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.