Measurements of jet quenching with semi-inclusive hadron+jet distributions in $\text{Au}+\text{Au}$ collisions at $\sqrt{s_{NN}}=200$ GeV

The STAR Collaboration reports the measurement of semi-inclusive distributions of charged-particle jets recoiling from a high transverse momentum hadron trigger, in central and peripheral $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathrm{NN}}}=200$ GeV. Charged jets are reconstructed with the anti-$k_{\mathrm{T}}$ algorithm for jet radii $R$ between 0.2 and 0.5 and with low infrared cutoff of track constituents ($p_{\mathrm{T}}>0.2 \mathrm{GeV}/\mathrm{c}$). A novel mixed-event technique is used to correct the large uncorrelated background present in heavy ion collisions. Corrected recoil jet distributions are reported at midrapidity, for charged-jet transverse momentum $p_{\mathrm{T},\mathrm{jet}}^{\mathrm{ch}}<30 \mathrm{GeV}/\mathrm{c}$. Comparison is made to similar measurements for $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s}=2.76$ TeV, to calculations for $p+p$ collisions at $\sqrt{s}=200$ GeV based on the pythia Monte Carlo generator and on a next-to-leading order perturbative QCD approach, and to theoretical calculations incorporating jet quenching. The recoil jet yield is suppressed in central relative to peripheral collisions, with the magnitude of the suppression corresponding to medium-induced charged energy transport out of the jet cone of $2.8\pm 0.2\left(\mathrm{stat}\right)\pm 1.5\left(\mathrm{sys}\right)$ $\mathrm{GeV}/c$, for $10<p_{\mathrm{T},\mathrm{jet}}^{\mathrm{ch}}<20$ $\mathrm{GeV}/c$ and $R=0.5$. No medium-induced change in jet shape is observed for $R<0.5$. The azimuthal distribution of low-$p_{\mathrm{T},\mathrm{jet}}^{\mathrm{ch}}$ recoil jets may be enhanced at large azimuthal angles to the trigger axis, due to scattering off quasiparticles in the hot QCD medium. Measurement of this distribution gives a 90% statistical confidence upper limit to the yield enhancement at large deflection angles in central $\mathrm{Au}+\mathrm{Au}$ collisions of $50\pm 30\left(\mathrm{sys}\right)\%$ of the large-angle yield in $p+p$ collisions predicted by pythia.

Figure 1

Centrality selection for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathrm{NN}}}=200$ GeV: distribution of uncorrected charged track multiplicity in $\left|\eta \right|<0.5$ (black histogram), with comparison to the result of a Glauber model [38] calculation (red points). The shaded regions show the windows for 0–10% (central) and 60–80% (peripheral) $\mathrm{Au}+\mathrm{Au}$ collisions.

Figure 2

Upper panel: distribution of $\rho$ for central and peripheral $\mathrm{Au}+\mathrm{Au}$ collisions (SE), and for mixed events (ME, see Sec. 5). Lower panel: ratio of distributions SE/ME for central $\mathrm{Au}+\mathrm{Au}$ collisions. Blue points are ME distribution used in analysis; red points are same distribution shifted by 60 MeV/($c$ sr). See discussion in Sec. 5.

Figure 3

Distribution of jets with $R=0.3$ in $p+p$ collisions at $\sqrt{s}=200$ GeV, generated by pythia: $p_{\mathrm{T},\mathrm{jet}}^{\det }$ (detector level) for fixed values of $p_{\mathrm{T},\mathrm{jet}}^{\mathrm{part}}$ (particle level). Detector-level effects are for the environment of central $\mathrm{Au}+\mathrm{Au}$ collisions. The red lines are Gaussian fits to the narrow peak, with relative width given as $\delta p_{\mathrm{T}}/p_{\mathrm{T}}$.

Figure 4

Event display showing the distribution of charged tracks and jets (anti-$k_{\mathrm{T}}, R=0.3$) in one $\mathrm{Au}+\mathrm{Au}$ collision from the central event population, as a function of $\eta$ and $\varphi$. Filled circles show charged tracks, open circles show ghost particles, and the centroid of each accepted jet is indicated by “x.” Charged tracks and ghost particles clustered into each reconstructed jet have the same color. The shaded text boxes give $p_{\mathrm{T},\mathrm{jet}}^{\mathrm{raw},\mathrm{ch}}$ for all jet candidates with $p_{\mathrm{T},\mathrm{jet}}^{\mathrm{raw},\mathrm{ch}}>5$ $\mathrm{GeV}/c$. The outer dashed rectangle is the tracking acceptance, while the red shaded area is the region of the tracking acceptance that is excluded by the $R$-dependent jet fiducial cut. The trigger particle is indicated by the star, while the blue shaded area is the recoil jet acceptance. The trigger particle in this event is associated with the jet candidate with largest $p_{\mathrm{T},\mathrm{jet}}^{\mathrm{raw},\mathrm{ch}}$.

