<html> <head> <title>Fourth-Generation Processes</title> <link rel="stylesheet" type="text/css" href="pythia.css"/> <link rel="shortcut icon" href="pythia32.gif"/> </head> <body> <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. </body> </html> <!-- Copyright (C) 2014 Torbjorn Sjostrand -->
