This document summarizes recent achievements of the RHIC spin program and their impact on our understanding of the nucleon's spin structure, i.e. the individual parton (quark and gluon) contributions to the helicity structure of the nucleon and to understand the origin of the transverse spin phenomena. Open questions are identified and a suite of future measurements with polarized beams at RHIC to address them is laid out. Machine and detector requirements and upgrades are briefly discussed.

Systems of correlated particles appear in many fields of modern science and represent some of the most intractable computational problems in nature. The computational challenge in these systems arises when interactions become comparable to other energy scales, which makes the state of each particle depend on all other particles¹. The lack of general solutions for the three-body problem and acceptable theory for strongly correlated electrons shows that our understanding of correlated systems fades when the particle number or the interaction strength increases. One of the hallmarks of interacting systems is the formation of multiparticle bound states^2-9. Here we develop a high-fidelity parameterizable fSim gate and implement the periodic quantum circuit of the spin-½ XXZ model in a ring of 24 superconducting qubits. We study the propagation of these excitations and observe their bound nature for up to five photons. We devise a phase-sensitive method for constructing the few-body spectrum of the bound states and extract their pseudo-charge by introducing a synthetic flux. By introducing interactions between the ring and additional qubits, we observe an unexpected resilience of the bound states to integrability breaking. This finding goes against the idea that bound states in non-integrable systems are unstable when their energies overlap with the continuum spectrum. Our work provides experimental evidence for bound states of interacting photons and discovers their stability beyond the integrability limit.

We present high precision measurements of elliptic flow near midrapidity (|y|<1.0) for multistrange hadrons and ϕ meson as a function of centrality and transverse momentum in Au+Au collisions at center of mass energy √[sNN]=200  GeV. We observe that the transverse momentum dependence of ϕ and Ω v2 is similar to that of π and p, respectively, which may indicate that the heavier strange quark flows as strongly as the lighter up and down quarks. This observation constitutes a clear piece of evidence for the development of partonic collectivity in heavy-ion collisions at the top RHIC energy. Number of constituent quark scaling is found to hold within statistical uncertainty for both 0%-30% and 30%-80% collision centrality. There is an indication of the breakdown of previously observed mass ordering between ϕ and proton v2 at low transverse momentum in the 0%-30% centrality range, possibly indicating late hadronic interactions affecting the proton v2.

We report the observation of transverse polarization-dependent azimuthal correlations in charged pion pair production with the STAR experiment in p^{↑}+p collisions at RHIC. These correlations directly probe quark transversity distributions. We measure signals in excess of 5 standard deviations at high transverse momenta, at high pseudorapidities η>0.5, and for pair masses around the mass of the ρ meson. This is the first direct transversity measurement in p+p collisions.

Dihadron correlations are analyzed in √sNN = 200 GeV d + Au collisions classified by forward charged particle multiplicity and zero-degree neutral energy in the Au-beam direction. It is found that the jetlike correlated yield increases with the event multiplicity. After taking into account this dependence, the non-jet contribution on the away side is minimal, leaving little room for a back-to-back ridge in these collisions.

Measurements of two-particle correlations on transverse momentum pt for Au-Au collisions at sqrt sNN = 130 GeV are presented. Significant large-momentum-scale correlations are observed for charged primary hadrons with 0.15 <_ pt <_ 2 GeV/c and pseudorapidity lbar eta rbar <_ 1.3. Such correlations were not observed in a similar study at lower energy and are not predicted by theoretical collision models. Their direct relation to mean-pt fluctuations measured in the same angular acceptance is demonstrated. Positive correlations are observed for pairs of particles which have large pt values while negative correlations occur for pairs in which one particle has large pt and the other has much lower pt. The correlation amplitudes per final state particle increase with collision centrality. The 3 observed correlations are consistent with a scenario in which the transverse momentum of hadrons