114
Baryogenesis
x = H3 is the colour-triplet Higgs particle with
14
mH3 ~ 10 GeV.
(4.118)
In these circumstances. the decay
~~xi
(4.119)
is kinematically forbidden. so if X particles are created. they must be created
by thermal production in the reheated universe. (This is why our comments in
section 4.5 about the possibility in other GUTs of baryon asymmetry arising at
a scale well below MG are pertinent.) So the next question is: What is the
abundance of the out-of-equilibrium X particles thus created? It is beyond our
scope to discuss here the calculation of the reheating temperature, the abundance,
and other questions which arise. in any detail. The interested reader is referred
to [31] and references therein. We shall content ourselves with noting the
conclusions which have been reached from these studies. A mechanism called
'parametric resonance', deriving from nonlinear quantum effects, leads to a
phenomenon called 'preheating' during which copious production of X particles
occurs even though these are heavier than the inflaton. It appears that the outof-equilibrium scenario, upon which our analysis was predicated, arises naturally
and that the right amount of baryon asymmetry is produced for a very wide range
of decay widths of the X particles.
Notwithstanding this highly welcome outcome, one is naturally led to
wonder whether the observed baryon asymmetry might not have a different origin.
Although, as we have noted, there is evidence of (supersymmetric) unification of
coupling strengths, this does not necessarily entail the existence of a GUT. It is
quite conceivable. in the context of string theory for example. that there is no
GUT. If so, the observed baryon asymmetry must have a different origin. This is
the topic to which we now turn.
4.7 Baryon-number non-conservation in the Standard Model
It is easy to see that the standard model Lagrangian, having the local gauge
symmetry group SU(3)c x SU(2)L x U(l)Y, is also invariant under the (classical)
global U(l) transformations associated with the baryon number (B) and lepton
numbers (Nt. l = e, 11-, r) in which fermion fields 'I/I(x) transform as
'I/I(x) ~ e iB8 '1/1(x)
(4.120)
'I/I(x) ~ e iNt8 '1/1(x).
(4.121)
When (J is local, the first of these (4.120), for example, applied to the kinetic term
produces a change 8S in the action
8S = - f d 4 x (ty" B1/I'I/I)a,,(J
Baryogenesis
x = H3 is the colour-triplet Higgs particle with
14
mH3 ~ 10 GeV.
(4.118)
In these circumstances. the decay
~~xi
(4.119)
is kinematically forbidden. so if X particles are created. they must be created
by thermal production in the reheated universe. (This is why our comments in
section 4.5 about the possibility in other GUTs of baryon asymmetry arising at
a scale well below MG are pertinent.) So the next question is: What is the
abundance of the out-of-equilibrium X particles thus created? It is beyond our
scope to discuss here the calculation of the reheating temperature, the abundance,
and other questions which arise. in any detail. The interested reader is referred
to [31] and references therein. We shall content ourselves with noting the
conclusions which have been reached from these studies. A mechanism called
'parametric resonance', deriving from nonlinear quantum effects, leads to a
phenomenon called 'preheating' during which copious production of X particles
occurs even though these are heavier than the inflaton. It appears that the outof-equilibrium scenario, upon which our analysis was predicated, arises naturally
and that the right amount of baryon asymmetry is produced for a very wide range
of decay widths of the X particles.
Notwithstanding this highly welcome outcome, one is naturally led to
wonder whether the observed baryon asymmetry might not have a different origin.
Although, as we have noted, there is evidence of (supersymmetric) unification of
coupling strengths, this does not necessarily entail the existence of a GUT. It is
quite conceivable. in the context of string theory for example. that there is no
GUT. If so, the observed baryon asymmetry must have a different origin. This is
the topic to which we now turn.
4.7 Baryon-number non-conservation in the Standard Model
It is easy to see that the standard model Lagrangian, having the local gauge
symmetry group SU(3)c x SU(2)L x U(l)Y, is also invariant under the (classical)
global U(l) transformations associated with the baryon number (B) and lepton
numbers (Nt. l = e, 11-, r) in which fermion fields 'I/I(x) transform as
'I/I(x) ~ e iB8 '1/1(x)
(4.120)
'I/I(x) ~ e iNt8 '1/1(x).
(4.121)
When (J is local, the first of these (4.120), for example, applied to the kinetic term
produces a change 8S in the action
8S = - f d 4 x (ty" B1/I'I/I)a,,(J