Baryogenesis in GUTs
103
5
5
10
10
Figure 4.2. Gauge vector boson vertices in the minimal SU(5) GUT.
so we may consistently assign (X, Y) this value of B - L, which shows that B - L
is conserved in all gauge-boson-mediated processes. B, however, is not separately
conserved. Indeed couplings (4.67) and their complex conjugates induce the
proton decay modes
p -+ 1r°e+,
1l'+v
(4.69)
at a rate which, in the non-supersymmetric model, is calculated [15] to be about
one hundred times the measured upper bound implied by (4.28). All of these
couplings arise from the Feynman diagram vertices shown in figure 4.2.
Higgs bosons are needed in a GUT to generate both the superheavy masses
needed for the non-standard model gauge bosons and Higgs particles, as well as
electroweak scale masses for the W± and Z gauge bosons. In the minimal nonsupersymmetric SUeS) GUT, the electroweak Higgs doublet is accommodated
in a 5 representation H, which in addition includes colour triplet scalars H3
transforming as (3, I, -}) of SU(3) x SU(2) x U(l). The Yukawa couplings
have the form
I-I
IIKLM
ey = X[IJ)ho1/l H +8
X[IJ)hUX[KL)HM +h.c.
(4.70)
where 1/1 1 , X[II) are the 5, 10 representations of SUeS) which include the matter
content (4.58) of the standard model. hu, ho are complex matrices (hu,o)jg
acting on the (undisplayed) generation-space labels of 1/1 1 and X(/ J). Then the
colour triplet Higgs particles have decay modes similar to those of the X -boson
H3 -+ uCd c ,
ul,
dv
(4.71)
all of which violate baryon-numberconservation. These are shown in figure 4.3.