Jet measurements in heavy ion physics

A hot, dense medium called a quark gluon plasma (QGP) is created in ultrarelativistic heavy ion collisions. Early in the collision, hard parton scatterings generate high momentum partons that traverse the medium, which then fragment into sprays of particles called jets. Understanding how these partons interact with the QGP and fragment into final state particles provides critical insight into quantum chromodynamics. Experimental measurements from high momentum hadrons, two particle correlations, and full jet reconstruction at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) continue to improve our understanding of energy loss in the QGP. Run 2 at the LHC recently began and there is a jet detector at RHIC under development. Now is the perfect time to reflect on what the experimental measurements have taught us so far, the limitations of the techniques used for studying jets, how the techniques can be improved, and how to move forward with the wealth of experimental data such that a complete description of energy loss in the QGP can be achieved. Measurements of jets to date clearly indicate that hard partons lose energy. Detailed comparisons of the nuclear modification factor between data and model calculations led to quantitative constraints on the opacity of the medium to hard probes. However, while there is substantial evidence for softening and broadening jets through medium interactions, the difficulties comparing measurements to theoretical calculations limit further quantitative constraints on energy loss mechanisms. Since jets are algorithmic descriptions of the initial parton, the same jet definitions must be used, including the treatment of the underlying heavy ion background, when making data and theory comparisons. An agreement is called for between theorists and experimentalists on the appropriate treatment of the background, Monte   Carlo generators that enable experimental algorithms to be applied to theoretical calculations, and a clear understanding of which observables are most sensitive to the properties of the medium, even in the presence of background. This will enable us to determine the best strategy for the field to improve quantitative constraints on properties of the medium in the face of these challenges.

Figure 1

A light cone diagram showing the stages of a heavy ion collision. The abbreviation $T_{\mathrm{f}\mathrm{o}}$ is for the thermal freeze-out temperature, $T_{\mathrm{c}\mathrm{h}}$ is for the chemical freeze-out temperature, and $T_{\mathrm{c}}$ is for the critical temperature where the phase transition between a hadron gas and a QGP occurs. ${\tau }_0$ is the formation time of the QGP. From Thomas Ullrich.

Figure 2

Schematic diagrams showing (left) the initial overlap region and (right) the spatial anisotropy generated by this anisotropic overlap region. This anisotropy can be quantified using the Fourier coefficients of the momentum anisotropy. From Boris Hippolyte.

Figure 3

Event display showing a dijet event in a $\mathrm{Pb}+\mathrm{Pb}$ collision at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$. This shows the large background for jet measurements in heavy ion collisions. From [207].

Figure 4

The correlation between the multiplicity $N_{\mathrm{c}\mathrm{h}}$, the impact parameter $b$, the number of binary nucleon-nucleon collisions $N_{\text{bin}}$, and the number of participating nucleons $N_{\text{part}}$. From [279], courtesy of Thomas Ullrich.

Figure 5

Schematic diagram showing the identification of a high-$p_T$ hadron in a $p+p$ collision and its use to define a coordinate system for dihadron correlations.

Figure 6

Dihadron correlations for trigger momenta $10<p_T^{\mathrm{t}}<15\mathrm{GeV}/c$ and $1.0<p_T^{\mathrm{a}}<2.0\mathrm{GeV}/c$ within pseudorapidities $|\eta |<0.5$ and associated particles within $|\eta |<0.9$ in $p+p$ collisions at $\sqrt{s}=2.76\mathrm{TeV}$ in pythia ([313]). The signal is normalized by the number of equivalent $\mathrm{Pb}+\mathrm{Pb}$ collisions. Left: Correlation function as a function of $\mathrm{\Delta }\varphi$ and $\mathrm{\Delta }\eta$. Right: Projection onto $\mathrm{\Delta }\varphi$.

