A measurement of the transverse momentum spectra of jets in Pb–Pb collisions at
Article funded by SCOAP3
36$) are rejected from the sample resulting in a tracking efficiency loss of 8\% for low \pt{} tracks ($\pttrack<1$\,\GeVc) and a few percent (1-2\%) for higher momentum tracks. For a large fraction (79\%) of the tracks used in the analysis, at least one point was found in one of the two inner pixel tracking layers (SPD) of the ITS. To improve the azimuthal uniformity of the selected tracks, tracks without SPD points were also used in the analysis. For those tracks the momentum was determined from a track fit constrained to the primary vertex, to guarantee good momentum resolution. The \pt{} resolution for tracks is estimated from the track residuals of the momentum fit and does not vary significantly with centrality. All track types have a relative transverse momentum resolution of $\sigma(\pt)/\pt\simeq 1\%$ at 1\,\GeVc. The resolution at $\pt=50$\,\GeVc{} is $\sigma(\pt)/\pt\simeq 10\%$ for tracks that have at least three out of six reconstructed space points in the ITS. For the remaining tracks (6\% of the track sample) the resolution is $\sigma(\pt)/\pt\simeq 20\%$ at $50$ \GeVc{}. The track \pt{} resolution is verified by cosmic muon events and the width of of the invariant mass peaks of $K_{\rm S}^{\rm 0}$, $\Lambda$ and $\bar{\Lambda}$~\cite{Abelev-ml-2012eq}. The track finding efficiency at $\pt=0.15$\,\GeVc{} is 60\% increasing to $\sim 90$\% for $\pt \simeq 1.5$\,\GeVc{} and then decreases to $\sim 86\%$ for $\pt \geq 2.5$\,\GeVc{}. In peripheral events the track finding efficiency is $\sim 2$\% larger than in central collisions due to the lower track multiplicity. Jets are reconstructed with the anti-\kT{} algorithm using the FastJet package~\cite{Cacciari2011,Cacciari2006} with resolution parameters $R=0.2$ and $R=0.3$. Charged tracks with $|\eta|<0.9$ and $\pt>0.15$\,\GeVc{} are used as input for the jet algorithm. The transverse momentum of the jets, \ptjetrawch, is calculated with the boost-invariant \pt\ recombination scheme. The area, $A$, for each jet is determined using the active area method as implemented in FastJet~\cite{Cacciari2008a}. So-called `ghost particles' with very small momentum ($\sim 10^{-100}$\,GeV/$c$) are added to the event and the number of ghost particles in a jet measures the area. Ghost particles are uniformly generated over the tracking acceptance ($0<\varphi<2\pi$ and $|\eta|<0.9$), with 200 ghost particles per unit area. Jets used in the analysis are required to have an area larger than 0.07 for $R=0.2$ jets and 0.2 for $R=0.3$ jets. This selection mostly removes low momentum jets with $\ptjetrawch < 20$\,\GeVc. Jets are selected to have $|\eta| < 0.5$, so that they are fully contained in the tracking acceptance. In addition, jets containing a track with a reconstructed $\pt>100$\,\GeVc{} are rejected from the analysis, to avoid possible contributions from tracks with poor momentum resolution (the momentum resolution is 20\% for tracks with $\pt=100$\,\GeVc). This selection has negligible effect in the reported range of jet momenta. ]]>
0.15} = 155.8 \pm 3.7$ \GeVc{} for the 10\% most central events, with a spread $\sigma(\rho_{\rm ch}^{\pt > 0.15}) = 20.5 \pm 0.4$\,\GeVc{} with no significant dependence on the distance parameter $R$ employed in the $\rho$ calculation. ]]>
5$ (green crosses) or $10$\,\GeVc{} (red squares).]]>
