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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 | <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>
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