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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 theRelativistic Heavy Ion Collider. Because heavy-flavor production is dominatedby gluon-gluon interactions at $\sqrt{s}=200$ GeV, these measurements offer aunique 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 crosssection and $1.25<p_T<5$ GeV/$c$ for the asymmetry measurements. The obtainedcross section is compared to a fixed-order-plus-next-to-leading-logperturbative-quantum-chromodynamics calculation. The asymmetry results areconsistent with zero within uncertainties, and a model calculation based ontwist-3 three-gluon correlations agrees with the data.

Cross section and transverse single-spin asymmetry of muons from open heavy-flavor decays in polarized $p$+$p$ collisions at $\sqrt{s}=200$ GeV