Baryogenesis in GUTs
109
q
... H
...
....
X,Y V\I\IV( : : I
x~
.... ....
q
.... H
Figure 4.7. CP-violating. baryon-number non-conserving decays of X.Y bosons.
replaced by h U . D ' Then. besides the radiative correction to H3 decay shown in
figure 4.5, there will be a similar diagram involving H) exchange. The difference
between the decay rates now satisfies
r(H3 -+ Uflg) - r(l13 -+ "fig} ex Im[h~h1huh~]lm(lH')
(4.91)
instead of (4.7S). In general. this is non-zero [IS].
Unfortunately, such a model is unsatisfactory in other respects. It will have
flavour-changing. Higgs-mediated neutral current decays [21] and. in addition.
like the model with a single 5 of Higgs, it continues to possess the strong CP
problem. (See section 5.3.1.) We shall see later that the most attactive solution
to the latter problem utilizes a Peccei-Quinn U(l) symmetry [22]. This requires
additional Higgs doublets. so that one doublet H is coupled only to dR quarks
and the other doublet H' only to UR quarks. This is realized in an SU(5) GUT
by coupling one Higgs 5 to the matter (5)(10) and the other to the (10)(10)
fields [23]. Thus, instead of (4.70). we have
.l.iH-J
hi
I
IJKLM
C Y = X[IJ) h D."
+ X[IJ) UX[KL]HME
+ h.c.
(4.92)
This looks as though the one-loop radiative correction shown in figure 4.5 is
now forbidden, since the exchanged Higgs has to have both D-type and Utype couplings. However, it is allowed, since the Higgs mass eigenstates mix
H and H'. Nevertheless, there is no CP-violation and, hence. no contibution
to the baryon asymmetry, for the reason (4.79) given earlier. Instead, in this
model. the (CP-violating) baryon asymmetry arises from the decays of X, Y
gauge bosons with a pair of Higgs bosons in the intermediate or final state [24.25]
(see figure 4.7), and a sufficient asymmetry arises for a wide range of parameters
[17,26].
Another variant of the SU(5) minimal model is to introduce a Higgs
multiplet belonging to a different representation, i.e. not a 5. Since, in SU(5),
"5 x"5 = 10+ 15
"5 x 10 = 5+45
10 x 10 ="5 + 45 + 50
(4.93)
109
q
... H
...
....
X,Y V\I\IV( : : I
x~
.... ....
q
.... H
Figure 4.7. CP-violating. baryon-number non-conserving decays of X.Y bosons.
replaced by h U . D ' Then. besides the radiative correction to H3 decay shown in
figure 4.5, there will be a similar diagram involving H) exchange. The difference
between the decay rates now satisfies
r(H3 -+ Uflg) - r(l13 -+ "fig} ex Im[h~h1huh~]lm(lH')
(4.91)
instead of (4.7S). In general. this is non-zero [IS].
Unfortunately, such a model is unsatisfactory in other respects. It will have
flavour-changing. Higgs-mediated neutral current decays [21] and. in addition.
like the model with a single 5 of Higgs, it continues to possess the strong CP
problem. (See section 5.3.1.) We shall see later that the most attactive solution
to the latter problem utilizes a Peccei-Quinn U(l) symmetry [22]. This requires
additional Higgs doublets. so that one doublet H is coupled only to dR quarks
and the other doublet H' only to UR quarks. This is realized in an SU(5) GUT
by coupling one Higgs 5 to the matter (5)(10) and the other to the (10)(10)
fields [23]. Thus, instead of (4.70). we have
.l.iH-J
hi
I
IJKLM
C Y = X[IJ) h D."
+ X[IJ) UX[KL]HME
+ h.c.
(4.92)
This looks as though the one-loop radiative correction shown in figure 4.5 is
now forbidden, since the exchanged Higgs has to have both D-type and Utype couplings. However, it is allowed, since the Higgs mass eigenstates mix
H and H'. Nevertheless, there is no CP-violation and, hence. no contibution
to the baryon asymmetry, for the reason (4.79) given earlier. Instead, in this
model. the (CP-violating) baryon asymmetry arises from the decays of X, Y
gauge bosons with a pair of Higgs bosons in the intermediate or final state [24.25]
(see figure 4.7), and a sufficient asymmetry arises for a wide range of parameters
[17,26].
Another variant of the SU(5) minimal model is to introduce a Higgs
multiplet belonging to a different representation, i.e. not a 5. Since, in SU(5),
"5 x"5 = 10+ 15
"5 x 10 = 5+45
10 x 10 ="5 + 45 + 50
(4.93)