<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 -->