  The cross section and transverse single-spin asymmetries of $\mu^{-}$ and
$\mu^{+}$ from open heavy-flavor decays in polarized $p$+$p$ collisions at
$\sqrt{s}=200$ GeV were measured by the PHENIX experiment during 2012 at the
Relativistic Heavy Ion Collider. Because heavy-flavor production is dominated
by gluon-gluon interactions at $\sqrt{s}=200$ GeV, these measurements offer a
unique opportunity to obtain information on the trigluon correlation functions.
The measurements are performed at forward and backward rapidity ($1.4<|y|<2.0$)
over the transverse momentum range of $1.25<p_T<7$ GeV/$c$ for the cross
section and $1.25<p_T<5$ GeV/$c$ for the asymmetry measurements. The obtained
cross section is compared to a fixed-order-plus-next-to-leading-log
perturbative-quantum-chromodynamics calculation. The asymmetry results are
consistent with zero within uncertainties, and a model calculation based on
twist-3 three-gluon correlations agrees with the data.
