Relics of minijets amid anisotropic flows in high-energy heavy-ion collisions

Two-dimensional low-$p_T$ dihadron correlations in azimuthal angle $\varphi$ and pseudorapidity $\eta$ in high-energy heavy-ion collisions are investigated within both the HIJING Monte Carlo model and an event-by-event $(3+1)$D ideal hydrodynamic model. Without final-state interaction and collective expansion, dihadron correlations from HIJING simulations have a typical structure from minijets that contains a near-side two-dimensional peak and an away-side ridge along the $\eta$ direction. In contrast, event-by-event $(3+1)$D ideal hydrodynamic simulations with fluctuating initial conditions from the $\mathrm{HIJING}+\mathrm{AMPT}$ model produce a strong dihadron correlation that has an away-side as well as a near-side ridge. Relics of intrinsic dihadron correlation from minijets in the initial conditions still remain as superimposed on the two ridges. By varying initial conditions from $\mathrm{HIJING}+\mathrm{AMPT}$, we study effects of minijets, nonvanishing initial flow, and longitudinal fluctuation on the final-state dihadron correlations. With a large rapidity gap, one can exclude near-side correlations from minijet relics and dihadron correlations can be described by the superposition of harmonic flows up to the sixth order. When long-range correlations with a large rapidity gap are subtracted from short-range correlations with a small rapidity gap, the remaining near-side short-range dihadron correlation is shown to result mainly from relics of minijets. Low-transverse-momentum hadron yields per trigger $(p_T^{\mathrm{trig}}<4\mathrm{GeV}/c,p_T^{\mathrm{asso}}<2\mathrm{GeV}/c)$ owing to this short-range correlation in central heavy-ion collisions are enhanced over that in peripheral heavy-ion collisions and $p+p$ collisions, while widths in azimuthal angle remain the same, in qualitative agreement with experimental data. The enhancement owing to influence by the transverse expansion of the bulk medium is also shown to increase with centrality and colliding energy but to be insensitive to the kinetic freeze-out temperature.

Figure 1

Dihadron correlation for charged hadrons in $p+p$ collisions at $\sqrt{s}=200$ GeV/nucleon given by the HIJING Monte Carlo model. The transverse momentum range for trigger and associated particles are $p_T^{\mathrm{trig}}\in (2,3)\mathrm{GeV}/c$ and $p_T^{\mathrm{asso}}\in (0,2)\mathrm{GeV}/c$, respectively.

Figure 2

The same as Fig. 1 except in semicentral (10%–20%) $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s}=200$ GeV/nucleon from HIJING without jet quenching.

Figure 3

The same as Fig. 1 except in semicentral (10%–20%) $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s}=200$ GeV/nucleon from HIJING with jet quenching.

Figure 4

Near-side dihadron correlations for charged hadrons as a function of $\Delta \eta$ in central $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s}=200$ GeV/nucleon in HIJING with (dashed line) and without jet quenching (solid line). The transverse momentum ranges for trigger and associated particles are $p_T^{\mathrm{trig}}\in (2,3)\mathrm{GeV}/c$ and $p_T^{\mathrm{asso}}\in (0,2)\mathrm{GeV}/c$, respectively.

Figure 5

Dihadron correlations for charged hadrons with large pseudorapidity gap ($2<\Delta \eta <4$) as a function of $\Delta \varphi$ in central $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s}=200$ GeV/nucleon in HIJING with (dashed line) and without jet quenching (solid line). The transverse momentum ranges for trigger and associated particles are $p_T^{\mathrm{trig}}\in (2,3)\mathrm{GeV}/c$ and $p_T^{\mathrm{asso}}\in (0,2)\mathrm{GeV}/c$, respectively.

Figure 6

Charged hadron distributions in $\eta$ and $\varphi$ within $p_T\in (1,2)\mathrm{GeV}/c$ from two typical hydrodynamic events of $0\%–10\% \mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s}=200$ GeV/nucleon.

Figure 7

Dihadron correlations for charged hadrons from $(3+1)$D ideal hydrodynamic simulations of $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s}=200$ GeV/nucleon with four centralities. The trigger and associated particles lie in the $p_T$ ranges $\in (2,4)\mathrm{GeV}/c$ and $\in (1,2)\mathrm{GeV}/c$, respectively.

Figure 8

Dihadron correlations for charged hadrons with large rapidity gap $\Delta \eta =2.5$ as a function of $\Delta \varphi$ from $(3+1)$D ideal hydrodynamic simulations of $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s}=200$ GeV/nucleon with four different centralities. The trigger and associated particles lie in the $p_T$ ranges $\in (2,4)\mathrm{GeV}/c$ and $\in (1,2)\mathrm{GeV}/c$, respectively.

Figure 9

Associated yield per trigger for charged hadrons at short range $\left|\Delta \eta \right|<1$ (solid circles) and long range $2<\left|\Delta \eta \right|<4$ (solid squares) as a function of $\Delta \varphi$ from $(3+1)$D ideal hydrodynamic simulations of $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s}=200$ GeV/nucleon with four different centralities. The trigger and associated particles lie in the $p_T$ ranges $\in (2,4)\mathrm{GeV}/c$ and $\in (1,2)\mathrm{GeV}/c$, respectively.