0.15$\,\GeVc{} is also reported in table~\ref{tab:deltapt}. It is multiplied by $\sqrt{\pi R^{2}}$ to re-introduce part of the area dependence, present in $\sigma(\deltapt)$. The FastJet fluctuation measures are reported to enable the comparison of fluctuations in heavy ion reactions by standard jet reconstruction tools in models and data. \begin{table}[t] \centering \renewcommand{\arraystretch}{1.3} \begin{tabular}{|>{\small}l|>{\small}r>{\small}r|>{\small}r|} \hline &\multicolumn{2}{c}{\small{$\sigma(\deltapt)$}} & \multicolumn{1}{|c|}{\small{$\sigma_{\rm FJ} \cdot \sqrt{\pi R^{2}}$}} \\ & \multicolumn{1}{c}{Measured} & \multicolumn{1}{c}{Corrected} & \multicolumn{1}{|c|}{Corrected} \\ \hline $R = 0.2$ &$4.47 \pm 0.00$\,\GeVc & $5.10 \pm 0.05$\,\GeVc & $4.04 \pm 0.05$\,\GeVc\\ $R = 0.3$ & $7.15 \pm 0.00$\,\GeVc & $8.21 \pm 0.09$\,\GeVc & $6.35 \pm 0.09$\,\GeVc\\ $R = 0.4$ & $10.17 \pm 0.01$\,\GeVc & $11.85 \pm 0.14$\,\GeVc & $8.59 \pm 0.12$\,\GeVc\\ \hline \end{tabular} ]]>
0.15$\,\GeVc. In addition, the corrected fluctuation measure from FastJet is provided, multiplied by $\sqrt{\pi R^{2}}$ to take into account the expected area dependence of the fluctuations. The values for $R=0.4$ are given for comparison with~\cite{Abelev-ml-2012ej}.]]>
5$ and $10$\,\GeVc. Those jets whose leading track is not reconstructed in the detector are rejected from the sample. This results in an improved jet energy resolution at low jet \pt{} while the jet finding efficiency is decreased, as shown in figure~\ref{fig:JetFindingEfficiencyLeadTrack}. \begin{figure}[t] \includegraphics[width=0.5\textwidth]{figures/Other/MeanResponseVsLeadHadronTrigInc69Det21R03.eps} \includegraphics[width=0.5\textwidth]{figures/Other/FractionPtGen_R03_TrigHad0.eps} ]]>
20$\,\GeVc. For leading track biased jets, the jet-finding efficiency is reduced and reaches 90\% at $\ptjetgen \approx 25$\,\GeVc\ for $\ptleadtrack>5$\,\GeVc\ and at $\ptjetgen \approx 60$\,\GeVc\ for $\ptleadtrack>10$\,\GeVc, which is consistent with the charged particle tracking efficiency. \begin{figure}[t] \includegraphics[width=0.5\textwidth]{figures/Other/JetEfficiencyVsLeadHadronTrigInc69R02Det21.eps} \includegraphics[width=0.5\textwidth]{figures/Other/JetEfficiencyVsLeadHadronTrigInc69R03Det21.eps} ]]>
0$\,\GeVc. The minimum \pt{} cut-off ($\ptminmeas$) on the measured spectrum removes a large fraction of combinatorial jets, which makes the unfolding procedure more stable. Feed-in from true jets with $\pt<\ptminmeas$ into the region used for unfolding is accounted for by extending the unfolded spectrum to $\ptjetch=0$\,\GeVc. The feed-in from low \pt{} true jets is a significant effect since the spectrum falls steeply with \ptjetch. Combinatorial jets still present in the measurement after applying the kinematical selections are transferred in the unfolding procedure to the region below \ptminmeas. Feed-in from jets with \ptjetch{} larger than the maximum measured \ptjetch{} is also included by extending the reach of the unfolded spectrum to $\ptjetch = 250$\,\GeVc. The optimal value of the minimum \pt{} cut-off has been studied using the jet background model described in~\cite{deBarros-ml-2012ws} and within simpler set-up in which a jet spectrum is folded with the measured background fluctuations. Stable unfolding is obtained with a minimum \pt{} cut-off of at least five times the width of the \deltapt{}-distribution $\sigma(\deltapt)$. For the most central collisions and $R=0.3$, this means that the spectrum is reported for $\ptjetch > 40$\,\GeVc. In addition, the maximum \pt{} cut-off is driven by the available statistics. The present data set allows for a measurement of $\ptjetch<110$\,\GeVc{} in central events and $\ptjetch<90$\,\GeVc{} in peripheral events. In case of leading track biased jets, the unfolding is more stable since the correction for combinatorial jets is reduced. ]]>
