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Since the discovery of the jet quenching at RHIC, the in-medium interaction of hard scattered partons with the nuclear medium created by highenergy heavy-ion collisions has been an excellent tool to understand not only the transport properties of the medium but also its time evolution towards hadronization. The multi-differential measurement of the high momentum twoparticle correlations can probe a particular space-time window as a function of energy transfer. Comparing the correlations with the prompt photon-triggered hadron spectra, one can extract the property of the medium from various aspects and contribute to distinct models. The PHENIX experiment at RHIC has collected its highest statistics of theγ and π⁰ triggered hadron events in Au+Au collisions at √s_NN= 200 GeV in the RHIC Year-2014 run, and measured not only the inclusive spectra of the triggered hadrons but also the angle and energy dependent I_AA and D_AA. We will discuss the in-medium modification of the energy-space structure of the jets at the RHIC energies with the results obtained. 

We present results for a Bayesian analysis of the location of the QCD critical point constrained by first-principles lattice QCD results at zero baryon density. We employ a holographic Einstein-Maxwell-dilaton model of the QCD equation of state, capable of reproducing the latest lattice QCD results at zero and finite baryon chemical potential. Our analysis is carried out for two different parametrizations of this model, resulting in confidence intervals for the critical point location that overlap at one sigma. While samples of the prior distribution may not even predict a critical point, or produce critical points spread around a large region of the phase diagram, posterior samples nearly always present a critical point at chemical potentials of μ_Bc∼ 550 − 630 MeV. 

We employ an Einstein-Maxwell-dilaton model, based on the gauge/gravity correspondence, to obtain the thermodynamics and transport properties for the hot and dense quark-gluon plasma. The model, which is constrained to reproduce lattice QCD thermodynamics at zero density, predicts a critical point and a first order line at finite temperature and density, is used to quantify jet energy loss through simulations of high-energy collision events. 

At high density, matter is expected to undergo a phase transition to deconfined quark matter. Although the density at which it happens and the strength of the transition are still largely unknown, we can model it to be in agreement with known experimental data and reliable theoretical results. We discuss how deconfinement in dense matter can be affected by both by temperature and by strong magnetic fields within the Chiral Mean Field (CMF) model. To explore different dependencies in our approach, we also explore how deconfinement can be affected by the assumption of different degrees of freedom, different vector coupling terms, and different deconfining potentials, all at zero temperature. Both zero-net-strangeness and isospin-symmetric heavy-ion collision matter and beta-equilibrated charge-neutral matter in neutron stars are discussed. 

Jets are produced in early stages of heavy-ion collisions and undergo modified showering in the quark-gluon plasma (QGP) medium relative to a vacuum case. These modifications can be measured using observables like jet momentum profile and generalized angularities to study the details of jetmedium interactions. Jet momentum profile (ρ(r)) encodes radially differential information about jet broadening and has shown migration of charged energy towards the jet periphery in Pb+Pb collisions at the LHC. Measurements of generalized angularities (girthgand momentum dispersionp_T^D) and LeSub (difference between leading and subleading constituents) from Pb+Pb collisions at the LHC show harder, or more quark-like jet fragmentation, in the presence of the medium. Measuring these distributions in heavy-ion collisions at RHIC will help us further characterize the jet-medium interactions in a phase-space region complimentary to that of the LHC. In this contribution, we present the first measurements of fully correctedg,p_T^Dand LeSub observables using hard-core jets in Au+Au collisions at √S_NN= 200 GeV, collected by the STAR experiment at RHIC. 

The BEST Collaboration equation of state combining lattice data with the 3D Ising critical point encounters limitations due to the truncated Taylor expansion up toμ_B/T~ 2.5. This truncation consequently restricts its applicability at high densities. Through a resummation scheme, the lattice results have been extended toμ_B/T= 3.5. In this article, we amalgamate these ideas with the 3D-Ising model, yielding a family of equations of state valid up toμ_B= 700MeV with the correct critical behavior. Our equations of state feature tunable parameters, providing a stable and causal framework-a crucial tool for hydrodynamics simulations. 

The equation of state of Quantum Chromodynamics has been in recent years the focus of intense effort from first principle methods, mostly lattice simulations, with particular interest to the finite baryon density regime. Because of the sign problem, various extrapolation methods have been used to reconstruct bulk properties of the theory up to as far asμ_B=T≃ 3:5. However, said efforts rely on the equation of state at vanishing baryon density as an integration constant, which up toμ_B=T≃ 2 - 2:5 proves to be the dominant source of uncertainty at the level of precision currently available. In this contribution we present the update of our equation of state at zero net baryon density from 2014, performing a continuum limit from lattices with Nτ = 8; 10; 12; 16. We show how the improved precision is translated in a lower uncertainty on the extrapolated equation of state at finite chemical potential. 

The proper treatment of hadronic resonances plays an important role for many aspects of heavy ion collisions. We expect this to be the case also for hadronization, due to the large degeneracies of excited states, and the abundant production of hadrons from their decays. We show how a comprehensive treatment of excited meson states can be incorporated into quark recombination, and in extension, into Hybrid Hadronization. We discuss in detail the quantum mechanics of forming excited states, utilizing the Wigner distribution functions of angular momentum eigenstates of isotropic 3-D harmonic oscillators. We describe how resonance decays can be handled, based on a set of minimal assumptions, by creating an extension of hadron decays in PYTHIA 8. Finally, we present a study of hadron production by jets using PYTHIA and Hybrid Hadronization with excited mesons up to orbital angular momentumL= 4. We find that states up toL= 2 are produced profusely by quark recombination. 

As an important set of thermodynamic quantities, knowledge of the equation of state over a broad range of temperatures and chemical potentials in the QCD phase diagram is crucial for our understanding of strongly-interacting matter. There is a good understanding from first-principles results in lattice QCD, perturbative QCD and chiral effective field theory about the equation of state. However, these approaches are valid in different regimes of the phase diagram, and therefore, a method of providing an equation of state that covers a full range of the phase diagram involves matching together these results with appropriate models in order to fill in the gaps between these regions. Furthermore, with such equations of state, important questions about QCD phase structure can begin to be addressed, such as whether there is a critical point in the QCD phase diagram. In this contribution to the proceedings, equations of state from first-principles and effective theories will be discussed in order to understand how QCD thermodynamics is affected by the presence of a critical point. 

Multi-differential measurements of dilepton spectra serve as a unique tool to characterize the properties of matter in the interior of the hot and dense fireball created in heavy-ion collisions. An important property of virtual photons is their spin polarization defined in the rest frame of the virtual photon with respect to a chosen quantization axis. Microscopic calculations of in-medium electromagnetic spectral functions have mostly focused on integrated yields which are proportional to the sum of the longitudinal and transverse components of the virtual photon’s self-energy, while photon polarization results from the difference of these components. As the processes that drive the medium effects in the spectral function change with invariant mass and momentum, this becomes a powerful tool for studying the medium composition. We present the polarization observables of thermal virtual photons as a function of mass and momentum and confront the results with existing measurements from HADES and NA60.