110
Baryogenesis
Higgs belonging to 10, 15, 45 or 50 representations can be coupled to the matter
fermions. In particular, the introduction of a 45 Higgs representation also allows
the generation of sufficient baryon asymmetry for a wide range of parameters [17].
4.5 8aryogenesis in SO(10) GUTs
We have discussed the SU(5) GUT at some length, despite its inadequacies.
There are, however, other GUTs, based on larger (higher-rank) groups, which
some consider to be more attractive, and which, in any case, possess features
which are not present in the SU(5) GUTs. In particular, as a vector-like theory,
S0(10) has the desirable feature of being automatically anomaly-free. Another
attraction is the fact that it includes all of the fermions of one generation within
a single irreducible 16-dimensional (spinor) representation of the group. In tenns
of the representations of SU(5) x U(I) C S0(10), it decomposes as
16 = (1, -5) + (5,3) + (10, -1)
(4.94)
with the second number specifying the U(1) charge of the SU(5) irreducible
representation. The 5 and 10 irreducible representations are precisely those to
which the matter fermions are assigned in SU(5), shown in (4.62),(4.63), and the
extra SU(5) singlet state, which must exist if SO(IO) is correct, could be a rightchiral neutrino VR '" vf: this latter possibility looks feasible as well as attractive
in the light of evidence [27] for neutrino oscillations which can, of course, only
arise if neutrinos have (different) masses and, therefore, possibly right-chiral
components. (The existence of such a state also allows for the possibility of
a Majorana mass tenn.) The inclusion of both of the chiral components of all
fermions within the same GUT representation means that charge conjugation (C)
and parity reversal (P) are naturally symmetries of the GUT and are spontaneously
broken when the GUT breaks to a gauge group which does not have this property.
This occurs at a high scale if, as it might, S0(10) breaks to SU(5) or to
S U (5) x U (I). This happens if, for instance, the GUT symmetry-breaking Higgs
are also in a 16 representation.
However, there are other possibilities. Clearly
S0(10) ::> SO(6) x SO(4)
(4.95)
so, since
SO(6) ~ SU(4)
SO(4) ~ SU(2) x SU(2)
(4.96)
one possibility is that the SO(IO) breaks at the GUT scale as
MG
S0(10) ..... SU(4) x SU(2)L x SU(2)R = G422.
(4.97)
Baryogenesis
Higgs belonging to 10, 15, 45 or 50 representations can be coupled to the matter
fermions. In particular, the introduction of a 45 Higgs representation also allows
the generation of sufficient baryon asymmetry for a wide range of parameters [17].
4.5 8aryogenesis in SO(10) GUTs
We have discussed the SU(5) GUT at some length, despite its inadequacies.
There are, however, other GUTs, based on larger (higher-rank) groups, which
some consider to be more attractive, and which, in any case, possess features
which are not present in the SU(5) GUTs. In particular, as a vector-like theory,
S0(10) has the desirable feature of being automatically anomaly-free. Another
attraction is the fact that it includes all of the fermions of one generation within
a single irreducible 16-dimensional (spinor) representation of the group. In tenns
of the representations of SU(5) x U(I) C S0(10), it decomposes as
16 = (1, -5) + (5,3) + (10, -1)
(4.94)
with the second number specifying the U(1) charge of the SU(5) irreducible
representation. The 5 and 10 irreducible representations are precisely those to
which the matter fermions are assigned in SU(5), shown in (4.62),(4.63), and the
extra SU(5) singlet state, which must exist if SO(IO) is correct, could be a rightchiral neutrino VR '" vf: this latter possibility looks feasible as well as attractive
in the light of evidence [27] for neutrino oscillations which can, of course, only
arise if neutrinos have (different) masses and, therefore, possibly right-chiral
components. (The existence of such a state also allows for the possibility of
a Majorana mass tenn.) The inclusion of both of the chiral components of all
fermions within the same GUT representation means that charge conjugation (C)
and parity reversal (P) are naturally symmetries of the GUT and are spontaneously
broken when the GUT breaks to a gauge group which does not have this property.
This occurs at a high scale if, as it might, S0(10) breaks to SU(5) or to
S U (5) x U (I). This happens if, for instance, the GUT symmetry-breaking Higgs
are also in a 16 representation.
However, there are other possibilities. Clearly
S0(10) ::> SO(6) x SO(4)
(4.95)
so, since
SO(6) ~ SU(4)
SO(4) ~ SU(2) x SU(2)
(4.96)
one possibility is that the SO(IO) breaks at the GUT scale as
MG
S0(10) ..... SU(4) x SU(2)L x SU(2)R = G422.
(4.97)