Q-balls in the Mssm

A Q-ball is a stable, charge Q soliton in a scalar field theory with a spontaneously broken global U(1) symmetry . The Q-ball solution arises provided the scalar potential V (φ) is such that V (φ)/|φ|2 has a minimum at non-zero φ. In the MSSM such solitons are necessarily part of the spectrum of the theory, as was first pointed out by Kusenko . This is due to the form of the MSSM scalar potential and the fact that squarks and sleptons carry a global B − L charge. The crucial question is whether B-balls and/or L-balls can be copiously created in the early Universe and whether they could naturally be sufficiently long-lived to have important consequences for cosmology. An interesting possibility for Q-ball formation is provided by the fact that there are many flat directions in the MSSM . During inflation the MSSM scalar fields are free to fluctuate along these flat directions and to form condensates. This is closely related to Affleck-Dine (AD) baryogenesis , in which a B violating scalar condensate forms along a D-flat direction of the MSSM scalar potential composed of squark and possibly of slepton fields. The difference now is that the condensate is naturally unstable with respect to the formation of Q-balls 1,5,2 with a very large charge . The properties of the MSSM Q-balls will depend upon the scalar potential associated with the condensate scalar, which in turn depends upon the SUSY breaking mechanism and on the order d at which the non-renormalizable terms lift the degeneracy of the potential; examples are the HuL-direction with d=4 and udd-direction with d=6. If SUSY breaking occurs at low energy scales, via gauge mediated SUSY breaking , Q-balls will be stable . Stable Bballs could have a wide range of astrophysical, experimental and practical implications.