  Recent reanalysis of ALEPH data on Z -> b bar{b} + X seems to indicate an
existence of the dimuon excess around 30 GeV with a branching fraction for Z ->
b bar{b} mu^+ mu^- around 1.1 X 10^{-5}. In this letter, we discuss three
different types of simplified models for this possible excess. In the first
class of models, we assume a new resonance couples to both b bar{b} and mu^+
mu^-. Within the allowed parameter space for the ALEPH data, this type of
models is excluded because of too large Drell-Yan production of dimuon from the
b bar{b} collision at the LHC. In the second model, we assume that the 30 GeV
excess is a new gauge boson Z' that couples to the SM b and a new vectorlike
singlet B quark heavier than Z and not to b bar{b}. Then one can account for
the ALEPH data without conflict with the DY constraint. The new vectorlike
quark B can be pair produced at the LHC 8/13 TeV by QCD with sigma(BB) ~
O(100-1000) pb, and Bq production rate is sigma(Bq) ~ a few pb which is larger
than sigma(Bb) roughly by an order of magnitude. Their signatures at the LHC
would be 2b + 4mu, bj + 2mu and 2b + 2mu, respectively, which however might
have been excluded already by LHC run I and II data since the multi-muon events
have low SM background and are rare at the LHC. In the third model, we consider
Z -> Z' phi followed by Z' -> mu^+ mu^- and phi -> b bar{b} assuming that the
Higgs field for Z' mass is also charged under the SM U(1)_Y gauge symmetry. In
this class of model, we could accommodate the Br(Z -> b bar{b} mu^+ mu^-) ~ 1.1
X 10^{-5} if we assume very large U(1)' charge for the U(1)' breaking Higgs
field. Finally, we study various kinematic distributions of muons and b jets in
all the three models, and find that none of the models we consider in this
paper are not compatible with the kinematic distributions extracted from the
ALEPH data.