5$ or 10\,\GeVc. Without this selection, the Bayesian method was found to be unreliable: large deviations up to $50$\% at low \ptjet{} are observed in central collisions with a resolution parameter $R=0.3$. Such deviations are also seen in the validation studies with a heavy-ion background model where the Bayesian method did not give the correct result, unless the truth was used as the prior. \paragraph{Prior.} The unfolding algorithm starts from a QCD inspired shape for the unfolded spectrum, the prior. The measured jet spectrum is used as a standard prior for all unfolding methods and the sensitivity to the choice of prior is evaluated by changing the shape and yield of the prior. When the prior is far from the truth (for example a uniform distribution), the \chisq{} unfolding takes more iterations to converge but eventually an unfolded jet spectrum is obtained, which is statistically not significantly different from the unfolded spectrum obtained with the measured spectrum as a prior. The choice of prior has a negligible effect on the final unfolded spectrum. ]]>
60$\,\GeVc. ]]>
5$\,\GeVc{} in 10\% most central collisions is 8\% at $\ptjet=40$\,\GeVc\ and decreases to 4\% at $\ptjet=100$\,\GeVc. A previous study has shown that the background fluctuations ($\delta\pt$-distribution) are almost independent of the orientation with respect to the reaction plane~\cite{Abelev-ml-2012ej}; this effect is negligible compared to the change in the average background. ]]>
{\small}l|>{\small}l>{\small}c>{\small}c>{\small}c>{\small}c|} \hline & \multicolumn{1}{r}{\small{Resolution parameter}} & \multicolumn{2}{c}{\small{$R=0.2$}} & \multicolumn{2}{c|}{\small{$R=0.3$}} \\ Centrality class & \multicolumn{1}{r}{\small{\pt-interval (\GeVc)}} & 30--40 & 70--80 & 30--40 & 70--80 \\ \hline \multirow{9}{*}{0--10\%} & Regularisation & $^{+3.4}_{-0.0}$ & $^{+2.3}_{-0.3}$ & $^{+9.9}_{-0.0}$ & $^{+2.6}_{-6.7}$\\ & Unfolding method & $^{+0.0}_{-3.5}$ & $^{+0.0}_{-1.1}$ & $^{+0.0}_{-7.3}$ & $^{+7.6}_{-0.0}$ \\ & Minimum \pt\ unfolded & $^{+9.6}_{-0.0}$ & $^{+0.3}_{-0.0}$ & $^{+0.0}_{-5.9}$& $^{+0.0}_{-1.8}$ \\ & Minimum \pt\ measured & $^{+1.7}_{-4.8}$ & $^{+0.2}_{-0.3}$ & $^{+0.0}_{-13}$ & $^{+0.0}_{-2.1}$\\ & Prior & \multicolumn{4}{c|}{\small{$<0.1$}} \\ & \deltapt & $^{+0.0}_{-4.9}$ & $^{+0.0}_{-2.1}$ & $^{+0.0}_{-27}$ & $^{+0.0}_{-4.6}$ \\ & Detector effects & $\pm 2.7$ & $\pm 5.5$ & $\pm 4.6$ & $\pm 5.2$ \\ & Flow bias & $^{+0.9}_{-5.8}$ & $^{+0.4}_{-4.1}$ & $^{+7.3}_{-5.9}$ & $^{+4.8}_{-4.1}$ \\ & Centrality determination & \multicolumn{4}{c|}{\small{0.8}} \\ \cline{2-6} & \bf{Total shape uncertainty} & $^{+10}_{-7.6}$ & $^{+2.4}_{-2.4}$ & $^{+9.9}_{-31}$ & $^{+7.6}_{-8.6}$\\ & \bf{Total correlated uncertainty} & $^{+2.9}_{-6.4}$ & $^{+5.6}_{-6.9}$ & $^{+8.6}_{-7.5}$ & $^{+7.1}_{-6.6}$ \\ \hline \multirow{9}{*}{50--80\%} & Regularisation & $^{+0.0}_{-5.5}$ & $^{+13}_{-4.1}$ & $^{+0.1}_{-5.1}$ & $^{+17}_{-2.2}$ \\ & Unfolding method & $^{+2.1}_{-0.0}$ & $^{+0.0}_{-20}$ & $^{+2.3}_{-0.0}$ & $^{+0.0}_{-20}$ \\ & Minimum \pt\ unfolded & $^{+0.3}_{-0.0}$ & $^{+0.1}_{-0.0}$ & $^{+1.0}_{-0.0}$ & $^{+0.6}_{-0.0}$ \\ & Minimum \pt\ measured & $^{+9.3}_{-0.0}$ & $^{+0.7}_{-0.4}$ & $^{+7.5}_{-0.0}$ & $^{+1.0}_{-0.0}$ \\ & Prior & \multicolumn{4}{c|}{\small{$<0.1$}} \\ & \deltapt & $^{+8.2}_{-0.0}$ & $^{+2.4}_{-0.0}$ & $^{+3.0}_{-0.0}$ & $^{+2.2}_{-0.0}$ \\ & Detector effects & $\pm 3.3$ & $\pm 6.2$ & $\pm 3.3$ & $\pm 3.1$ \\ & Flow bias & $^{+1.9}_{-1.9}$ & $^{+0.3}_{-0.3}$ & $^{+0.4}_{-7.2}$ & $^{+0.3}_{-4.0}$ \\ & Centrality determination & \multicolumn{4}{c|}{\small{1.9}} \\ \cline{2-6} & \bf{Total shape uncertainty} & $^{+13}_{-5.5}$ & $^{+13}_{-20}$ & $^{+8.5}_{-5.1}$ & $^{+17}_{-20}$ \\ & \bf{Total correlated uncertainty} & $^{+4.2}_{-4.2}$ & $^{+6.5}_{-6.5}$ & $^{+3.8}_{-8.2}$ & $^{+3.6}_{-5.4}$ \\ \hline \end{tabular} ]]>
5$\,\GeVc. Relative uncertainties are given in percentiles for two \pt-intervals and two different centrality intervals.]]>
0.15$ \GeVc. The jet spectra are unfolded for detector effects and background fluctuations, and corrected for the jet finding efficiency as described in the preceding sections. The upper panels show the inclusive jet spectra while for the center and lower panels the jet spectra with a leading track bias of at least $5$ and $10$\,\GeVc\ are shown. The markers represent the central values of the unfolded jet spectra. It should be noted that the unfolding procedure leads to correlations between the data points, because the width of the response function is similar to the bin width: neighboring \pt-bins tend to fluctuate together (correlated) while bins with some distance tend to be anti-correlated. The vertical error bars represent the statistical uncertainties. The filled and open boxes indicate the corresponding shape and correlated systematic uncertainties discussed previously. \begin{figure}[p] \includegraphics[width=\textwidth]{figures/Results/ChargedJetSpectraAllPanels.eps} ]]>
5$\,\GeVc{} (middle panels), and $\ptleadtrack > 10 $\,\GeVc{} (bottom panels). The uncertainty bands at $\ptjetch<20\,\GeVc$ indicate the normalisation uncertainty due to the scaling with $1/N_\mathrm{coll}$. ]]>
20$ \GeVc, the PYTHIA vacuum expectation from the Perugia-2011 tune~\cite{Skands-ml-2010ak} is that almost all jets have a constituent of at least $5$\,\GeVc, resulting in a ratio at unity as indicated by the PYTHIA data points. The ratio between the unbiased and $5$\,\GeVc\ biased measured \PbPb\ jet spectra is consistent in peripheral and central collisions with the vacuum expectation. No evidence of the modification of the hard jet core is observed. \begin{figure}[p] \centering \includegraphics[width=.95\textwidth]{figures/Results/RatioNJetsBiased5R02.eps} \includegraphics[width=.95\textwidth]{figures/Results/RatioNJetsBiased5R03.eps} ]]>
5$\,\GeVc. Right panels: ratio of spectra with $\ptleadtrack > 10$\,\GeVc{} to $\ptleadtrack > 5$\,\GeVc. ]]>
5$\,\GeVc, with $R=0.2$ (left panels) and $R=0.3$ (right panels) and different centrality selections.]]>
10$\,\GeVc{} are shifted to the left and right respectively. ]]>
5$\,\GeVc\ in \PbPb{} data and simulated PYTHIA events.]]>
