The $μ$-Problem in Theories with Gauge-Mediated Supersymmetry Breaking
G. Dvali, G. F. Giudice, A. Pomarol
TL;DR
This work identifies a severe μ-problem in gauge-mediated SUSY breaking, where μ and Bμ are typically generated at the same one-loop order, risking incompatible electroweak breaking. It introduces a natural mechanism in which μ arises from a D^2[X†X]-dependent operator, ensuring B_μ is not produced at the same order and enabling two-loop generation of B_μ and Higgs soft masses; a concrete two-singlet model yields μ ∼ (1/16π^2) Λ and B_μ ∼ (1/16π^2)^2 Λ^2, effectively achieving B_μ ∼ μ^2. The explicit model demonstrates that the Higgs doublets can be interpreted as pseudo-Goldstone bosons of an approximate global symmetry, providing a symmetry-based rationale for the scale separation. This framework solves the μ-problem within GMSB without introducing new light states, offering a natural path to EW symmetry breaking and a consistent Higgs sector.
Abstract
We point out that the $μ$-problem in theories in which supersymmetry breaking is communicated to the observable sector by gauge interactions is more severe than the one encountered in the conventional gravity-mediated scenarios. The difficulty is that once $μ$ is generated by a one-loop diagram, then usually $\bmu$ is also generated at the same loop order. This leads to the problematic relation $\bmu \sim μΛ$, where $Λ\sim$ 10--100 TeV is the effective supersymmetry-breaking scale. We present a class of theories for which this problem is naturally solved. Here, without any fine tuning among parameters, $μ$ is generated at one loop, while $\bmu$ arises only at the two-loop level. This mechanism can naturally lead to an interpretation of the Higgs doublets as pseudo-Goldstone bosons of an approximate global symmetry.