B-ball Dark Matter and Baryogenesis

It has been recently suggested that stable, supersymmetric B-balls formed in the early universe could not only be the dark matter at the present epoch, but also be responsible for baryogenesis by their partial evaporation at high temperatures. We reinvestigate the efficiency of B-ball baryogenesis and find it to be limited by the diffusion of baryon number away from the B-balls. Successful baryogenesis may only occur for B-balls with charges Q< ∼ 1020 − 5× 1023, which is close to the observational lower limits on the Q of a significant B-ball dark matter component. We also present some cosmological constraints on the abundances of larger B-balls in the early universe. PACS numbers: 95.35.+d, 98.80.Cq, 98.80.Ft It is well known that particle physics models containing an unbroken U(1) symmetry allow for the existence of non-topological solitons [1,2], i.e. Q-balls, which carry a large number of a conserved global charge [3]. If the effective potential U(Φ), of the scalar Φ carrying the global charge grows slower than the second power of Φ, the mass of the solitonic object scales with the U(1) charge Q as MQ ≈ M̃ Q (0 < p < 1), where M̃ is some energy scale. The minimal supersymmetric standard model (MSSM) with supersymmetry breaking communicated at low energy scale contains an effective potential which is nearly flat ∼ M at large Φ. In this case, MQ ≈ M Q, where M ≈ 1−10 TeV is the SUSY breaking scale [3]. Such Q-balls are absolutely stable at zero temperature if their mass MQ becomes smaller than the total mass of individual U(1) charged particles mQ. Moreover, large baryonic Q-balls may be efficiently produced in the early universe [4,5] within a scenario of a collapsing unstable Affleck-Dine condensate [6]. In the MSSM the role of the global charge is played by baryon or lepton number carried by squarks or sleptons respectively [7]. Whereas L-balls (carrying leptonic charge) are not expected to survive until the present epoch for Q < ∼ 10(M/TeV) due to emission of massless neutrinos, B-balls (containing baryonic charge) with Q > ∼ 10 (M/TeV) are 1 e-mail: [email protected], [email protected] Preprint submitted to Elsevier Preprint 1 February 2008 stable because of the largeness of the nucleon mass. It has thus been proposed that B-balls produced in the early universe are not only an attractive dark matter candidate but may also be responsible for baryogenesis via partial evaporation of B-balls in the early universe [8]. (This is distinct from a scenario of evaporation of unstable B-balls [9] which could be responsible for baryogenesis and the creation of neutralino dark matter.) In this paper we reinvestigate the evaporation of B-balls. We find the efficiency of this process to be limited by the transport of baryon number away from the soliton, resulting in somewhat different conclusions than drawn in prior work [8]. We also give some previously unmentioned cosmological limits on the abundances of B-balls. B-balls may release baryonic charge via evaporation of squarks at temperatures T > mχ, where mχ is the squark mass [8]. Assuming that B-balls constitute dark matter at present (with fractional contribution to the critical density of ΩQ), there number density nQ in the early universe at temperature T has been nQ ≈ 0.8× 10 g∗ mp M ΩQ Qp T 3 . (1) Here mp is proton mass, g∗ is the number of relativistic degrees of freedom at the considered epoch (g∗ = 3.909 today), and we have assumed a Hubble constant of H = 70 km s Mpc. Consider B-balls with the general properties for their mass