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\title{Probing initial and final state effects of heavy-ion collisions with STAR experiment}

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\noindent Understanding the initial conditions, the transport properties, and the dynamical evolution of the quark-gluon plasma are central objectives of the heavy-ion program at RHIC. 
%Measurements that are selectively sensitive to both initial state effects and final state viscous attenuation can provide invaluable constraints for temperature ($T$) and chemical potential ($\mu_{B}$) dependence of the specific shear viscosity $\eta/s$. 
The transverse momentum correlator $G_{2}\left(\Delta\eta,\Delta\varphi\right)$ has been shown to be sensitive to the shear viscosity $\eta/s$~[1,2]. On the other hand, the $\rho(v^{2}_{2},\langle p_{T} \rangle)$ correlator 
%that measures the strength of the correlation between an event¡¯s mean-transverse momentum $[p_{\mathrm{T}}]$ and its $v_2$ magnitude, 
indicates more sensitivity to the initial-state than to final-state effects~[3,4]. 
A comprehensive set of  $G_{2}\left(\Delta\eta,\Delta\varphi\right)$ and $\rho(v^{2}_{2},\langle p_{T} \rangle)$ measurements for Au+Au collisions spanning the beam energy range $\sqrt{s_{\rm NN}}$ = 11.5-200 GeV will be presented for several centralities and event shape selections. Furthermore, we also explore the initial-state effects in longitudinal directions using the de-correlation observables which measure the factorization ratio for  flow harmonics, $r_{n}(\eta)(n = 2,3)$ and $R_{2}(\eta)$. The new results from isobar collisions as well as BES II energy Au+Au collisions will provide important insights on the 3D modeling of initial-state of heavy-ion collisions, especially its collision energy and collision size dependence. These results are also compared to LHC measurements and theoretical model calculations~[2,4] to provide constraints on initial-state fluctuations and $\eta/s(\mu_{B},T)$.
%. The data-model comparisons indicate that the measurements provide significant constraints for the respective influence of initial-state fluctuations, system-size, system-shape, and $\eta/s(\mu_{B},T)$. 
 
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[1]~S. Gavin and M. Abdel-Aziz, Phys. Rev. Lett. 97, 162302 (2006) 

[2]~N. Magdy et al., arXiv:2111.07406

[3]~P. Bozek,  Phys. Rev. C 93, 044908 (2016).

[4]~N. Magdy et al., Phys. Lett. B 821 (2021) 136625

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