Q-ball Formation through Affleck-Dine Mechanism

We present the full nonlinear calculation of the formation of a Q-ball through the Affleck-Dine (AD) mechanism by numerical simulations. It is shown that large Q-balls are actually produced by the fragmentation of the condensate of a scalar field whose potential is very flat. We find that the typical size of a Q-ball is determined by the most developed mode of linearized fluctuations, and almost all the initial charges which the AD condensate carries are absorbed into the formed Q-balls, whose sizes and the charges depend only on the initial charge densities.Comment: 4 pages, RevTex, 3 postscript figures included, the published versio

Q-ball formation in the gravity-mediated SUSY breaking scenario

We study the formation of Q-balls which are made of flat directions that appear in the supersymmetric extension of the standard model in the context of gravity-mediated supersymmetry breaking. The full non-linear calculations for the dynamics of the complex scalar field are made. Since the scalar potential in this model is flatter than \phi^2, we have found that fluctuations develop and go non-linear to form non-topological solitons, Q-balls. The size of a Q-ball is determined by the most amplified mode, which is completely determined by the model parameters. On the other hand, the charge of Q-balls depends linearly on the initial charge density of the Affleck-Dine (AD) field. Almost all the charges are absorbed into Q-balls, and only a tiny fraction of the charges is carried by a relic AD field. It may lead to some constraints on the baryogenesis and/or parameters in the particle theory. The peculiarity of gravity-mediation is the moving Q-balls. This results in collisions between Q-balls. It may increase the charge of Q-balls, and change its fate.Comment: 9 pages, RevTex, 11 postscript figures included, to appear in Phys. Rev.

Numerical simulations of fragmentation of the Affleck-Dine condensate

We present numerical simulations of fragmentation of the Affleck-Dine condensate in two spatial dimensions. We argue analytically that the final state should consist of both Q-balls and anti-Q-balls in a state of maximum entropy, with most of the balls small and relativistic. Such a behaviour is found in simulations on a 100x100 lattice with cosmologically realistic parameter values. During fragmentation process, we observe filament-like texture in the spatial distribution of charge. The total charge in Q-balls is found to be almost equal to the charge in anti-Q-balls and typically orders of magnitude larger than charge asymmetry. Analytical considerations indicate that, apart from geometrical factors, the results of the simulated two dimensional case should apply also to the fully realistic three dimensional case.Comment: 28 pages, 39 figure

Q-ball formation: Obstacle to Affleck-Dine baryogenesis in the gauge-mediated SUSY breaking ?

We consider the Affleck-Dine baryogenesis comprehensively in the minimal supersymmetric standard model with gauge-mediated supersymmetry breaking. Considering the high temperature effects, we see that the Affleck-Dine field is naturally deformed into the form of the Q ball. In the natural scenario where the initial amplitude of the field and the A-terms are both determined by the nonrenormalizable superpotential, we obtain only very a narrow allowed region in the parameter space in order to explain the baryon number of the universe for the case that the Q-ball formation occurs just after baryon number production. Moreover, most of the parameter sets suited have already been excluded by current experiments. We also find new situations in which the Q-ball formation takes place rather late compared with baryon number creation. This situation is more preferable, since it allows a wider parameter region for naturally consistent scenarios, although it is still difficult to realize in the actual cosmological scenario.Comment: 27 pages, RevTeX, 21 postscript figures included. The version to be publishe

Q-ball formation in the wake of Hubble-induced radiative corrections

We discuss some interesting aspects of the $\rm Q$-ball formation during the early oscillations of the flat directions. These oscillations are triggered by the running of soft $({\rm mass})^2$ stemming from the nonzero energy density of the Universe. However, this is quite different from the standard $\rm Q$-ball formation. The running in presence of gauge and Yukawa couplings becomes strong if $m_{1/2}/m_0$ is sufficiently large. Moreover, the $\rm Q$-balls which are formed during the early oscillations constantly evolve, due to the redshift of the Hubble-induced soft mass, until the low-energy supersymmtery breaking becomes dominant. For smaller $m_{1/2}/m_0$, $\rm Q$-balls are not formed during early oscillations because of the shrinking of the instability band due to the Hubble expansion. In this case the $\rm Q$-balls are formed only at the weak scale, but typically carry smaller charges, as a result of their amplitude redshift. Therefore, the Hubble-induced corrections to the flat directions give rise to a successful $\rm Q$-ball cosmology.Comment: 7 revtex pages, few references corrected and added, final version to appear in Phys. Rev.

