  Experimental observations of strikingly large transverse single-spin
asymmetries (TSSAs) opened a window into quark and gluon dynamics present in
hadronic collisions, revealing large spin-momentum correlations within nucleons
and in the process of forming hadrons. Though originally measured in lower
energy fixed target experiments, they have been found to persist in collisions
with momentum transfer well into the perturbative regime of quantum
chromodynamics (QCD) and yet their origin remains poorly understood. TSSA
measurements have allowed for the development of both transverse momentum
dependent and collinear twist-3 descriptions of nonperturbative spin-momentum
correlations for both initial- and final-state effects. Results are presented
for the TSSAs of direct photons, neutral pions, and eta mesons in the
pseudorapidity range $|\eta|<0.35$ from $p^\uparrow+p$ collisions with
$\sqrt{s} = 200$ GeV at PHENIX. As hadrons, $\pi^0$ and $\eta$ mesons are
sensitive to both initial- and final-state effects. At midrapidity, $\pi^0$ and
$\eta$ measurements are sensitive to the dynamics of gluons along with a mix of
quark flavors. These results are a factor of three increase in statistical
precision and extend to higher transverse momentum when compared with previous
PHENIX measurements in this kinematic region. Because direct photon production
does not include hadronization, the direct photon TSSA is only sensitive to
spin-momentum correlations in the proton. The kinematics of this result in
particular make the direct photon TSSA a clean probe of gluon dynamics in the
transversely polarized proton. All three of these asymmetries will help
constrain the twist-3 trigluon collinear correlation function as well as the
gluon Sivers function, improving our knowledge of spin-dependent gluon dynamics
in QCD.
