Study Of Anisotropic Flow Correlations In Heavy-ion Collisions At LHC Energy

The ultra-relativistic heavy-ion collisions at LHC provides opportunities to generate and study the Quark-Gluon Plasma.Since the colliding system is small in both size and time scale,models are used with final obersables to study the colliding mechanism phe-nomenologically.One of the most important final observables,anisotropic flows,support the generation of QGP and identy it as the nearly perfect liquid.Because of the Event-by-Event fluctuations in initial state,different orders of fianl anisotropic flows are correlated.In this thesis,2+1 D viscous hydrodynamic model VISH2+1 are used to simulate Pb+Pb collisions at 2.76 TeV.Correlations between different anisotropic flows are analysed as following:We study the nonlinear mode-coupling effects in high anisotropic flow vectos,ie.anisotropic flow vectos with n>3 are composed with not only linear response to corre-sponding eccentricities,but also mode coupling to lower orders of anistropic flows.It has been suggested that the associated nonlinear hydrodynamic response coefficients probe the transport properties and are largely insensitive to the spectrum of initial density fluc-tuations of the medium created in these collisions.To test this suggestion,we explore nonlinear mode coupling effects in event-by-event viscous fluid dynamics,using two dif-ferent models for the fluctuating initial density profiles,and compare the nonlinear cou-pling coefficients between the initial eccentricity vectors before hydrodynamic expansion and the final flow vectors after the expansion.For several mode coupling coefficients we find significant sensitivity to the initial fluctuation spectrum.They all exhibit strong sensitivity to the specific shear viscosity at freeze-out,but only weak dependence on the shear viscosity during hydrodynamic evolution.We study the correlations between differernt flow magnitudes due to the effects of event-by-event fluctuations in the initial state.It has been observed by ATLAS collabo-ration that v2 and v3 are anti-correlated while V2,3 and vn are(anti-)correlated.We use hydrodynamic simulations to study the amplitude correlations between different orders of event-by-event fluctuating anisotropic flow harmonics.While the general trends seen in the experimental data are qualitatively reproduced by the model,deviations in detail,in particular for peripheral collisions,point to the need for more elaborate future calcu-lations with a hybrid approach that describes the late hadronic stage of the evolution mi-croscopically.It is demonstrated explicitly that the observed anti-correlation between v2 and v3 is the consequence of approximately linear hydrodynamic response to a similar anti-correlation of the corresponding initial eccentricities ?2 and ?3.For n>3,the hydro-dynamic correlations between v2,3 and vn deviate from the rescaled correlations among the corresponding initial eccentricities,demonstrating nonlinear mode coupling effect in higher order flows.The contributions of linear term and nonlinear mode-coupling term to anisotropic flow magnitudes and their dependence on colliding centrality are also studied.In central collisions,linear term is the major contribution to flow magnitudes while the importance of nonlinear mode-coupling term grows with the impact parameter.We study the correlations between differernt flow angles due to the effects of event-by-event fluctuations in the initial state.We discuss the relationship between the cor-relations between different flow angles(previously called Event-Plane correlations)and the correlations between corresponding initial eccentricity angles(also called Participant-Plane correlations),especially the sign change in some terms.We discuss how the def-inition of eccentricities affect participant-plane correlations and explain almost all sign changes.We establish the relationship between event-plane correlations and correlations between different orders of flows and nonlinear mode-coupling effects in higher order of flow vectors.For the fourth-and fifth-order flow vectors V4 and V5 we argue that the event plane correlations can be understood as the ratio between the mode coupling contributions to these flows and and the flow magnitudes.Based on the study of anisotropic flow correlations with integrated flows in previ-ous three chapters,a systematic analysis of correlations between different orders of PT-differential flow is presented,including mode coupling effects in flow vectors,correlations between flow angles(event-plane correlations),and correlations between flow magni-tudes.We study the transverse momentum dependence of these correlations.Event-plane correlations of differential flows are found almost independent of PT and close to those of integrated flows except for small pT region.Correlations between the magnitudes of the differential flows of different order have similar strength and centrality dependence as those between the corresponding integrated flows.We find that the mode coupling effects among differential flows largely mirror those among the corresponding integrated flows.The exception is small transverse momenta region where the significant flow angle fluc-tuations disrupt differential flow correlations,and this affect the mode coupling effects,flow magnitude correlations and flow angle correlations.