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