Study of jet-medium interactions using jet shape observables in heavy ion collisions at LHC energies with JEWEL

TL;DR

This study uses the JEWEL model to analyze how jets interact with the quark-gluon plasma in heavy ion collisions at LHC energies, focusing on jet shape modifications and their agreement with experimental data.

Contribution

It demonstrates that JEWEL can qualitatively reproduce jet shape modifications and provides insights into in-medium jet fragmentation at LHC energies.

Findings

Jet yields are suppressed in Pb-Pb collisions compared to proton-proton.

Jet shape variables indicate harder, more collimated fragmentation in medium.

Modifications depend on jet transverse momentum, especially below 100 GeV/c.

Abstract

Based on a pQCD inspired dynamical model of jet-medium interactions, Jewel, we have studied possible modifications to inclusive jet yields and a set of jet shape observables, namely, the fragmentation functions and radial momentum distributions when jets propagate through a deconfined partonic medium created in collisions of heavy nuclei at Large Hadron Collider (LHC) energies. Jets are reconstructed with anti-k T algorithm in the pseudorapidity range $|\eta_{\rm jet} | < 2.1$ for resolution parameter R= 0.2, 0.3 and 0.4. For background subtraction, a Jewel-compatible 4-Momenta subtraction technique (4MomSub) have been used. The modification of inclusive jet-yields in Pb-Pb collisions relative to proton-proton interactions, quantified by $R^{\rm jet}_{AA}$, are seen to be in reasonable agreement with ALICE, ATLAS and CMS data over a broad transverse momentum range. Jewel is able to capture the qualitative features of the modifications to the fragmentation functions and radial momentum distributions in data but not always quantitatively. This quantitative discrepancy may be related to the simplified treatment of recoil partons in the background model and partly due to background subtraction procedure itself. Nevertheless, observed modification of jet shape variables in Jewel corroborates the fact that in-medium fragmentation is harder and more collimated than the fragmentation in vacuum. We further observe that these modifications depend on the transverse momentum of jets and it seems that medium resolves the core structure of low momentum jets below 100 GeV/c at LHC energies.

Tables

Table 1. Table 1: Details of the parameters used for JEWEL

$\sqrt{s_{NN}}$	${\sigma }_{NN}$	${\tau }_i$	$T_i$
5.02 TeV	72 mb	0.4	590 MeV[38]
2.76 TeV	64 mb	0.6	485 MeV[39]

Equations

$$R_{AA}^{jet}=\frac{d^2{N}_{AA}^{jet}/d{p}_{T,jet}d\eta }{<N_{coll}>d^2{N}_{pp}^{jet}/d{p}_{T,jet}d\eta },$$

$$FF(z)=\frac{1}{N_{jet}}\frac{dN}{dz},$$

$$<\frac{d{p}_T^{sum}}{dr}>(r)=\frac{1}{\Delta r}\frac{1}{N_{jets}}\sum _{i=1}^{N_{tracks}}{p}_T^i(r-\Delta r/2,r+\Delta r/2)$$

Full text

Keywords: Jet-energy loss, Jet shapes, Jewel

1 Introduction

In relativistic collisions heavy nuclei (A-A), large suppression of single inclusive yields of high (transverse) momentum (pT) particles formed the basis for the landmark discovery of a new phase of QCD matter, characterized by a strongly interacting but deconfined state of quarks and gluons (partons), namely the Quark Gluon Plasma (QGP) [1, 2]. It is known since long that the production of high-$p_{T}$ particles involve parton scatterings of large momentum transfer (hard scatterings), occurring at a time scale $<$ 1 fm/c [3]. Each of these hard scattered partons then develop a shower of secondary partons through repeated gluon emission and/or quark-antiquark splitting that eventually fragment into collimated spray of hadronic final states known as the Jet. In a marked contrast to proton-proton (pp) interactions, jet production in heavy ion collisions is strongly suppressed, compatible with Bjorken-conjectured signature for the QGP formation, referred to as the “Jet quenching” [4, 5, 6, 7, 8, 9].

The jet-quenching phenomena in its simplest form is mainfested as the suppression of the single inclusive cross-sections of high-$p_{T}$ particles against a scaled pp reference at the same collision energy [10, 11, 12, 13, 14]. This suppression, in general, encodes the characteristic features of parton energy loss in a dense QGP, quantified by the nuclear modification factor or RAA [15, 16, 17, 18]. But the measurements of RAA alone is not sufficient to decipher the complete picture of the parton energy loss mechanisms because of its insensitivity to the complex nature of parton shower evolution and the interaction between the shower and medium constituents in QGP [19].

