Baryogenesis in SO( 10) GUTs
I11
This happens if, for instance. the GUT symmetry-breaking Higgs transforms as a
S4-dimensional representation. Then the 16-dimensional fermion representation
is given by
16 = (4,2. I) + (4. 1.2)
= [(~: t·(:: )J+[( !!r t,(!v~)J (4.98)
for the first generation. At later stages. the SV(4) breaks at a scale Mc and the
SV(2)R breaks at a scale MR as
SV(4) ~ SV(3)c x V(I)'
(4.99)
and
MR
SV(2)R -+ V(I)T)'
(4.100)
R
So either
Mc
MR
MJ
G422 -+ G3122 -+ G3121 -+ G sm
(4.101)
or
MR
Mc
MJ
G422 -+ G421 -+ G3121 -+ G sm
(4.102)
where
G3122 == SV(3)c x V(I)' x SV(2)L x SV(2)R
(4.103)
G3121 == SV(3)c x V(I)' x SV(2)L x V(I)T)
(4.104)
R
G421 == SV(4) X SV(2)L x V(I)T)
(4.105)
R
and Gsm = SU(3)c X SV(2)L x V(I)y is the standard model gauge group.
The content of the 4 representation of SV (4) under the decomposition (4.99)
is
4=(3.!)+(1.-1)
(4.106)
since V(I)' is a (traceless) generator of SV(4). We have used a normalization of
the hypercharge Y' which shows that, for fermions only.
y' = B-L.
(4.107)
This was first noted by Pati and Salam [28] and. for this reason V (I)' is sometimes
denoted V(I)B-L. At any rate, unlike the SV(5) GUTs. it ;s possible to break
B - L conservation in SO(lO) models. As previously noted. the scale MI at
which V (I)' and. therefore. B - L conservation is broken is not necessarily the
scale at which S0(10) is broken.
In fact, the SO(IO) group has an element D which interchanges the charge
conjugate doublets within the 16 representation (4.98). To see this. we choose
the decomposition (4.95) so that the Cartan subalgebra of SO(6) is generated by