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<title>Fourth-Generation Processes</title>
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<h2>Fourth-Generation Processes</h2>
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A fourth generation can be accommodated within the Standard Model,
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without the introduction of any new concepts. Many experimental
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constraints exist, but it has not been fully excluded. Therefore
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we offer a simple implementation, along the lines of the top.
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It could also be useful as a template for studies of other
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new particles with similar characteristics.
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The fourth generation are given names as in the third, but with a prime,
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i.e. <i>b'</i> with PDG code 7, <i>t'</i> with code 8,
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<i>tau'</i> with code 17, and <i>nu'_tau</i> with code 18.
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Most important for you is to assign a mass hierarchy, to decide which
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fermions can decay into which. The current implementation assumes that
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mass splittings are big enough that fourth-generation fermions can
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decay to third-generation ones by the emission of an on-shell <i>W</i>.
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To this end, the standard three-generation CKM mixing matrix has been
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extended to include a fourth generation, see below. Since no mixing has
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been implemented in the neutrino sector it would be assumed that the
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lighter of <i>tau'</i> and <i>nu'_tau</i> is stable. No decay modes
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have been implemented that go beyond the Standard Model, so
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modifications would be needed if e.g. also SUSY is included in the game.
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<h3>Production processes</h3>
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<h4>1) <i>b'</i> processes</h4>
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Different ways to produce <i>b'</i> quarks, singly or in pairs.
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For a <i>b' t'</i> pair see section 3 below.
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<p/><code>flag </code><strong> FourthBottom:all </strong>
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(<code>default = <strong>off</strong></code>)<br/>
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Common switch for the group of <i>b'</i> production.
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Also includes the process <i>f fbar' -> t' b'bar</i> in section 3 below.
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<p/><code>flag </code><strong> FourthBottom:gg2bPrimebPrimebar </strong>
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(<code>default = <strong>off</strong></code>)<br/>
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Scatterings <i>g g -> b' b'bar</i>.
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<p/><code>flag </code><strong> FourthBottom:qqbar2bPrimebPrimebar </strong>
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(<code>default = <strong>off</strong></code>)<br/>
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Scatterings <i>q qbar -> b' b'bar</i> by gluon exchange.
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<p/><code>flag </code><strong> FourthBottom:qq2bPrimeq(t:W) </strong>
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(<code>default = <strong>off</strong></code>)<br/>
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Scatterings <i>q q' -> b' q''</i> by <i>t</i>-channel exchange
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of a <i>W^+-</i> boson.
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<p/><code>flag </code><strong> FourthBottom:ffbar2bPrimebPrimebar(s:gmZ) </strong>
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(<code>default = <strong>off</strong></code>)<br/>
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Scatterings <i>f fbar -> b' b'bar</i> by <i>s</i>-channel exchange
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of a <i>gamma^*/Z^0</i> boson.
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<p/><code>flag </code><strong> FourthBottom:ffbar2bPrimeqbar(s:W) </strong>
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(<code>default = <strong>off</strong></code>)<br/>
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Scatterings <i>f fbar' -> b' qbar''</i> by <i>s</i>-channel exchange
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of a <i>W^+-</i> boson. Here <i>q''</i> is either <i>u</i> or
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<p/><code>flag </code><strong> FourthBottom:ffbar2bPrimetbar(s:W) </strong>
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(<code>default = <strong>off</strong></code>)<br/>
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Scatterings <i>f fbar' -> b' tbar</i> by <i>s</i>-channel exchange
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of a <i>W^+-</i> boson.
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<h4>2) <i>t'</i> processes</h4>
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Different ways to produce <i>t'</i> quarks, singly or in pairs.
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For a <i>b' t'</i> pair see section 3 below.
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<p/><code>flag </code><strong> FourthTop:all </strong>
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(<code>default = <strong>off</strong></code>)<br/>
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Common switch for the group of <i>t'</i> production.
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Also includes the process <i>f fbar' -> t' b'bar</i> in section 3 below.
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<p/><code>flag </code><strong> FourthTop:gg2tPrimetPrimebar </strong>
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(<code>default = <strong>off</strong></code>)<br/>
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Scatterings <i>g g -> t' t'bar</i>.
