  Supersymmetric models based on the scenario of gague mediation often suffer
from the well-known $\mu$ problem. In this paper, we reconsider this problem in
low-scale gauge mediation in terms of effective field theory analysis. In this
paradigm, all high energy input soft mass can be expressed via loop expansions.
If the corrections coming from messenger thresholds are small, as we assume in
this letter, then RG evaluations can be taken as linearly approximation for
low-scale supersymmetric breaking. Due to these observations, the parameter
space can be systematically classified and studied after constraints coming
from electro-weak symmetry breaking are imposed. We find that some old
proposals in the literature are reproduced, and two new classes are uncovered.
We refer to a microscopic model, where the specific relations among
coefficients in one of the new classes are well motivated. Also, we discuss
some primary phenomenologies.
