Dynamically solving the μ/Bμ problem in gauge-mediated supersymmetry breaking

We provide a simple solution to the mu/B mu problem in the gauge- mediated Next-to-Minimal Supersymmetric Standard Model. In this model the messenger sector contains one pair of 3 + (3) over bar and one pair of 2 + (2) over bar messengers. These two messenger pairs couple to different gauge singlets in the hidden sector in which supersymmetry (SUSY) is broken. Such a gauge- mediation structure can naturally arise in many backgrounds. Because of the two effective SUSY breaking scales < F-i >/< M-i > in the messenger sector, the renormalization group evolutions of the soft SUSY breaking parameters can be properly modified, leading to a negative enough singlet soft mass square m(N)(2)(Lambda(EW)) and hence reasonable mu/B-mu values. In most of the perturbative (up to the GUT scale) parameter region, as a result, the electroweak scale is stabilized and phenomenologically interesting mass spectra of particles and superparticles are obtained. In addition, this model favors large values of tan beta: 5 similar to 50 and a heavy scalar spectrum. With the relatively large tan beta, the light U(1)(R) pseudoscalar (mainly appearing in the low-scale gauge-mediated SUSY breaking models) becomes extremely singlet-like, and is no longer a problem in this model. These features apply to all cases of low-, intermediate- and high-scale gauge-mediated SUSY breaking.