We report the transverse single-spin asymmetries of $J/\psi$ production at forward and backward rapidity, $1.2<|y|<2.2$, as a function of $J/\psi$ transverse momentum ($p_T$) and Feynman-$x$ ($x_F$). The data analyzed were recorded by the PHENIX experiment at the Relativistic Heavy Ion Collider in 2015 from $p$$+$$p$, $p$$+$Al, and $p$$+$Au collisions with transversely polarized proton beams at $\sqrt{s_{_{NN}}}=200$ GeV. At this collision energy, single-spin asymmetries for heavy-flavor particle production of $p$$+$$p$ collisions provide access to the spin-dependent gluon distribution and higher-twist correlation functions inside the nucleon, such as the gluon Qiu-Sterman and trigluon correlation functions. Proton+nucleus collisions offer an excellent opportunity to study nuclear effects on the correlation functions. The data indicate negative asymmetries at the two-standard-deviation level in the $p$$+$Au data for $p_T<2$ GeV/$c$ at both forward and backward rapidity, while in $p$$+$$p$ and $p$$+$Al collisions the asymmetries are consistent with zero within the range of experimental uncertainties.

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.

We have measured the azimuthal anisotropy of pi0's for 1 < pT < 18 GeV/c for Au+Au collisions at sqrt s_NN = 200 GeV. The observed anisotropy shows a gradual decrease in 3 < pT < 7 - 10 GeV/c, but remains positive beyond 10 GeV/c. The magnitude of this anisotropy is under-predicted, up to at least 10 GeV/c, by current perturbative QCD (pQCD) energy-loss model calculations. An estimate of the increase in anisotropy expected from initial-geometry modification due to gluon saturation effects and initial-geometry fluctuations is insufficient to account for this discrepancy. Calculations which implement a path length dependence steeper than what is implied by current pQCD energy-loss models, show reasonable agreement with the data.

The PHENIX collaboration presents a systematic study of $\pi^0$ production from $p$ $+$ $p$, $p$ $+$Al, $p$ $+$Au, $d$ $+$Au, and $^{3}$He$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV. Measurements were performed with different centrality selections as well as the total inelastic, 0%--100%, selection for all collision systems. For 0%--100% collisions, the nuclear modification factors, $R_{xA}$, are consistent with unity for $p_T$ above 8 GeV/$c$, but exhibit an enhancement in peripheral collisions and a suppression in central collisions. The enhancement and suppression characteristics are similar for all systems for the same centrality class. It is shown that for high-$p_T$-$\pi^0$ production, the nucleons in the $d$ and $^3$He interact mostly independently with the Au nucleus and that the counter intuitive centrality dependence is likely due to a physical correlation between multiplicity and the presence of a hard scattering process. These observations disfavor models where parton energy loss has a significant contribution to nuclear modifications in small systems. Nuclear modifications at lower $p_T$ resemble the Cronin effect -- an increase followed by a peak in central or inelastic collisions and a plateau in peripheral collisions. The peak height has a characteristic ordering by system size as $p$ $+$Au $>$ $d$ $+$Au $>$ $^{3}$He$+$Au $>$ $p$ $+$Al. For collisions with Au ions, current calculations based on initial state cold nuclear matter effects result in the opposite order, suggesting the presence of other contributions to nuclear modifications, in particular at lower $p_T$.

Suppression of the $J/\psi$ nuclear-modification factor has been seen as a trademark signature of final-state effects in large collision systems for decades. In small systems, the nuclear modification was attributed to cold-nuclear-matter effects until the observation of strong differential suppression of the $\psi(2S)$ state in $p/d$ $+$ $A$ collisions suggested the presence of final-state effects. Results of $J/\psi$ and $\psi(2S)$ measurements in the dimuon decay channel are presented here for $p$ $+$ $p$, $p$ $+$Al, and $p$ $+$Au collision systems at $\sqrt{s_{_{NN}}}=200$ GeV. The results are predominantly shown in the form of the nuclear-modification factor, $R_{pA}$, the ratio of the $\psi(2S)$ invariant yield per nucleon-nucleon collision in collisions of proton on target nucleus to that in $p$ $+$ $p$ collisions. Measurements of the $J/\psi$ and $\psi(2S)$ nuclear-modification factor are compared with shadowing and transport-model predictions, as well as to complementary measurements at Large-Hadron-Collider energies.

