Measurement Methods Of Radial Flow In Relativistic Heavy-ion Collisions

Collectivity,or flow,is one of the main characteristics of the newly formed quark-gluon plasma in relativistic heavy-ion collisions.Radial flow and elliptic flow are the two prominent classes.Elliptic flow measures the anisotropy of azimuthal multiplicity distribution,and provides information about initial conditions and system properties.As we know,the initial geometric asymmetry will lead not only the anisotropy of density distribution,but also the kinetics radial expansion.The interplay of radial expansion and elliptic flow results in what we observe as the particle mass splitting of the differential elliptic flow.Namely,the heavier particles show smaller elliptic flow values.This mass ordering of elliptic flow has been well understood by hydrodynamics with a set of kinetic freeze-out constraints,i.e.,radial flow,temperature,and source deformation.In addition,momentum transfer due to viscosity is proportional to the first derivative of the velocity in hydrodynamics.Bulk viscosity is associated with isotropic transverse velocity,whereas shear viscosity is associated with the anisotropic transverse velocity.Therefore,the determination of anisotropic radial flow is essential for hydrodynamic calculations and for measuring the shear viscosity in relativistic heavy-ion collisions.Conventionally,anisotropic radial flow is extracted by fitting the transverse momentum spectrum of particles with the blast-wave parametrization.However,the method used in this paper is that radial flow can be directly extracted from the azimuthal distribution of mean transverse rapidity,which is model-independent measurement.The aim of this paper is to estimate the anisotropic radial flow in relativistic heavy-ion collisions.The event-plane method and the two-particle correlation method are two common methods for estimating the anisotropy coefficients(elliptic flow)of azimuthal multiplicity distribution.The estimation of the anisotropic radial flow is similar to how we estimate elliptic flow.For the azimuthal distributions of various observations,the particles’ weights selected in the estimation of Fourier expansion coefficients are different.For elliptic flow and anisotropic total transverse rapidity flow,their weights are unity and the transverse rapidity of particles.For anisotropic radial flow,the weight is the ratio of all particles’ total transverse rapidity and the number of particles in the one azimuthal angle bin.It measures the raw kinetic expansion in a specified azimuthal direction.The contribution of the number of particles is removed.In this paper,we first introduce the measurement methods of elliptic flow,the eventplane method and the two-particle correlation method.In nuclear-nuclear collisions,the angle of reaction plane is unknown in experiments and fluctuates from event to event.This estimation where the reaction plane is instead estimated from the reconstructed particles is the so-called event-plane method.We found we can extract the elliptic flow from the peak position of event elliptic flow distribution.As we know,event plane should fluctuate around the true reaction plane.The event elliptic flow parameter also fluctuate from event to event around it true value.Although the distribution of event elliptic flow may deviate from the standard Gaussian due to propagation of error and systematic reasons,the position of its peak is still the most probable value of elliptic flow.It should be closest to the elliptic flow obtained by the true reaction plane.Base on AMPT model with string melting,elliptic flow estimated by this method is positively correlated with the event plane resolution,and the measurement results of elliptic flow by the event plane method and the two-particle correlation method are consistent with the expectation.Then,we estimate the anisotropic radial flow by the event-plane method and the twoparticle correlation method.Using the event sample of Au+Au collisions at 200GeV generated by the AMPT model with string melting,we show that the event-plane method and the two-particle correlation method are both effective in estimating the anisotropic total transverse rapidity flow.The is event-plane method also effective in estimating anisotropic radial flow.For central collisions and mid-central collisions,the two-particle correlation method is effective in estimating anisotropic radial flow.However,for the two peripheral-collision bins,this method fails when the mean number of particles in a bin becomes less than ten.Therefore,anisotropic radial flow can be estimated in a model-independent way by the eventplane method and the two-particle correlation method in relativistic heavy-ion collisions.For the two-particle correlation method to be reliable,the mean number of particles in an azimuthal bin must be above a certain threshold.Moreover,base on AMPT model with string melting,we find that the summation of the true elliptic flow and true anisotropic radial flow is consistent with the true anisotropic total transverse rapidity flow.This relationship also holds for the corresponding coefficients estimated by the event-plane method and the two-particle correlation method.Therefore,elliptic flow and anisotropic radial flow are additive.