Figure 7

Comparing HYDJET ([269]) calculations to STAR data ([34]). Particle production in HYDJET is separated into those from hard and soft processes. This shows that at sufficiently high momenta, particle production is dominated by hard processes. From [270].

Figure 8

Left: The standard deviation of the combined jet response (black circles) for $R=0.2$ anti-$k_T$ jets, including background fluctuations (red squares) and detector effects (blue triangles) for 0%–10% central $\mathrm{Pb}+\mathrm{Pb}$ events. Right: The standard deviation of the combined jet response (black circles) for $R=0.3$ anti-$k_T$ jets, including background fluctuations (red squares) and detector effects (blue triangles) for 0%–10% central Pb-Pb events. The background effects increase the jet energy resolution more for larger jets, as can be seen from the difference in the background distributions in both plots. For high momentum jets, where the momentum of the jet is much larger than background fluctuations, the jet energy resolution will be dominated by detector effects. From [29].

Figure 9

The nuclear modification factor of charged hadrons in $p+\mathrm{Pb}$ collisions at $\sqrt{s_{NN}}=5.02\mathrm{TeV}$ measured by the ALICE ([28]), ATLAS ([15]), and CMS ([253]) experiments. The data in this figure used an extrapolation of $p+p$ data from $\sqrt{s_{NN}}=2.76$ and 7 TeV as there was not a $p+p$ reference at the same energy available at this time. This shows that $R_{p\mathrm{P}\mathrm{b}}$ is consistent with one within uncertainties for high $p_T$ hadrons. From [15].

Figure 10

The nuclear modification factor of jets in $p+\mathrm{Pb}$ collisions measured by the CMS experiment in various rapidity bins. This shows that cold nuclear matter effects are small for jets. From [254].

Figure 11

$R_{AA}$ from PHENIX for direct photons ([125]), ${\pi }^0$ ([83]), $\eta$ ([88]), $\varphi$ ([105]), $p$ ([100]), $J/\psi$ ([79]), $\omega$ ([90]), $e^{\pm }$ from heavy flavor decays ([92]), and $K^{\pm }$ ([100]). This demonstrates that colored probes (high-$p_T$ final state hadrons) are suppressed while electroweak probes (direct photons) are not at RHIC.

Figure 12

$R_{AA}$ from ALICE for identified ${\pi }^{\pm }$, $K^{\pm }$, and $p$ ([55]) and $D$ mesons ([61]) and CMS for charged hadrons ($h^{\pm }$) ([194]), direct photons ([192]), $W$ bosons ([195]), and $Z$ bosons ([190]). The $W$ and $Z$ bosons are shown at their rest mass and identified through their leptonic decay channel. This demonstrates that colored probes (high-$p_T$ final state hadrons) are suppressed while electroweak probes (direct photons, $W$, and $Z$) are not at the LHC.

Figure 13

(Left) Demonstration of how $\delta p_T$ is determined. The fractional energy loss $S_{\text{loss}}$ measured as a function of the multiplicity $d{N}_{\mathrm{c}\mathrm{h}}/d\eta$ is plotted for several heavy ion collision energies for hadrons with $p_T^{pp}$ of 12 GeV (middle) and $6\mathrm{GeV}/c$ (right), where $p_T^{pp}$ refers to the transverse momentum measured in $p+p$ collisions. The $\mathrm{Pb}+\mathrm{Pb}$ data are from ALICE measured over $|\eta |<0.8$ while all other data are from PHENIX which measures particles in the range $|\eta |<0.35$. These results indicate that the fractional energy loss scales with the energy density of the system. Adapted from [106].

Figure 14

Reconstructed anti-$k_T$ jet $R_{AA}$ from ALICE ([48]) with $R=0.2$ for $|\eta |<0.5$, ATLAS ([12]) with $R=0.4$ for $|\eta |<2.1$, and CMS ([259]) with $R=0.2$, 0.3, and 0.4 for $|\eta |<2.0$. The ALICE and CMS data are consistent within uncertainties while the ATLAS data are higher. This may be due to the ATLAS technique, which could impose a survivor bias and lead to a higher jet $R_{AA}$ at low momenta. From Raghav Elayavalli Kunnawalkam.