5$ or $10\;\GeVc$ is similar in \PbPb{} collisions and in PYTHIA \pp{} events, which indicates that the longitudinal momentum distribution of (leading) high \pt{} tracks in jets reconstructed in Pb-Pb collisions remains largely unmodified. This observation is in qualitative agreement with measurements of fragmentation properties by CMS~\cite{Chatrchyan-ml-2012gw,Chatrchyan-ml-2013kwa} and ATLAS~\cite{ATLAS_ff_conf}. A further impression of the importance of soft radiation can be obtained by comparing the calorimetric jet measurement by ATLAS to the ALICE results in this paper. The ALICE measurement is more sensitive to low-momentum fragments due to the high tracking efficiency and good momentum resolution of charged particle tracks at low \pt. The agreement between these two jet measurements in figure~\ref{fig:compareAll} suggests that the contribution of low momentum fragments to the jet energy is small. A study of PYTHIA events shows that the expected contribution of fragments with $\pT < 1(2)$\,\GeVc{} is 4(7)\% of the jet energy at $\ptjetch=40$\,\GeVc{} with cone radius $R=0.2(0.3)$ in \pp{} collisions. The results indicate that this contribution is also limited in \PbPb{} collisions. The measured ratios of jet cross sections with $R=0.2$ and $R=0.3$ and with and without leading particle selection show that the transverse and longitudinal fragment distributions of the reconstructed jets are similar in \pp{} (PYTHIA calculations) and \PbPb{} collisions. This `unmodifed hard core' of the jet may be due to formation time effects (the parton leaves the medium with relatively high momentum and then fragments without further interactions)~\cite{Renk-ml-2009nz,CasalderreySolana-ml-2011gx}, quantum interference effects (a group of partons with small opening angles interacts with the medium as one parton)~\cite{Mehtar-Tani-ml-2013pia}, kinematics (large momentum emissions are kinematically favoured at small angles)~\cite{Renk-ml-2009nz} and/or selection bias effects~\cite{Renk-ml-2009nz,Renk-ml-2012ve}. First results from the JEWEL event generator show a strong suppression of jets, in agreement with the \RCP{} shown in figure~\ref{fig:compareAll}~\cite{Zapp-ml-2012ak}. However, more extensive comparisons of theoretical models to the different experimental measurements are needed to determine how well they constrain the dynamics of parton energy loss models. In summary, a measurement of charged jet spectra in \PbPb{} collisions at different centralities was reported, using charged hadrons with $\pT > 0.15$\,GeV/$c$. The analysis was performed for a jet sample with a minimal fragmentation bias by introducing different \pt-ranges in the unfolding procedure for the unfolded and measured spectrum. To suppress combinatorial jets from the measured population, jet spectra with a leading track selection of $\ptleadtrack>5$ and 10\,\GeVc{} were also reported. The effect of the leading track cut at 5 \GeVc{} is small for the measured range \mbox{$\ptjetch > 20$\,\GeVc}, while for \mbox{$\ptleadtrack>10$\,\GeVc}, the effect is sizeable, but consistent with expectations from jet fragmentation in PYTHIA events, indicating that the high-\pT{} fragmentation is not strongly modified by interactions with the medium. The ratio of jets reconstructed with $R=0.2$ and $R=0.3$ is found to be similar in central and peripheral \PbPb\ events, and similar to PYTHIA calculations, indicating no strong broadening of the radial jet profile within $R=0.3$. The nuclear modification factor \RCP\ for jets is in the range 0.3--0.5, and tends to be lower at low $\ptjetch \approx 30$\,\GeVc\ than at high $\ptjetch \approx 100$\,\GeVc. The value of \RCP\ for jets is similar to charged hadrons, which suggests that interactions with the medium redistribute energy and momentum to relatively large angles with respect to the jet axis. ]]>