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Fourth-Generation Processes

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.

The fourth generation are given names as in the third, but with a prime, i.e. b' with PDG code 7, t' with code 8, tau' with code 17, and nu'_tau 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 W. 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 tau' and nu'_tau 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.

Production processes

1) b' processes

Different ways to produce b' quarks, singly or in pairs. For a b' t' pair see section 3 below.

FourthBottom:all On Off   (default = off)
Common switch for the group of b' production. Also includes the process f fbar' → t' b'bar in section 3 below.

FourthBottom:gg2bPrimebPrimebar On Off   (default = off)
Scatterings g g → b' b'bar. Code 801.

FourthBottom:qqbar2bPrimebPrimebar On Off   (default = off)
Scatterings q qbar → b' b'bar by gluon exchange. Code 802.

FourthBottom:qq2bPrimeq(t:W) On Off   (default = off)
Scatterings q q' → b' q'' by t-channel exchange of a W^+- boson. Code 803.

FourthBottom:ffbar2bPrimebPrimebar(s:gmZ) On Off   (default = off)
Scatterings f fbar → b' b'bar by s-channel exchange of a gamma^*/Z^0 boson. Code 804.

FourthBottom:ffbar2bPrimeqbar(s:W) On Off   (default = off)
Scatterings f fbar' → b' qbar'' by s-channel exchange of a W^+- boson. Here q'' is either u or c. Code 805.

FourthBottom:ffbar2bPrimetbar(s:W) On Off   (default = off)
Scatterings f fbar' → b' tbar by s-channel exchange of a W^+- boson. Code 806.

2) t' processes

Different ways to produce t' quarks, singly or in pairs. For a b' t' pair see section 3 below.

FourthTop:all On Off   (default = off)
Common switch for the group of t' production. Also includes the process f fbar' → t' b'bar in section 3 below.

FourthTop:gg2tPrimetPrimebar On Off   (default = off)
Scatterings g g → t' t'bar. Code 821.

FourthTop:qqbar2tPrimetPrimebar On Off   (default = off)
Scatterings q qbar → t' t'bar by gluon exchange. Code 822.

FourthTop:qq2tPrimeq(t:W) On Off   (default = off)
Scatterings q q' → t' q'' by t-channel exchange of a W^+- boson. Code 823.

FourthTop:ffbar2tPrimetPrimebar(s:gmZ) On Off   (default = off)
Scatterings f fbar → t' t'bar by s-channel exchange of a gamma^*/Z^0 boson. Code 824.

FourthTop:ffbar2tPrimeqbar(s:W) On Off   (default = off)
Scatterings f fbar' → t' qbar'' by s-channel exchange of a W^+- boson. Code 825.

3) Pair-processes with different flavours

Different ways to produce two different fourth-generation fermions.

FourthPair:ffbar2tPrimebPrimebar(s:W) On Off   (default = off)
Scatterings f fbar' → t' b'bar by s-channel exchange of a W^+- boson. Code 841.

FourthPair:ffbar2tauPrimenuPrimebar(s:W) On Off   (default = off)
Scatterings f fbar' → tau' nu'_taubar by s-channel exchange of a W^+- boson. Code 842.

Missing in this list is scatterings q q' → t' b' by t-channel exchange of a W^+- 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.

Parameters

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.

FourthGeneration:VubPrime   (default = 0.001; minimum = 0.0; maximum = 1.0)
The V_ub' matrix element in the 4 * 4 CKM matrix.

FourthGeneration:VcbPrime   (default = 0.01; minimum = 0.0; maximum = 1.0)
The V_cb' matrix element in the 4 * 4 CKM matrix.

FourthGeneration:VtbPrime   (default = 0.1; minimum = 0.0; maximum = 1.0)
The V_tb' matrix element in the 4 * 4 CKM matrix.

FourthGeneration:VtPrimed   (default = 0.001; minimum = 0.0; maximum = 1.0)
The V_t'd matrix element in the 4 * 4 CKM matrix.

FourthGeneration:VtPrimes   (default = 0.01; minimum = 0.0; maximum = 1.0)
The V_t's matrix element in the 4 * 4 CKM matrix.

FourthGeneration:VtPrimeb   (default = 0.1; minimum = 0.0; maximum = 1.0)
The V_t'b matrix element in the 4 * 4 CKM matrix.

FourthGeneration:VtPrimebPrime   (default = 0.99; minimum = 0.0; maximum = 1.0)
The V_t'b' matrix element in the 4 * 4 CKM matrix. "?>