Figure 5

Distribution in ($\eta ,\varphi$) of charged particles from central $\mathrm{Au}+\mathrm{Au}$ collisions, with $p_{\mathrm{T}}<0.5$ $\mathrm{GeV}/c$. Top panel: real or “same events” (SE); middle panel: mixed events (ME) for one event mixing class; lower panel: projection of SE and ME distributions onto $\varphi$.

Figure 6

Distribution of SE and ME jet populations ($R=0.3$) for one event-mixing class in central $\mathrm{Au}+\mathrm{Au}$ collisions, as a function of $p_{\mathrm{T},\mathrm{jet}}^{\mathrm{reco},\mathrm{ch}}$ and $A_{\mathrm{jet}}$. Top panel: real events (SE); middle panel: mixed events (ME); bottom panel: projection of SE and ME distributions onto $A_{\mathrm{jet}}$. The lower panel also shows the recoil jet area distribution for $p+p$ collisions at $\sqrt{s}=200$ GeV from pythia-simulated events at the particle level with $p_{\mathrm{T},\mathrm{trig}}>9$ $\mathrm{GeV}/c$, for all recoil jets and for recoil $p_{\mathrm{T},\mathrm{jet}}^{\mathrm{part}}>5$ $\mathrm{GeV}/c$. The hatched region to the right of the dashed line is the accepted region for the $A_{\mathrm{jet}}$ cut.

Figure 7

Distribution of $p_{\mathrm{T},\mathrm{jet}}^{\mathrm{reco},\mathrm{ch}}$ for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathrm{NN}}}=200$ GeV: (a) central, $R=0.2$; (b) peripheral, $R=0.2$; (c) central, $R=0.3$; (d) peripheral, $R=0.3$. Upper subpanels show the distributions for SE (red points) and ME (shaded region), with the blue shaded region indicating the range used for ME normalization. Error bars on SE distributions are statistical. Lower subpanels show the ratio of the SE and normalized ME distributions, while the insert shows the ratio in the normalization region. See text for details.

Figure 8

Same as Fig. 7, but for $R=0.4$ and 0.5.

Figure 9

Same as Fig. 7, for central $\mathrm{Au}+\mathrm{Au}$ collisions and $R=0.3$. Upper panel: SE distribution is shown for two different ranges of $p_{\mathrm{T},\mathrm{trig}}$: $9<p_{\mathrm{T},\mathrm{trig}}<30$ $\mathrm{GeV}/c$ (grey points), which is used in the primary analysis, and $3<p_{\mathrm{T},\mathrm{trig}}<30$ $\mathrm{GeV}/c$ (red points). The ME distribution is the same as Fig. 7. Lower panel: ratio SE/ME for $9<p_{\mathrm{T},\mathrm{trig}}<30$ $\mathrm{GeV}/c$ (grey points), and for $3<p_{\mathrm{T},\mathrm{trig}}<30$ $\mathrm{GeV}/c$ with $\rho$ as defined in the primary analysis (red points) and $\rho$ shifted by $60\mathrm{MeV}/c$ (dashed line). See text for details. The insert shows the ratio for the $3<p_{\mathrm{T},\mathrm{trig}}<30$ $\mathrm{GeV}/c$ SE distribution, in the region of $f^{\mathrm{ME}}$ normalization.

Figure 10

Recoil jet distributions after mixed event subtraction for (a) peripheral $\mathrm{Au}+\mathrm{Au}$ STAR events and (b) $p+p$ collisions generated by pythia detector-level simulations. (c)–(f) Projections onto $\mathrm{\Delta }\phi$ for two different ranges in $p_{\mathrm{T},\mathrm{jet}}^{\mathrm{reco},\mathrm{ch}}$, indicated by the blue and grey shaded areas in the upper plot. The projected distributions are fitted with a function that is the sum of two Gaussian distributions, with fit widths ${\sigma }_1$ and ${\sigma }_2$. The values of ${\sigma }_1$ and ${\sigma }_2$ are highly correlated, with negligible statistical error.

Figure 11

Same as Fig. 10, but for central $\mathrm{Au}+\mathrm{Au}$ STAR data (a),(c),(e) and detector-level pythia simulations of $p+p$ collisions at $\sqrt{s}=200$ GeV embedded into mixed events from central $\mathrm{Au}+\mathrm{Au}$ STAR data at the track level (b),(d),(f).