Figure 15

(a) Dihadron correlations before background subtraction in $p+p$ and $d+\mathrm{Au}$ and (b) comparison of dihadron correlations after background subtraction in $p+p$, $d+\mathrm{Au}$, and $\mathrm{Au}+\mathrm{Au}$ at $\sqrt{s_{NN}}=200\mathrm{GeV}$ for associated momenta $2.0\mathrm{GeV}/c<p_T^{\mathrm{a}}<p_T^{\mathrm{t}}$ and trigger momenta $4<p_T^{\mathrm{t}}<6\mathrm{GeV}/c$. This measurement is now understood to be quantitatively incorrect because of erroneous assumptions in the background subtraction. We now see only partial suppression on the away side ([282]). From [71].

Figure 16

Top row: Comparisons of $A_J=(E_{T1}-E_{T2})/(E_{T1}+E_{T2})$ from $p+p$ and $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$ with leading jets above $p_T>100\mathrm{GeV}$ and subleading jets above 25 GeV. Bottom row: The angular distribution of the jet pairs. This shows that the momenta of jets in jet pairs is not balanced in central $A+A$ collisions, indicating energy loss. From [3].

Figure 17

The left two Feynman diagrams show direct photon production through Compton scattering and the right two diagrams show direct photon production through quark-antiquark annihilation. These are the leading order processes which contribute to the production of a gamma and a jet approximately 180° apart. From [87].

Figure 18

The away side $I_{AA}$ for direct photon-hadron correlations (red squares) and ${\pi }^0$-hadron correlations (blue circles) plotted as a function of $z_T=p_{T,h}/p_{T,\text{trig}}$ as measured by STAR in central 200 GeV $\mathrm{Au}+\mathrm{Au}$ collisions. This shows the suppression of hadrons 180° away from a direct photon. The data are consistent with theory calculations which show the greatest suppression at high $z_T$ and less suppression at low $z_T$. The curves are theory calculations from [290], [298], and ZOWW ([341]; [203]). From [66].

Figure 19

Isolated photons with $p_T>60\mathrm{GeV}/c$ and associated jets with $p_T>30\mathrm{GeV}/c$. (a) Average ratio of jet transverse momentum to photon transverse momentum $⟨x_{J\gamma }⟩$ as a function of the number of participating nucleons $N_{\mathrm{part}}$. (b) Average fraction of isolated photons with an associated jet above $30\mathrm{GeV}/c$, $R_{J\gamma }$, as a function of $N_{\mathrm{part}}$. This demonstrates that the quark jet 180° away from a direct photon loses energy with the energy loss increasing with increasing centrality. From [198].

Figure 20

$\mathrm{\Delta }{I}_{AA}={\mathrm{\Delta }}_{\text{recoil}}^{\mathrm{P}\mathrm{b}\mathrm{P}\mathrm{b}}/{\mathrm{\Delta }}_{\text{recoil}}^{\mathrm{P}\mathrm{Y}\mathrm{T}\mathrm{H}\mathrm{I}\mathrm{A}}$, where ${\mathrm{\Delta }}_{\text{recoil}}$ is the difference between the number of jets within $\pi -\mathrm{\Delta }\varphi <0.6$ of a hadron with $20<p_T<50\mathrm{GeV}/c$ and a hadron with $8<p_T<9\mathrm{GeV}/c$. The green line indicates the momentum of the higher momentum hadron, an approximate lower threshold on the jet momentum. This demonstrates the suppression of a jet 180° away from a hard hadron. From [50].

Figure 21

Jet $v_2$ from charged jets by ALICE ([52]) and calorimeter jets by ATLAS ([5]) compared to the charged hadron $v_2$ for 5%–10% (left) and 30%–50% collisions ([191]; [24]). This demonstrates that partonic energy loss is path length dependent. From [52].

