New approach to initializing hydrodynamic fields and mini-jet propagation in quark-gluon fluids

We propose a new approach to initialize the hydrodynamic fields, such as energy density distributions and four-flow velocity fields in hydrodynamic modeling of high-energy nuclear collisions at the collider energies. Instead of matching the energy-momentum tensor or putting the initial conditions of quark-gluon fluids at a fixed initial time, we utilize a framework of relativistic hydrodynamic equations with source terms to describe the initial stage. Putting the energy and momentum loss rate of the initial partons into the source terms, we obtain hydrodynamic initial conditions dynamically. The resultant initial profile of the quark-gluon fluid looks highly bumpy as seen in the conventional event-by-event initial conditions. In addition, initial random flow velocity fields also are generated as a consequence of momentum deposition from the initial partons. We regard the partons that survive after the dynamical initialization process as the mini-jets and find sizable effects of both mini-jet propagation in the quark-gluon fluids and initial random transverse flow on the final momentum spectra and anisotropic flow observables. We perform event-by-event (3+1)-dimensional ideal hydrodynamic simulations with this new framework that enables us to describe the hydrodynamic bulk collectivity, parton energy loss, and interplay among them in a unified manner.

Figure 1

The $p_T$ spectrum of the initial partons in one central ($b=0\mathrm{fm}$) Pb + Pb collision at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$. The number of binary collisions is estimated to be $N_{\mathrm{coll}}=1983$ in this particular event.

Figure 2

Snapshots of the medium energy density distribution in units of ${\mathrm{GeV}}^4$ (left panels) and the transverse flow velocity (right panels) on the transverse plane in a Pb + Pb collision at the LHC energy. From top to bottom, $\tau =0.15,0.4$, and 0.6 fm, respectively. The impact parameter is $b=0.0\mathrm{fm}$ for illustrative purposes.

Figure 3

An example of the time evolution of the energy density in units of ${\mathrm{GeV}}^4$ at four representative transverse positions $(x,y)=(0,0),(3,0),(0,3)$, and (3,3) fm during dynamical initialization ${\tau }_{00}<\tau <{\tau }_0$.

Figure 4

The $p_T$ spectra of the partons at $\tau =0$ (red solid line) and ${\tau }_0$ (blue dashed line) in a 30%–40% Pb + Pb collision at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$. The impact parameter is $b=9.32\mathrm{fm}$, and the number of the event is $N_{\mathrm{ev}}={10}^2$.

Figure 5

The $p_T$ spectra of charged pions in a 40%–50% Pb + Pb collision at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$ with different settings for the initial flow and for the mini-jets' energy deposition. The impact parameter is $b=10.58\mathrm{fm}$, and the number of the event is $N_{\mathrm{ev}}={10}^2$.

Figure 6

The transverse-momentum dependence of elliptic flow parameter $v_2$ of the charged pions at midrapidity $Y=0$ for centrality classes 0%, 30%–40%, and 60%–70% in Pb + Pb collisions at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$.

Figure 7

The transverse-momentum dependence of elliptic flow parameter $v_2$ of the charged pions at midrapidity $Y=0$ in 40%–50% Pb + Pb collision at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$ with different settings for the initial flow and for the mini-jets' energy deposition. The impact parameter is $b=10.58\mathrm{fm}$, and the number of the event is $N_{\mathrm{ev}}={10}^2$.

Figure 8

The transverse-momentum dependence of triangular flow parameter $v_3$ of the charged pions at midrapidity $Y=0$ in 40%–50% Pb + Pb collision at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$ with different settings for the initial flow and for the mini-jets' energy deposition. The impact parameter is $b=10.58\mathrm{fm}$, and the number of the event is $N_{\mathrm{ev}}={10}^2$.