar" default="off">
Scatterings <ei>q qbar → b' b'bar</ei> by gluon exchange.
Code 802.
</flag>
<flag name="FourthBottom:qq2bPrimeq(t:W)" default="off">
Scatterings <ei>q q' → 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 → 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' → 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' → 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' → t' b'bar</ei> in section 3 below.
</flag>
<flag name="FourthTop:gg2tPrimetPrimebar" default="off">
Scatterings <ei>g g → t' t'bar</ei>.
Code 821.
</flag>
<flag name="FourthTop:qqbar2tPrimetPrimebar" default="off">
Scatterings <ei>q qbar → t' t'bar</ei> by gluon exchange.
Code 822.
</flag>
<flag name="FourthTop:qq2tPrimeq(t:W)" default="off">
Scatterings <ei>q q' → 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 → 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' → 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' → 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' → 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' → 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 -->
Marcin Chrzaszcz