Figure 22

The $R_{AA}$ and $R_{p\mathrm{P}\mathrm{b}}$ of heavy flavor associated jets measured by the CMS Collaboration ([199]; [255]; [311]). This shows that $b$ quarks lose energy in the medium. From Kurt Jung.

Figure 23

Ratio of fragmentation functions from reconstructed jets measured by ATLAS for jets in $\mathrm{Pb}+\mathrm{Pb}$ collisions at various centralities to those in 60%–80% central collisions at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$. This shows that fragmentation functions are modified in $A+A$ collisions, with an enhancement at low momenta (low $z$) and a depletion at intermediate momenta (intermediate $z$), with the modification increasing from more peripheral to more central collisions. From [9].

Figure 24

Comparison of CMS measurements of fragmentation functions in $\mathrm{Pb}+\mathrm{Pb}$ over $pp$ from reconstructed jets for jets in $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$ from 2010 and 2011 data ([196], [201]). Even though the two measurements are consistent, the 2010 data in isolation indicate that fragmentation is not modified while the 2011 data, which extend to lower momenta and use a less biased jet sample, show modification at low momenta (high $\xi$). This highlights the difficulty in drawing conclusions from a single measurement, particularly when neglecting possible biases.

Figure 25

$\xi =-\ln (x_E)$ distributions where $x_E=-|p_T^{\mathrm{a}}/p_T^{\mathrm{t}}|\cos (\mathrm{\Delta }\varphi )\approx z$ for isolated direct photon-hadron correlations for several photon $p_T$ ranges from $p+p$ collisions at $\sqrt{s}=200\mathrm{GeV}$ compared to TASSO measurements in $e^{+}+e^{-}$ collisions at $\sqrt{s}=14$ and 44 GeV. This demonstrates that direct photon measurements can be used reliably to extract quark fragmentation functions in $p+p$ collisions and that fragmentation functions are the same in $e^{+}+e^{-}$ and $p+p$ collisions. From [87].

Figure 26

Top panel: $I_{AA}$ for the away side as a function of $\xi =\log (1/z)=\log (p^{\text{jet}}/p^{\text{had}})$. The points are shifted for clarity. Bottom panel: The ratio of the $I_{AA}$ for $|\mathrm{\Delta }\varphi -\pi |<\pi /2$ to $|\mathrm{\Delta }\varphi -\pi |<\pi /6$. This demonstrates the enhancement at low momentum combined with a suppression at high momentum, a shift consistent with expectations from energy loss models. The change is largest for wide angles from the direct photon. From [97].

Figure 27

Compilation of $⟨p_T{⟩}_{\text{pair}}=\sqrt{2}{k}_T$ measurements where $k_T$ is the acoplanarity momentum vector. Dihadron correlation measurements in $p+p$ collisions from PHENIX are consistent with the trend from dimuon, dijet, and diphoton measurements at other collision energies. Dimuon and dijet measurements are from fixed target experiments and the diphoton measurements are from the Tevatron. From [116].

Figure 28

Dependence of the Gaussian widths in $\mathrm{\Delta }\varphi$ and $\mathrm{\Delta }\eta$ on $p_T^{\mathrm{t}}$ for $1.5\mathrm{GeV}/c<p_T^{\mathrm{a}}<p_T^{\mathrm{t}}$, $p_T^{\mathrm{a}}$ for $3<p_T^{\mathrm{t}}<6\mathrm{GeV}/c$, and $⟨N_{\mathrm{part}}⟩$ for $3<p_T^{\mathrm{t}}<6\mathrm{GeV}/c$, and $1.5\mathrm{GeV}/c<p_T^{\mathrm{a}}<p_T^{\mathrm{t}}$ for 0%–95% $d+\mathrm{Au}$, 0%–60% $\mathrm{Cu}+\mathrm{Cu}$ at $\sqrt{s_{NN}}=62.4\mathrm{GeV}$ and $\sqrt{s_{NN}}=200\mathrm{GeV}$, 0%–80% $\mathrm{Au}+\mathrm{Au}$ at $\sqrt{s_{NN}}=62.4\mathrm{GeV}$, and 0%–12% and 40%–80% $\mathrm{Au}+\mathrm{Au}$ at $\sqrt{s_{NN}}=200\mathrm{GeV}$. This demonstrates that the correlation is broadened in central $\mathrm{Au}+\mathrm{Au}$ collisions. From [128].