Hybridized Affleck-Dine baryogenesis

We propose a novel scenario for Affleck-Dine baryogenesis in the braneworld, considering the hybrid potential for the Affleck-Dine field. Destabilization of the flat direction is not due to the Hubble parameter, but is induced by a trigger field. The moduli for the brane distance plays the role of the trigger field. Q-balls are unstable in models with large extra dimensions.Comment: 10pages, plain latex2e, references added, to appear in PR

Supersymmetric D-term Inflation and B-ball Baryogenesis

We consider the B-ball cosmology of the MSSM in the context of D-term inflation models where the reheating temperature is determined by the Affleck-Dine mechanism to be of the order of 1 GeV. We show that such a low reheating temperature can arise quite naturally as the result of a symmetry which is required to maintain the flatness of the inflaton potential. In this case the B-balls will decay well after the freeze-out temperature of the LSP, allowing baryons and cold dark matter to originate primarily from B-ball decays.Comment: 12 pages LaTeX. Final published version (Phys.Rev.Lett. 81 (1998) 3071

Condensate cosmology in O'Raifeartaigh models

Flat directions charged under an R-symmetry are a generic feature of O'Raifeartaigh models. Non-topological solitons associated with this symmetry, R-balls, are likely to form through the fragmentation of a condensate, itself created by soft terms induced during inflation. In gravity mediated SUSY breaking R-balls decay to gravitinos, reheating the universe. For gauge mediation R-balls can provide a good dark matter candidate. Alternatively they can decay, either reheating or cooling the universe. Conserved R-symmetry permits decay to gravitinos or gauginos, whereas spontaneously broken R-symmetry results in decay to visible sector gauge bosons.Comment: 29 pages, 5 figures. Comments and references added, accepted for publication in JHE

The fate of the B ball

The gauge-mediated SUSY-breaking (GMSB) model needs entropy production at a relatively low temperature in the thermal history of the Universe for the unwanted relics to be diluted. This requires a mechanism for the baryogenesis after the entropy production, and the Affleck and Dine (AD) mechanism is a promising candidate for it. The AD baryogenesis in the GMSB model predicts the existence of the baryonic Q ball, that is the B ball, and this may work as the dark matter in the Universe. In this article, we discuss the stability of the B ball in th presence of baryon-number violating interactions. We find that the evaporation rate increases monotonically with the B-ball charge because the large field value inside the B ball enhances the effect of the baryon-number-violating operators. While there are some difficulties to evaluate the evaporation rate of the B ball, we derive the evaporation time (lifetime) of the B ball for the mass-to-charge ratio \omega_0\gsim 100 \MEV. The lifetime of the B ball and the distortion of the cosmic ray positron flux and the cosmic background radiation from the B ball evaporation give constraints on the baryon number of the B ball and the interaction, if the B ball is the dark matter. We also discuss some unresolved properties of the B ball.Comment: 27 pages incl 8 figs, LaTe

Stabilizing dilaton and baryogenesis

Entropy production by the dilaton decay is studied in the model where the dilaton acquires potential via gaugino condensation in the hidden gauge group. Its effect on the Affleck-Dine baryogenesis is investigated with and without non-renormalizable terms in the potential. It is shown that the baryon asymmetry produced by this mechanism with the higher-dimensional terms is diluted by the dilaton decay and can be regulated to the observed value.Comment: 20 pages, 3 figures, baryon asymmetry revised, errors corrected, references and comments adde