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<p/><code>flag </code><strong> FourthTop:qqbar2tPrimetPrimebar </strong>
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(<code>default = <strong>off</strong></code>)<br/>
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Scatterings <i>q qbar -> t' t'bar</i> by gluon exchange.
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<p/><code>flag </code><strong> FourthTop:qq2tPrimeq(t:W) </strong>
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(<code>default = <strong>off</strong></code>)<br/>
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Scatterings <i>q q' -> t' q''</i> by <i>t</i>-channel exchange
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of a <i>W^+-</i> boson.
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<p/><code>flag </code><strong> FourthTop:ffbar2tPrimetPrimebar(s:gmZ) </strong>
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(<code>default = <strong>off</strong></code>)<br/>
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Scatterings <i>f fbar -> t' t'bar</i> by <i>s</i>-channel exchange
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of a <i>gamma^*/Z^0</i> boson.
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<p/><code>flag </code><strong> FourthTop:ffbar2tPrimeqbar(s:W) </strong>
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(<code>default = <strong>off</strong></code>)<br/>
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Scatterings <i>f fbar' -> t' qbar''</i> by <i>s</i>-channel exchange
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of a <i>W^+-</i> boson.
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<h4>3) Pair-processes with different flavours</h4>
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Different ways to produce two different fourth-generation fermions.
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<p/><code>flag </code><strong> FourthPair:ffbar2tPrimebPrimebar(s:W) </strong>
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(<code>default = <strong>off</strong></code>)<br/>
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Scatterings <i>f fbar' -> t' b'bar</i> by <i>s</i>-channel exchange
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of a <i>W^+-</i> boson.
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<p/><code>flag </code><strong> FourthPair:ffbar2tauPrimenuPrimebar(s:W) </strong>
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(<code>default = <strong>off</strong></code>)<br/>
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Scatterings <i>f fbar' -> tau' nu'_taubar</i> by <i>s</i>-channel
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exchange of a <i>W^+-</i> boson.
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Missing in this list is scatterings <i>q q' -> t' b'</i> by
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<i>t</i>-channel exchange of a <i>W^+-</i> boson, since currently
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the matrix element for such processes have not been implemented for
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two massive particles in the final state. Since this process would
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involve two CKM-suppressed vertices it ought to be small.
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The Cabibbo-Kobayashi-Maskawa matrix is extended by seven further values.
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So as not to mess up the Standard Model, the normal 3 * 3 matrix is
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kept unitary, and so the new off-diagonal elements lead to a slight
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breaking of this. For exploratory studies this should be good enough;
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more detailed 4 * 4 tunes to data would only make sense the day there
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are evidence for the existence of a fourth generation.
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<p/><code>parm </code><strong> FourthGeneration:VubPrime </strong>
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(<code>default = <strong>0.001</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)<br/>
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The <i>V_ub'</i> matrix element in the 4 * 4 CKM matrix.
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<p/><code>parm </code><strong> FourthGeneration:VcbPrime </strong>
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(<code>default = <strong>0.01</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)<br/>
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The <i>V_cb'</i> matrix element in the 4 * 4 CKM matrix.
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<p/><code>parm </code><strong> FourthGeneration:VtbPrime </strong>
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(<code>default = <strong>0.1</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)<br/>
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The <i>V_tb'</i> matrix element in the 4 * 4 CKM matrix.
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<p/><code>parm </code><strong> FourthGeneration:VtPrimed </strong>
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(<code>default = <strong>0.001</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)<br/>
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The <i>V_t'd</i> matrix element in the 4 * 4 CKM matrix.
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<p/><code>parm </code><strong> FourthGeneration:VtPrimes </strong>
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(<code>default = <strong>0.01</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)<br/>
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The <i>V_t's</i> matrix element in the 4 * 4 CKM matrix.
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<p/><code>parm </code><strong> FourthGeneration:VtPrimeb </strong>
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(<code>default = <strong>0.1</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)<br/>
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The <i>V_t'b</i> matrix element in the 4 * 4 CKM matrix.
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<p/><code>parm </code><strong> FourthGeneration:VtPrimebPrime </strong>
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(<code>default = <strong>0.99</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 1.0</code>)<br/>
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The <i>V_t'b'</i> matrix element in the 4 * 4 CKM matrix.
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