- -
10
H- ______ hu
10
10
H- _ _ __
hb
5
Baryogenesis in GUTs
105
Figure 4.4. Higgs (5) hoson vertices in the minimal SU(5) GUT. Single lines represent 5
representations. double lines 10 representations.
We have already noted that. in the minimal SU(5) GUT. the requirements
(4.40). (4.44) necessary for departure from thennal equilibrium are more likely to
be satisfied by the massive. colour-triplet Higgs scalar H3 than by the massive
gauge bosons. so X.Y decays will not contribute significantly to the baryon
asymmetry of the universe. Nevertheless. for completeness. we consider the
contributions to AB defined in (4.49) from both sources. First we note that the
tree-level contribution shown in figures 4.1 and 4.2 is zero. This is clear because
in the Born approximation the process X -. dv. for example. and i -. dii
derive from tenns in the Lagrangian which are Hennitian conjugate to each other.
so their amplitudes are complex conjugates. Since the kinematics of the two
processes is identical.
r(x -. dv)IBom = rei -. dii)IBom
(4.73)
and the contribution to ll. B given in (4.49) is zero. The same argument applies to
the decays of Y and H3.
At the next order. we need to include radiative corrections and look for (CPviolating) contributions to ll.B arising from the interference between the Born
tenns and these single-loop radiative corrections. For example. consider the
radiative correction to the decay
H3 -. uft,
(4.74)
shown in figure 4.5 (f. g are generation labels).
10
H- ______ hu
10
10
H- _ _ __
hb
5
Baryogenesis in GUTs
105
Figure 4.4. Higgs (5) hoson vertices in the minimal SU(5) GUT. Single lines represent 5
representations. double lines 10 representations.
We have already noted that. in the minimal SU(5) GUT. the requirements
(4.40). (4.44) necessary for departure from thennal equilibrium are more likely to
be satisfied by the massive. colour-triplet Higgs scalar H3 than by the massive
gauge bosons. so X.Y decays will not contribute significantly to the baryon
asymmetry of the universe. Nevertheless. for completeness. we consider the
contributions to AB defined in (4.49) from both sources. First we note that the
tree-level contribution shown in figures 4.1 and 4.2 is zero. This is clear because
in the Born approximation the process X -. dv. for example. and i -. dii
derive from tenns in the Lagrangian which are Hennitian conjugate to each other.
so their amplitudes are complex conjugates. Since the kinematics of the two
processes is identical.
r(x -. dv)IBom = rei -. dii)IBom
(4.73)
and the contribution to ll. B given in (4.49) is zero. The same argument applies to
the decays of Y and H3.
At the next order. we need to include radiative corrections and look for (CPviolating) contributions to ll.B arising from the interference between the Born
tenns and these single-loop radiative corrections. For example. consider the
radiative correction to the decay
H3 -. uft,
(4.74)
shown in figure 4.5 (f. g are generation labels).