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<title>Fourth-Generation Processes</title>
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<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. <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.
<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.
<p/><code>flag </code><strong> FourthBottom:all </strong>
(<code>default = <strong>off</strong></code>)<br/>
Common switch for the group of <i>b'</i> production.
Also includes the process <i>f fbar' → t' b'bar</i> in section 3 below.
<p/><code>flag </code><strong> FourthBottom:gg2bPrimebPrimebar </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>g g → b' b'bar</i>.
Code 801.
<p/><code>flag </code><strong> FourthBottom:qqbar2bPrimebPrimebar </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>q qbar → b' b'bar</i> by gluon exchange.
Code 802.
<p/><code>flag </code><strong> FourthBottom:qq2bPrimeq(t:W) </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>q q' → b' q''</i> by <i>t</i>-channel exchange
of a <i>W^+-</i> boson.
Code 803.
<p/><code>flag </code><strong> FourthBottom:ffbar2bPrimebPrimebar(s:gmZ) </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>f fbar → b' b'bar</i> by <i>s</i>-channel exchange
of a <i>gamma^*/Z^0</i> boson.
Code 804.
<p/><code>flag </code><strong> FourthBottom:ffbar2bPrimeqbar(s:W) </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>f fbar' → 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.
<p/><code>flag </code><strong> FourthBottom:ffbar2bPrimetbar(s:W) </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>f fbar' → 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.
<p/><code>flag </code><strong> FourthTop:all </strong>
(<code>default = <strong>off</strong></code>)<br/>
Common switch for the group of <i>t'</i> production.
Also includes the process <i>f fbar' → t' b'bar</i> in section 3 below.
<p/><code>flag </code><strong> FourthTop:gg2tPrimetPrimebar </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>g g → t' t'bar</i>.
Code 821.
<p/><code>flag </code><strong> FourthTop:qqbar2tPrimetPrimebar </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>q qbar → t' t'bar</i> by gluon exchange.
Code 822.
<p/><code>flag </code><strong> FourthTop:qq2tPrimeq(t:W) </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>q q' → t' q''</i> by <i>t</i>-channel exchange
of a <i>W^+-</i> boson.
Code 823.
<p/><code>flag </code><strong> FourthTop:ffbar2tPrimetPrimebar(s:gmZ) </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>f fbar → t' t'bar</i> by <i>s</i>-channel exchange
of a <i>gamma^*/Z^0</i> boson.
Code 824.
<p/><code>flag </code><strong> FourthTop:ffbar2tPrimeqbar(s:W) </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>f fbar' → 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.
<p/><code>flag </code><strong> FourthPair:ffbar2tPrimebPrimebar(s:W) </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>f fbar' → t' b'bar</i> by <i>s</i>-channel exchange
of a <i>W^+-</i> boson.
Code 841.
<p/><code>flag </code><strong> FourthPair:ffbar2tauPrimenuPrimebar(s:W) </strong>
(<code>default = <strong>off</strong></code>)<br/>
Scatterings <i>f fbar' → 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' → 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.
<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.
<p/><code>parm </code><strong> FourthGeneration:VubPrime </strong>
(<code>default = <strong>0.001</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)<br/>
The <i>V_ub'</i> matrix element in the 4 * 4 CKM matrix.
<p/><code>parm </code><strong> FourthGeneration:VcbPrime </strong>
(<code>default = <strong>0.01</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)<br/>
The <i>V_cb'</i> matrix element in the 4 * 4 CKM matrix.
<p/><code>parm </code><strong> FourthGeneration:VtbPrime </strong>
(<code>default = <strong>0.1</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)<br/>
The <i>V_tb'</i> matrix element in the 4 * 4 CKM matrix.
<p/><code>parm </code><strong> FourthGeneration:VtPrimed </strong>
(<code>default = <strong>0.001</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)<br/>
The <i>V_t'd</i> matrix element in the 4 * 4 CKM matrix.
<p/><code>parm </code><strong> FourthGeneration:VtPrimes </strong>
(<code>default = <strong>0.01</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)<br/>
The <i>V_t's</i> matrix element in the 4 * 4 CKM matrix.
<p/><code>parm </code><strong> FourthGeneration:VtPrimeb </strong>
(<code>default = <strong>0.1</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)<br/>
The <i>V_t'b</i> matrix element in the 4 * 4 CKM matrix.
<p/><code>parm </code><strong> FourthGeneration:VtPrimebPrime </strong>
(<code>default = <strong>0.99</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)<br/>
The <i>V_t'b'</i> matrix element in the 4 * 4 CKM matrix.
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