This White Paper aims at highlighting the important benefits in the science reach of the EIC. High luminosity operation is generally desirable, as it enables producing and harvesting scientific results in a shorter time period. It becomes crucial for programs that would require many months or even years of operation at lower luminosity.

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.

A search for the quantum chromodynamics (QCD) critical point was performed by the STAR experiment at the BNL Relativistic Heavy Ion Collider, using dynamical fluctuations of unlike particle pairs. Heavy ion collisions were studied over a large range of collision energies with homogeneous acceptance and excellent particle identification, covering a significant range in the QCD phase diagram where a critical point may be located. Dynamical Kπ, pπ, and Kp fluctuations as measured by the STAR experiment in central 0-5% Au + Au collisions from center-of-mass collision energies sNN=7.7 to 200 GeV are presented. The observable νdyn was used to quantify the magnitude of the dynamical fluctuations in event-by-event measurements of the Kπ, pπ, and Kp pairs. The energy dependences of these fluctuations from central 0-5% Au + Au collisions all demonstrate a smooth evolution with collision energy.

The STAR Collaboration presents for the first time two-dimensional di-hadron correlations with identified leading hadrons in 200 GeV central Au. +. Au and minimum-bias d. +. Au collisions to explore hadronization mechanisms in the quark gluon plasma. The enhancement of the jet-like yield for leading pions in Au. +. Au data with respect to the d. +. Au reference and the absence of such an enhancement for leading non-pions (protons and kaons) are discussed within the context of a quark recombination scenario. The correlated yield at large angles, specifically in the ridge region, is found to be significantly higher for leading non-pions than pions. The consistencies of the constituent quark scaling, azimuthal harmonic model and a mini-jet modification model description of the data are tested, providing further constraints on hadronization.

Balance functions have been measured in terms of relative pseudorapidity (Δη) for charged particle pairs at the BNL Relativistic Heavy Ion Collider from Au + Au collisions at sNN=7.7GeV to 200 GeV using the STAR detector. These results are compared with balance functions measured at the CERN Large Hadron Collider from Pb + Pb collisions at sNN=2.76TeV by the ALICE Collaboration. The width of the balance function decreases as the collisions become more central and as the beam energy is increased. In contrast, the widths of the balance functions calculated using shuffled events show little dependence on centrality or beam energy and are larger than the observed widths. Balance function widths calculated using events generated by UrQMD are wider than the measured widths in central collisions and show little centrality dependence. The measured widths of the balance functions in central collisions are consistent with the delayed hadronization of a deconfined quark gluon plasma (QGP). The narrowing of the balance function in central collisions at sNN=7.7 GeV implies that a QGP is still being created at this relatively low energy.

We report on measurements of dielectron (e+e-) production in Au+Au collisions at a center-of-mass energy of 200 GeV per nucleon-nucleon pair using the STAR detector at BNL Relativistic Heavy Ion Collider. Systematic measurements of the dielectron yield as a function of transverse momentum (pT) and collision centrality show an enhancement compared to a cocktail simulation of hadronic sources in the low invariant-mass region (Mee<1GeV/c2). This enhancement cannot be reproduced by the ρ-meson vacuum spectral function. In minimum-bias collisions, in the invariant-mass range of 0.30-0.76GeV/c2, integrated over the full pT acceptance, the enhancement factor is 1.76±0.06(stat.)±0.26(sys.)±0.29(cocktail). The enhancement factor exhibits weak centrality and pT dependence in STAR's accessible kinematic regions, while the excess yield in this invariant-mass region as a function of the number of participating nucleons follows a power-law shape with a power of 1.44±0.10. Models that assume an in-medium broadening of the ρ-meson spectral function consistently describe the observed excess in these measurements. Additionally, we report on measurements of ω- and φ-meson production through their e+e- decay channel. These measurements show good agreement with Tsallis blast-wave model predictions, as well as, in the case of the φ meson, results through its K+K- decay channel. In the intermediate invariant-mass region (1.1

Collisions between prolate uranium nuclei are used to study how particle production and azimuthal anisotropies depend on initial geometry in heavy-ion collisions. We report the two- and four-particle cumulants, v_{2}{2} and v_{2}{4}, for charged hadrons from U+U collisions at sqrt[s_{NN}]=193  GeV and Au+Au collisions at sqrt[s_{NN}]=200  GeV. Nearly fully overlapping collisions are selected based on the energy deposited by spectators in zero degree calorimeters (ZDCs). Within this sample, the observed dependence of v_{2}{2} on multiplicity demonstrates that ZDC information combined with multiplicity can preferentially select different overlap configurations in U+U collisions. We also show that v_{2} vs multiplicity can be better described by models, such as gluon saturation or quark participant models, that eliminate the dependence of the multiplicity on the number of binary nucleon-nucleon collisions.

We present ΛΛ correlation measurements in heavy-ion collisions for Au+Au collisions at sqrt[s_{NN}]=200  GeV using the STAR experiment at the Relativistic Heavy-Ion Collider. The Lednický-Lyuboshitz analytical model has been used to fit the data to obtain a source size, a scattering length and an effective range. Implications of the measurement of the ΛΛ correlation function and interaction parameters for dihyperon searches are discussed.