Figure 12

Raw correlated jet yield distributions for $R=0.2$ (upper) and $R=0.5$ (lower) in central and peripheral $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathrm{NN}}}=200$ GeV. The uncorrelated background has been removed by subtraction of the scaled ME distribution from the SE distribution, but no other corrections have been applied. The gray shaded band shows the mixed event normalization uncertainty.

Figure 13

Probability distributions for $\delta p_{\mathrm{T}}$ in central $\mathrm{Au}+\mathrm{Au}$ collisions. Upper: single-track embedding with different values of $p_{\mathrm{T}}^{\mathrm{embed}}\left(p_T^e\right)$. Lower: $p_{\mathrm{T}}^{\mathrm{embed}}=20$ $\mathrm{GeV}/c$ with three different embedded-jet models: pythia-generated detector-level jets, single tracks, and single tracks with $v_2$ modulation of average background density. See text for details.

Figure 14

Response matrices for $R=0.3$ jets in central $\mathrm{Au}+\mathrm{Au}$ collisions. Upper: uncorrelated background response matrix $R_{\mathrm{bkg}}$. Lower: instrumental response matrix $R_{\det }$.

Figure 15

Jet reconstruction efficiency for peripheral and central $\mathrm{Au}+\mathrm{Au}$ collisions, as a function of particle-level $p_{\mathrm{T},\mathrm{jet}}^{\mathrm{part}}$. See text for details.

Figure 16

Estimation of the magnitude of corrections for jets with $R=0.3$, in central $\mathrm{Au}+\mathrm{Au}$ collisions.

Figure 17

Closure test for central $\mathrm{Au}+\mathrm{Au}$ collisions. Upper panel: particle-level input distribution from pythia (red line), unfolded spectrum for $\mathrm{Au}+\mathrm{Au}$ detector effects and background (grey band), and central value for fully corrected peripheral STAR data (blue dashed, systematic uncertainty not shown for clarity). Lower panel: ratio of unfolded over input distribution from upper panel. See text for details.

Figure 18

Calculation of the semi-inclusive recoil jet distribution in $p+p$ collisions at $\sqrt{s}=200$ GeV, for jets with $R=0.4$. The parton-level distribution is calculated perturbatively at NLO [33]. The band shows the theoretical uncertainty due to scale variations. The charged-jet distribution is the transformation of the parton-level jet distribution using pythia.

Figure 19

Fully corrected distributions of $Y\left(p_{\mathrm{T},\mathrm{jet}}^{\mathrm{ch}}\right)$ (upper subpanels) and its ratio $I_{\mathrm{CP}}$ (lower subpanels) for central and peripheral $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathrm{NN}}}=200$ GeV, for anti-$k_{\mathrm{T}}$ jets with $R=0.2$, 0.3, 0.4, and 0.5. The upper subpanels also show $Y\left(p_{\mathrm{T},\mathrm{jet}}^{\mathrm{ch}}\right)$ for $p+p$ collisions at $\sqrt{s}=200$ GeV, calculated using pythia at the charged-particle level and NLO pQCD transformed to the charged-particle level (Sec. 10). The uncertainty of the NLO calculation is not shown.

Figure 20

Distributions of $Y\left(p_{\mathrm{T},\mathrm{jet}}^{\mathrm{ch}}\right)$ for $R=0.2$ and 0.5 (upper subpanels) and their ratios (lower subpanels) in peripheral (a) and central (b) $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathrm{NN}}}=200$ GeV.

Figure 21

Distribution of $\mathrm{\Phi }\left(\mathrm{\Delta }\varphi \right)$ at $\sqrt{s}=200$ GeV, for $\mathrm{Au}+\mathrm{Au}$ collisions measured by STAR and $p+p$ collisions generated by pythia (detector level). Vertical dashed lines show limits of integration for $Y\left(p_{\mathrm{T},\mathrm{jet}}^{\mathrm{ch}}\right)$. Top panel: peripheral $\mathrm{Au}+\mathrm{Au}$ compared to $p+p$. Blue dashed curve shows pythia distribution scaled to have the same integral as data between the vertical dashed lines. Middle panel: central $\mathrm{Au}+\mathrm{Au}$ compared to $p+p$ detector-level events embedded into central $\mathrm{Au}+\mathrm{Au}$ mixed events. Shaded bands show systematic uncertainty due to mixed-event normalization. Bottom panel: same as middle panel, but with pythia distribution scaled to have the same integral as data between the vertical dashed lines.