Affleck-Dine baryogenesis
137
where
_ 3Arsph
b=--3'
(4.247)
2vw T
Consequently, the quark asymmetry ~qL ' found from solving the coupled diffusion
equations in terms of the Higgsino sources Sii) (z) and Sii 2 (z), determines the
baryon asymmetry n B and, hence, the baryon-to-photon and baryon-to-entropy
ratios TlB == nB/ny ~ 7nB/s.
The conclusion is that the MSSM can explain the observed value (4.18) but
several independent parameters must be optimally tuned to do so. First, the CPviolating phase in the chargino mass matrix must be close to maximal. In order
to accommodate experimental data on electric dipole moments, especially that
of mercury, this requires that the lower generation squarks must have masses of
order 10 TeV. Actually this is necessary to maximize the chiral quark asymmetry.
Also mh '" 10 TeV is required to give sufficiently large radiative corrections to
mho given the already noted need for a light tR (miR ;S mt) to satisfy the washout
condition. In addition, tan fJ == Vu/Vd ;S 3 is required, the wall velocity Vw must
be close to its optimal value of 0.02 and the walls should be as thin as they can be
for the validity of the classical force method, about 6fT. (V",d are, respectively,
the VEVs of the (two) Higgs doublets hi in (4.59), used to give masses to the
uplike quarks, and h2 in (4.60), used to give masses to the downlike quarks.)
Similar conclusions have been reached by Huber and Schmidt [70].
Although the MSSM can explain the observed baryon asymmetry, it is
evidently not generic. The region of parameter space in which it does so is
very constrained. and might well be excluded by future experiments that set
new bounds on sparticle masses, for example. We therefore comment briefly on
alternatives that have been proposed but which, however, have not been as fully
studied as the other methods we have described.
4.12 Ameck-Dine baryogenesis
The discussion of baryogenesis in the previous section made hardly any use
of the super symmetry of the MSSM. Rather, the MSSM supplied new fields
that strengthened the first-order phase transition and which also developed the
chiral asymmetries that were subsequently converted to a baryon asymmetry.
In contrast, the Affleck-Dine mechanism [71] uses a generic feature of any
supersynunetric theory, namely the existence of 'flat' directions, to generate
a large VEV for a field carrying non-zero B - L in the early universe; at
temperatures higher than the electroweak phase transition, we have already
noted that weak sphaleron processes are in equilibrium, so that any B + L
asymmetry is erased. In fact, perturbative baryon-number conservation in the
MSSM is achieved by imposing a discrete R-synunetry that has the effect of
excluding certain dimension-four operators from the superpotential that would
otherwise explicitly generate baryon-number non-conservation, see [11] for
137
where
_ 3Arsph
b=--3'
(4.247)
2vw T
Consequently, the quark asymmetry ~qL ' found from solving the coupled diffusion
equations in terms of the Higgsino sources Sii) (z) and Sii 2 (z), determines the
baryon asymmetry n B and, hence, the baryon-to-photon and baryon-to-entropy
ratios TlB == nB/ny ~ 7nB/s.
The conclusion is that the MSSM can explain the observed value (4.18) but
several independent parameters must be optimally tuned to do so. First, the CPviolating phase in the chargino mass matrix must be close to maximal. In order
to accommodate experimental data on electric dipole moments, especially that
of mercury, this requires that the lower generation squarks must have masses of
order 10 TeV. Actually this is necessary to maximize the chiral quark asymmetry.
Also mh '" 10 TeV is required to give sufficiently large radiative corrections to
mho given the already noted need for a light tR (miR ;S mt) to satisfy the washout
condition. In addition, tan fJ == Vu/Vd ;S 3 is required, the wall velocity Vw must
be close to its optimal value of 0.02 and the walls should be as thin as they can be
for the validity of the classical force method, about 6fT. (V",d are, respectively,
the VEVs of the (two) Higgs doublets hi in (4.59), used to give masses to the
uplike quarks, and h2 in (4.60), used to give masses to the downlike quarks.)
Similar conclusions have been reached by Huber and Schmidt [70].
Although the MSSM can explain the observed baryon asymmetry, it is
evidently not generic. The region of parameter space in which it does so is
very constrained. and might well be excluded by future experiments that set
new bounds on sparticle masses, for example. We therefore comment briefly on
alternatives that have been proposed but which, however, have not been as fully
studied as the other methods we have described.
4.12 Ameck-Dine baryogenesis
The discussion of baryogenesis in the previous section made hardly any use
of the super symmetry of the MSSM. Rather, the MSSM supplied new fields
that strengthened the first-order phase transition and which also developed the
chiral asymmetries that were subsequently converted to a baryon asymmetry.
In contrast, the Affleck-Dine mechanism [71] uses a generic feature of any
supersynunetric theory, namely the existence of 'flat' directions, to generate
a large VEV for a field carrying non-zero B - L in the early universe; at
temperatures higher than the electroweak phase transition, we have already
noted that weak sphaleron processes are in equilibrium, so that any B + L
asymmetry is erased. In fact, perturbative baryon-number conservation in the
MSSM is achieved by imposing a discrete R-synunetry that has the effect of
excluding certain dimension-four operators from the superpotential that would
otherwise explicitly generate baryon-number non-conservation, see [11] for