Figure 29

The $\mathrm{\Delta }\varphi$ and $\mathrm{\Delta }\eta$ projections of the correlation for $|\mathrm{\Delta }\eta |<0.78$ and $|\mathrm{\Delta }\varphi |<\pi /4$, respectively, for pion triggers (left two panels) and nonpion triggers (right two panels). Filled symbols show data from the 0%–10% most central $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$. Open symbols show data from minimum bias $d+\mathrm{Au}$ data at $\sqrt{s_{NN}}=200\mathrm{GeV}$. This shows that the yield is higher for pion trigger particles than nonpion trigger particles, which are mostly kaons and protons, and that there is a higher yield for pion trigger particles in central $\mathrm{Au}+\mathrm{Au}$ collisions than in $d+\mathrm{Au}$ collisions. This may be an indication of differences in partonic energy loss for quarks and gluons in the medium. From [65].

Figure 30

Symmetrized $\mathrm{\Delta }\eta$ distributions correlated with $\mathrm{Pb}+\mathrm{Pb}$ and $p+p$ inclusive jets with $p_T>120\mathrm{GeV}$ are shown in the top panels for tracks with $1<p_T<2\mathrm{GeV}$. The differences between per-jet yields in $\mathrm{Pb}+\mathrm{Pb}$ and $p+p$ collisions are shown in the bottom panels. These measurements indicate that the jet is broadened and softened as expected from energy loss models. From [256].

Figure 31

Gaussian widths of the away-side peaks (${\sigma }_{AS}$) for $p+p$ collisions (open squares) and central $\mathrm{Au}+\mathrm{Au}$ collisions (solid squares) (upper) and away-side momentum difference $D_{AA}$ as defined in Eq. (13) (lower) are both plotted as a function of $p_T^{\mathrm{a}}$. The widths (note the log scale on the $y$ axis) show no evidence of broadening in $\mathrm{Au}+\mathrm{Au}$ relative to $p+p$ due to the large uncertainties in the $\mathrm{Au}+\mathrm{Au}$ measurement. However, $D_{AA}$ shows the suppression of high momentum particles associated with the jet is balanced by the enhancement of lower momentum associated particles. The point at which enhancement transitions to suppression appears to occur at the same associated particle’s momentum and does not depend on the jet momentum. Data are for $\sqrt{s_{NN}}=200\mathrm{GeV}$ collisions and YaJEM-DE model calculations are from [300]. From [63].

Figure 32

Differential jet shapes in $\mathrm{Pb}+\mathrm{Pb}$ and $p+p$ collisions for four $\mathrm{Pb}+\mathrm{Pb}$ centralities. Each spectrum is normalized so that its integral is unity. This shows that there are more particles in jets in central collisions and these modifications are primarily at large angles relative to the jet axis, as expected from partonic energy loss. From [202].

Figure 33

The $\mathrm{\Lambda }/K_S^0$ ratio measured in jetlike correlations in 0%–60% $\mathrm{Cu}+\mathrm{Cu}$ collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$ for $3<p_T^{\text{trigger}}<6\mathrm{GeV}/c$ and $2<p_T^{\text{associated}}<3\mathrm{GeV}/c$ along with this ratio obtained from inclusive $p_T$ spectra in $p+p$ collisions. Data are compared to calculations from pythia ([313]) using the Perugia 2011 tunes ([314]) and Tune A ([227]). This shows that, within the large uncertainties, there is no indication that the particle composition of jets is modified in $A+A$ collisions, where $\mathrm{\Lambda }/K_S^0$ reaches a maximum of 1.6 ([127]). From [30].