Figure 10

The short-range $\left(\left|\Delta \eta \right|<1\right)$ yield per trigger with long range $\left(2<\left|\Delta \eta \right|<4\right)$ subtracted for charged hadrons as a function of $\Delta \varphi$ from $(3+1)$D ideal hydrodynamic simulations of $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s}=200$ GeV/nucleon with four centralities (open diamonds and open circles), compared with HIJING $p+p$ results (dashed histogram) and PHENIX data [28] (solid diamonds), where $v_2,v_3,v_4\left({\Psi }_4\right)$ contributions are ZYAM subtracted from the short-range per-trigger particle yield. The trigger and associated particles lie in $p_T$ range $\in (2,4)\mathrm{GeV}/c$ and $\in (1,2)\mathrm{GeV}/c$, respectively. See text for explanation on scaled hydro results.

Figure 11

(Top) The transverse momentum distribution of the charged hadrons in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s}=200$ GeV/nucleon from event-by-event $(3+1)$D hydrodynamic simulations (open symbols) [48] compared with PHENIX experimental data (solid symbols) [90, 91] and (bottom) their ratio. The shaded region indicates the $p_T$ range for associated hadrons in our calculation of dihadron correlations.

Figure 12

Associated yield of charged hadrons per trigger from $(3+1)$D ideal hydrodynamic simulations of $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s}=2.76$ TeV/nucleon with four different centralities. The trigger and associated particles lie in the $p_T$ ranges $\in (3,3.5)\mathrm{GeV}/c$ and $\in (1,1.5)\mathrm{GeV}/c$, respectively.

Figure 13

The transverse momentum distribution of the charged hadrons in $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s}=2.76$ TeV/nucleon from event-by-event $(3+1)$D hydrodynamic simulations (open symbols) [48] compared with ALICE experimental data (solid symbols) [44]. The shaded region indicates the $p_T$ range for associated hadrons in our calculation of dihadron correlations.

Figure 14

The difference between associated yield per trigger for charged hadrons in $\left|\Delta \eta \right|<1$ and $2<\left|\Delta \eta \right|<4$ as a function of $\Delta \varphi$ from ideal hydrodynamic simulations (open circles and open diamonds) of $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s}=2.76$ TeV/nucleon with four centralities, compared with CMS data for $\mathrm{Pb}+\mathrm{Pb}$ (solid squares) and $p+p$ (dashed) collisions [43]. The trigger and associated particles lie in the $p_T$ ranges $\in (3,3.5)\mathrm{GeV}/c$ and $\in (1,1.5)\mathrm{GeV}/c$, respectively. See text for explanations on scaled hydro results.

Figure 15

The short-range $\left(\left|\Delta \eta \right|<1\right)$ yield per trigger with long range $\left(2<\left|\Delta \eta \right|<4\right)$ subtracted for charged hadrons as a function of $\Delta \varphi$ from $(3+1)$D ideal hydrodynamic simulations of $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s}=19.6$ GeV/nucleon (solid circles), $\sqrt{s}=62.4$ GeV/nucleon (solid squares), and $\sqrt{s}=200$ GeV/nucleon (solid diamonds) with centrality 20%–30%. The trigger and associated particles lie in the $p_T$ ranges $\in (2,4)\mathrm{GeV}/c$ and $\in (1,2)\mathrm{GeV}/c$, respectively.

Figure 16

The short-range $\left(\left|\Delta \eta \right|<1\right)$ yield per trigger with long range $\left(2<\left|\Delta \eta \right|<4\right)$ subtracted for charged hadrons as a function of $\Delta \varphi$ from $(3+1)$D ideal hydrodynamic simulations of $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s}=62.4$ GeV/nucleon with freeze-out temperature $T_f=0.136$ GeV (solid circles), $T_f=0.140$ GeV (solid squares), and $T_f=0.150$ GeV (solid diamonds) with centrality 20%–30%. The trigger and associated particles lie in the $p_T$ ranges $\in (2,4)\mathrm{GeV}/c$ and $\in (1,2)\mathrm{GeV}/c$, respectively.

Figure 17

Dihadron correlations from event-by-event ideal hydrodynamic simulations with full AMPT initial conditions (top) and tubelike AMPT initial conditions (middle) in semicentral $30\%–40\% \mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s}=200$ GeV/nucleon, and their ratio (lower). The trigger and associated particles lie in the same momentum range $p_T\in (2,3)\mathrm{GeV}/c$.

Figure 18

Dihadron correlations in central $10\%–20\% \mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s}=200$ GeV/nucleon from ideal hydrodynamic simulations with full AMPT initial conditions (top) and AMPT initial conditions without initial transverse fluid velocity (middle) and their ratio (bottom). The trigger and associated particles lie in the same momentum range $p_T\in (2,3)\mathrm{GeV}/c$.

Figure 19

The $v_n$ reconstruction of dihadron correlations for $0\%–5\%$ central $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s}=2.76$ TeV/nucleon with $p_T\in (2,3)\mathrm{GeV}/c$.

Figure 20

The same as Fig. 19, except for seminal central $10\%–20\% \mathrm{Pb}+\mathrm{Pb}$ collisions.