Measurements of transverse-single-spin asymmetries ($A_{N}$) in $p$$+$$p$ collisions at $\sqrt{s}=$62.4 and 200 GeV with the PHENIX detector at RHIC are presented. At midrapidity, $A_{N}$ is measured for neutral pion and eta mesons reconstructed from diphoton decay, and at forward rapidities, neutral pions are measured using both diphotons and electromagnetic clusters. The neutral-pion measurement of $A_{N}$ at midrapidity is consistent with zero with uncertainties a factor of 20 smaller than previous publications, which will lead to improved constraints on the gluon Sivers function. At higher rapidities, where the valence quark distributions are probed, the data exhibit sizable asymmetries. In comparison with previous measurements in this kinematic region, the new data extend the kinematic coverage in $\sqrt{s}$ and $p_T$, and it is found that the asymmetries depend only weakly on $\sqrt{s}$. The origin of the forward $A_{N}$ is presently not understood quantitatively. The extended reach to higher $p_T$ probes the transition between transverse momentum dependent effects at low $p_T$ and multi-parton dynamics at high $p_T$.

We present azimuthal angular correlations between charged hadrons and energy deposited in calorimeter towers in central $d$$+$Au and minimum bias $p$$+$$p$ collisions at $\sqrt{s_{_{NN}}}=200$ GeV. The charged hadron is measured at midrapidity $|\eta|<0.35$, and the energy is measured at large rapidity ($-3.7<\eta<-3.1$, Au-going direction). An enhanced near-side angular correlation across $|\Delta\eta| >$ 2.75 is observed in $d$$+$Au collisions. Using the event plane method applied to the Au-going energy distribution, we extract the anisotropy strength $v_2$ for inclusive charged hadrons at midrapidity up to $p_T=4.5$ GeV/$c$. We also present the measurement of $v_2$ for identified $\pi^{\pm}$ and (anti)protons in central $d$$+$Au collisions, and observe a mass-ordering pattern similar to that seen in heavy ion collisions. These results are compared with viscous hydrodynamic calculations and measurements from $p$$+$Pb at $\sqrt{s_{_{NN}}}=5.02$ TeV. The magnitude of the mass-ordering in $d$$+$Au is found to be smaller than that in $p$$+$Pb collisions, which may indicate smaller radial flow in lower energy $d$$+$Au collisions.

We present measurements of J/psi yields in d+Au collisions at sqrt(s_NN) = 200 GeV recorded by the PHENIX experiment and compare with yields in p+p collisions at the same energy per nucleon-nucleon collision. The measurements cover a large kinematic range in J/psi rapidity (-2.2 < y < 2.4) with high statistical precision and are compared with two theoretical models: one with nuclear shadowing combined with final state breakup and one with coherent gluon saturation effects. To remove model dependent systematic uncertainties we also compare the data to a simple geometric model. We find that calculations where the nuclear modification is linear or exponential in the density weighted longitudinal thickness are difficult to reconcile with the forward rapidity data.

The PHENIX experiment has studied nuclear effects in $p$$+$Al and $p$$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV on charged hadron production at forward rapidity ($1.4<\eta<2.4$, $p$-going direction) and backward rapidity ($-2.2<\eta<-1.2$, $A$-going direction). Such effects are quantified by measuring nuclear modification factors as a function of transverse momentum and pseudorapidity in various collision multiplicity selections. In central $p$$+$Al and $p$$+$Au collisions, a suppression (enhancement) is observed at forward (backward) rapidity compared to the binary scaled yields in $p$+$p$ collisions. The magnitude of enhancement at backward rapidity is larger in $p$$+$Au collisions than in $p$$+$Al collisions, which have a smaller number of participating nucleons. However, the results at forward rapidity show a similar suppression within uncertainties. The results in the integrated centrality are compared with calculations using nuclear parton distribution functions, which show a reasonable agreement at the forward rapidity but fail to describe the backward rapidity enhancement.

We present measurements of azimuthal correlations of charged hadron pairs in $\sqrt{s_{_{NN}}}=200$ GeV Au$+$Au collisions after subtracting an underlying event using a model that includes higher-order azimuthal anisotropy $v_2$, $v_3$, and $v_4$. After subtraction, the away-side ($\Delta\phi\sim\pi)$ of the highest transverse-momentum trigger ($p_T>4$ GeV/$c$) correlations is suppressed compared to that of correlations measured in $p$$+$$p$ collisions. At the lowest associated particle $p_T$, the away-side shape and yield are modified. These observations are consistent with the scenario of radiative-jet energy loss. For the lowest-$p_T$ trigger correlations, an away-side yield exists and we explore the dependence of the shape of the away-side within the context of an underlying-event model. Correlations are also studied differentially versus event-plane angle $\Psi_n$. The angular correlations show an asymmetry when selecting the sign of the trigger-particle azimuthal angle with respect to the $\Psi_2$ event plane. This asymmetry and the measured suppression of the pair yield out of plane is consistent with a path-length-dependent energy loss. No $\Psi_3$ dependence can be resolved within experimental uncertainties.