## 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.

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

`flag` FourthBottom:gg2bPrimebPrimebar (`default = off`)
Scatterings g g -> b' b'bar. Code 801.

`flag` FourthBottom:qqbar2bPrimebPrimebar (`default = off`)
Scatterings q qbar -> b' b'bar by gluon exchange. Code 802.

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

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

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

`flag` FourthBottom:ffbar2bPrimetbar(s:W) (`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.

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

`flag` FourthTop:gg2tPrimetPrimebar (`default = off`)
Scatterings g g -> t' t'bar. Code 821.

`flag` FourthTop:qqbar2tPrimetPrimebar (`default = off`)
Scatterings q qbar -> t' t'bar by gluon exchange. Code 822.

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

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

`flag` FourthTop:ffbar2tPrimeqbar(s:W) (`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.

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

`flag` FourthPair:ffbar2tauPrimenuPrimebar(s:W) (`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.

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

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

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

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

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

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

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