We present measurements of two-particle angular correlations between high-transverse-momentum ($2<p_T<11$ GeV/$c$) $\pi^0$ observed at midrapidity ($|\eta|<0.35$) and particles produced either at forward ($3.1<\eta<3.9$) or backward ($-3.7<\eta<-3.1$) rapidity in $d$$+$Au and $p$$+$$p$ collisions at $\sqrt{s_{_{NN}}}=200$ GeV. The azimuthal angle correlations for particle pairs with this large rapidity gap in the Au-going direction exhibit a ridge-like structure that persists up to $p_T{\approx}6$ GeV/$c$ and which strongly depends on collision centrality, which is a similar characteristic to the hydrodynamical particle flow in A+A collisions. The ridge-like structure is absent in the $d$-going direction as well as in $p$$+$$p$ collisions, in the transverse-momentum range studied. The results indicate that the ridge-like structure is shifted in the Au-going direction toward more central collisions, similar to the charged-particle pseudorapidity distributions.

The PHENIX experiment at the Relativistic Heavy Ion Collider has measured the differential cross section, mean transverse momentum, mean transverse momentum squared of inclusive $J/\psi$ and cross-section ratio of $\psi(2S)$ to $J/\psi$ at forward rapidity in \pp collisions at \sqrts = 510 GeV via the dimuon decay channel. Comparison is made to inclusive $J/\psi$ cross sections measured at \sqrts = 200 GeV and 2.76--13 TeV. The result is also compared to leading-order nonrelativistic QCD calculations coupled to a color-glass-condensate description of the low-$x$ gluons in the proton at low transverse momentum ($p_T$) and to next-to-leading order nonrelativistic QCD calculations for the rest of the $p_T$ range. These calculations overestimate the data at low $p_T$. While consistent with the data within uncertainties above $\approx3$ GeV/$c$, the calculations are systematically below the data. The total cross section times the branching ratio is BR $d\sigma^{J/\psi}_{pp}/dy (1.2<|y|<2.2, 0<p_T<10~\mbox{GeV/$c$}) =$ 54.3 $\pm$ 0.5 (stat) $\pm$ 5.5 (syst) nb.

The PHENIX experiment has measured the spin alignment for inclusive $J/\psi\rightarrow e^{+}e^{-}$ decays in $p$+$p$ collisions at $\sqrt{s}=510$ GeV at midrapidity. The angular distributions have been measured in three different polarization frames, and the three decay angular coefficients have been extracted in a full two-dimensional analysis. Previously, PHENIX saw large longitudinal net polarization at forward rapidity at the same collision energy. This analysis at midrapidity, complementary to the previous PHENIX results, sees no sizable polarization in the measured transverse momentum range of $0.0<p_T<10.0$ GeV/$c$. The results are consistent with a previous one-dimensional analysis at midrapidity at $\sqrt{s}=200$ GeV. The transverse-momentum-dependent cross section for midrapidity $J/\psi$ production has additionally been measured, and after comparison to world data we find a simple logarithmic dependence of the cross section on $\sqrt{s}$.

We report the first measurement of the full angular distribution for inclusive $J/\psi\rightarrow\mu^{+}\mu^{-}$ decays in $p$$+$$p$ collisions at $\sqrt{s}=510$ GeV. The measurements are made for $J/\psi$ transverse momentum $2<p_{T}<10$ GeV/$c$ and rapidity $1.2<y<2.2$ in the Helicity, Collins-Soper, and Gottfried-Jackson reference frames. In all frames the polar coefficient $\lambda_{\theta}$ is strongly negative at low $p_{T}$ and becomes close to zero at high $p_{T}$, while the azimuthal coefficient $\lambda_{\phi}$ is close to zero at low $p_{T}$, and becomes slightly negative at higher $p_{T}$. The frame-independent coefficient $\tilde{\lambda}$ is strongly negative at all $p_{T}$ in all frames. The data are compared to the theoretical predictions provided by nonrelativistic quantum chromodynamics models.