Figure 34

Fully corrected jet mass distribution for anti-$k_T$ jets with $R=0.4$ in the 10% most central $\mathrm{Pb}+\mathrm{Pb}$ collisions compared to pythia ([313]) with the Perugia 2011 tune ([314]) and predictions from the jet quenching event generators jewel ([337]) and q-pythia ([144]). No difference is observed between pythia and the data. This shows that there is no modification of the jet mass within uncertainties. From [43].

Figure 35

Unfolded $p_T^D$ shape distribution in $\mathrm{Pb}+\mathrm{Pb}$ collisions for $R=0.2$ charged jets with momenta between 40 and $60\mathrm{GeV}/c$ compared to pythia simulations, to jewel calculations, and to $q/g$ pythia templates. This shows that the dispersion is larger in $\mathrm{Pb}+\mathrm{Pb}$ collisions than in $p+p$ collisions. This may indicate either modifications or a quark bias. From [216].

Figure 36

The girth $g$ for $R=0.2$ charged jets in $\mathrm{Pb}+\mathrm{Pb}$ collisions with jet $p_T^{\mathrm{c}\mathrm{h}}$ between 40 and $60\mathrm{GeV}/c$ compared to pythia simulations, to jewel calculations, and to $q/g$ pythia templates. This shows that jets are somewhat more collimated in $\mathrm{Pb}+\mathrm{Pb}$ collisions than in $p+p$ collisions. This may indicate a quark bias in surviving jets in $\mathrm{Pb}+\mathrm{Pb}$ collisions. From [216].

Figure 37

Ratio of the splitting function $z_g=p_{T2}/(p_{T1}+p_{T2})$ in $\mathrm{Pb}+\mathrm{Pb}$ and $p+p$ collisions with the jet energy resolution smeared to match that in $\mathrm{Pb}+\mathrm{Pb}$ for various centrality selections and $160<p_T^{\mathrm{j}\mathrm{e}\mathrm{t}}<180\mathrm{GeV}$. This shows that the splitting function is modified in central $\mathrm{Pb}+\mathrm{Pb}$ collisions compared to $p+p$ collisions, which may indicate either a difference in the structure of jets in the two systems or an impact of the background. From [310].

Figure 38

${\tau }_2/{\tau }_1$ fully corrected recoil $R=0.4$ jet shape in 0%–10% $\mathrm{Pb}+\mathrm{Pb}$ collisions at $40\le p_{t,\text{jet}}^{\mathrm{c}\mathrm{h}}<60\mathrm{GeV}/c$. This shows that, at least for this kinematic selection, the subjettiness is not modified. The trigger tracks are $8–9\mathrm{GeV}/c$ for the background dominated region and $15–45\mathrm{GeV}/c$ for the signal dominated region. From [339].

Figure 39

Schematic diagram showing the definitions used in Fig. 40.

Figure 40

Average missing transverse momentum for tracks with $p_T>0.5\mathrm{GeV}/c$, projected onto the leading jet axis is shown as solid circles. The average missing $p_T$ values are shown as a function of dijet asymmetry $A_J$ for 0%–30% centrality, inside a cone of $\mathrm{\Delta }R<0.8$ of one of the leading or subleading jet cones on the left, and outside ($\mathrm{\Delta }R>0.8$) the leading and subleading jet cones on the right. The solid circles, vertical bars, and brackets represent the statistical and systematic uncertainties, respectively. For the individual $p_T$ ranges, the statistical uncertainties are shown as vertical bars. This shows that missing momentum is found outside of the jet cone, indicating that the lost energy may have equilibrated with the medium. From [188].