grand unification
DESCRIPTION
-. Grand Unification. of the. strong. weak. and. electromagnetic. interactions. Standard Model. SU(3) x SU(2) x U(1). how to go beyond?. Leptons as a fourth color?. ( Pati-Salam - 1974 ). lepton number as fourth color?. SU(3) x SU(2) x U(1). - PowerPoint PPT PresentationTRANSCRIPT
Leptons as a fourth color?
lepton number as fourth color?
ddde
uuue
ddde
uuue
numberleptonL
numberbaryonB
LBTTQ RLEM
:
:
)(2
133
SU(3)xSU(2)xU(1) < SU(5)(Georgi, Glashow, 1974)
SU(3)xSU(2)xU(1) < SO(10)(Fritzsch, Minkowski, 1975 )
SU(3) x SU(2) x U(1) < SU(5)
fermions of one family in
two different representations:
)5()10(
e
d
d
d
b
g
r
5 )()10( e
d
uu
umdm
tmbm
em
cm
u
d
m
HM
2m
1m
2
3
e e
5SUrd
gd
bd
guburu
bd
gd
rd
e
ru
gu
bu
Gauge bosons in SU(5) > SU(2) x U(1):
adjoint representation ~ (24)
5 x 5* = 24 + 1
24 = (8,1) + (1,3) + (1,1) + (3,2) + (3*,2)
Grand unification takes placeabove a very high unified mass scale M.Above this energy there is only one unified coupling constant g. The coupling constants for QCD and for the SU(2) x U(1) theory are the same, apart from Clebsch-Gordan coefficients.
The rather different values
of the three coupling constants at low energies are due to renormalization effects.
No convergence of coupling constants
1)( i
convergence in case of
supersymmetry
Grand unification
SU(3) x SU(2) x U(1) < SU(4) x SU(2,L) x SU(2,R)
~ SO(6) x SO(4)
=> SO(10)
Representations of SO(10):16-dimensional spinor representation( => Pauli spinor ~ SO(3) )
SO(10)
ee uuuuuu ::: edddddde :::
SO(10):due to the two intermediate energy scales there is no problem with the convergence of the coupling constants at the grand unified mass scale