We present the first measurements of long-range angular correlations and the transverse momentum dependence of elliptic flow $v_2$ in high-multiplicity $p$$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV. A comparison of these results with previous measurements in high-multiplicity $d$$+$Au and $^3{\rm He}$$+$Au collisions demonstrates a relation between $v_2$ and the initial collision eccentricity $\varepsilon_2$, suggesting that the observed momentum-space azimuthal anisotropies in these small systems have a collective origin and reflect the initial geometry. Good agreement is observed between the measured $v_2$ and hydrodynamic calculations for all systems, and an argument disfavoring theoretical explanations based on momentum-space domain correlations is presented. The set of measurements presented here allows us to leverage the distinct intrinsic geometry of each of these systems to distinguish between different theoretical descriptions of the long-range correlations observed in small collision systems.

Dihadron and isolated direct photon-hadron angular correlations are measured in $p$$+$$p$ collisions at $\sqrt{s}=200$ GeV. The correlations are sensitive to nonperturbative initial-state and final-state transverse momentum $k_T$ and $j_T$ in the azimuthal nearly back-to-back region $\Delta\phi\sim\pi$. In this region, transverse-momentum-dependent evolution can be studied when several different hard scales are measured. To have sensitivity to small transverse momentum scales, nonperturbative momentum widths of $p_{\rm out}$, the out-of-plane transverse momentum component perpendicular to the trigger particle, are measured. These widths are used to investigate possible effects from transverse-momentum-dependent factorization breaking. When accounting for the longitudinal momentum fraction of the away-side hadron with respect to the near-side trigger particle, the widths are found to increase with the hard scale; this is qualitatively similar to the observed behavior in Drell-Yan and semi-inclusive deep-inelastic scattering interactions. The momentum widths are also studied as a function of center-of-mass energy by comparing to previous measurements at $\sqrt{s}=510$ GeV. The nonperturbative jet widths also appear to increase with $\sqrt{s}$ at a similar $x_T$, which is qualitatively consistent to similar measurements in Drell-Yan interactions. To quantify the magnitude of any transverse-momentum-dependent factorization breaking effects, calculations will need to be performed to compare to these measurements.

We present measurements of the transverse-momentum dependence of elliptic flow $v_2$ for identified pions and (anti)protons at midrapidity ($|\eta|<0.35$), in 0%--5% central $p$$+$Au and $^3$He$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV. When taken together with previously published measurements in $d$$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV, the results cover a broad range of small-collision-system multiplicities and intrinsic initial geometries. We observe a clear mass-dependent splitting of $v_2(p_{T})$ in $d$$+$Au and $^3$He$+$Au collisions, just as in large nucleus-nucleus ($A$$+$$A$) collisions, and a smaller splitting in $p$$+$Au collisions. Both hydrodynamic and transport model calculations successfully describe the data at low $p_T$ ($< 1.5$ GeV/$c$), but fail to describe various features at higher $p_T$. In all systems, the $v_2$ values follow an approximate quark-number scaling as a function of the hadron transverse kinetic energy per constituent quark($KE_T/n_q$), which was also seen previously in $A$$+$$A$ collisions.

We report on the nuclear dependence of transverse single-spin asymmetries (TSSAs) in the production of positively-charged hadrons in polarized $p^{\uparrow}+p$, $p^{\uparrow}+$Al and $p^{\uparrow}+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV. The measurements have been performed at forward rapidity ($1.4<\eta<2.4$) over the range of $1.8<p_{T}<7.0$ GeV$/c$ and $0.1<x_{F}<0.2$. We observed a positive asymmetry $A_{N}$ for positively-charged hadrons in \polpp collisions, and a significantly reduced asymmetry in $p^{\uparrow}$+$A$ collisions. These results reveal a nuclear dependence of charged hadron $A_N$ in a regime where perturbative techniques are relevant. These results provide new opportunities to use \polpA collisions as a tool to investigate the rich phenomena behind TSSAs in hadronic collisions and to use TSSA as a new handle in studying small-system collisions.