This incompleteness can however, be alleviated from the measurements of fully reconstructed jets that are known to be a reasonable proxy to the shower initiating hard scattered partons. Jet being a composite object of hadronic final states (clustered together in a cone of radius, R), it’s energy loss has a subtle difference to the energy loss of an individual parton. It is perceived that the modification of jet-yields in a medium not only depends on the energy loss of it’s individual constituents, but also on how this lost energy is redistributed [20]. The effective energy loss of jets in a medium is therefore, consequences of the competing contributions of the jet-medium interactions causing the jet constituents to diffuse out-of the jet-cone leading to the degradation of its initial energy, while being compensated to a certain degree by the in-cone emission of medium-induced gluons [21, 22, 23, 24]. Thus, the medium modifications of jets reflect the multifacet aspect of jet-medium interactions to which inclusive particle spectra are not at all sensitive. This substantiates on the necessity for studies with fully reconstructed jets in-order to examine the criticality of jet-medium interactions leading to the manifested features of jet-quenching phenomena: the suppression of jet-yields and the modification of intra-jet properties.

At Relativistic Heavy Ion Collider (RHIC) in BNL because of limited kinematic reach, measurements related to jet quenching were restricted to inclusive hadron RAA or high-pT two-particle correlations [25] (studies with fully reconstructed jets are currently persued at RHIC as well [26, 27]). At LHC, almost 10-fold increase in the collision energy resulted in a significant rise in hard scattering processes, pushing the kinematic reach to several orders of magnitude. This has largely facillitated studies with reconstructed jets. By now, we also have very rich theoretical insight on jet energy loss mechanisms based on plethora of dynamical modelling of jet-medium interactions in an evolving QGP [28, 29, 30, 31, 32, 33]. However, the multi-scale nature of the problem makes the theoretical modelling of the jet-medium interactions highly non-trivial. To be a complete theoretical framework, models need to consistently address different scales, ranging from the weakly interacting perturbative scale associated with initial hard scatterings and subsequent showering, to a non-perturbative scale of the order-of $\Lambda_{QCD}$ when jets interact with the medium strongly. In addition, models need to incorporate jet-induced medium response (recoil partons) that contribute to the so-called soft correlated background that can not be uniquely distinguished from the original jet-fragments.

To this end, Jet Evolution With Energy Loss model or Jewel [30, 34] has the necessary ingradients to demonstrate its effectiveness in describing variety of inclusive and differential jet observables. In this work we make an attempt to study different aspects of the jet-quenching phenomena within Jewel and try to achieve further insight on the medium modification of fully reconstructed jets via a systematic data-to-model comparison at the LHC energies. The organization of this paper is as follows. In section II an overview of Jewel and the parameter settings used for this work will be presented. Followed by results and discussions, and summary in section III and IV, respectively.

2 JEWEL

Jewel offers a dynamical framework to simulate jet quenching phenomena in A-A collisions on the basis of QCD evolution of parton showers in presence of a thermalized partonic background. The initial state parton showers in Jewel are generated with PYTHIA6.4 [35] event generator on top-of Cteq6LL [36] parton distribution function (PDF) for pp events and EPS09 [37] nuclear PDF for heavy-ion collisions. A pp interaction in Jewel is identical with PYTHIA6, where as, for nuclear collisions PYTHIA generated parton showers are coupled with Bjorken-type hydrodynamic background. The hydrodynamic expansion in Jewel follows an ideal-gas equation of state (EOS) with number and energy densities of medium partons being calculated taking local temperature in the medium as an input [40]. The in-medium scatterings of hard partons, resulting in elastic and in-elastic energy loss (QCD bremsstrahlung), are described by 2$\rightarrow$n (n $\geq$ 2) leading order (LO) pQCD matrix elements protected against infra-red divergence. Radiations induced by re-scatterings are however, ordered according to its hardness, i.e, the parton shower will be perturbed by the hardest re-scattering [30, 41]. In addition, each re-scattering in Jewel is associated with a production of a recoil parton that propagates through the medium without further interactions. Re-scatterings are terminated once the local temperature drops down to a critical temperature Tc (170 MeV), order of QCD phase transition temperature at baryon chemical potential $\mu_{B}\sim 0$. For hadronization, recoil partons are first converted to gluons and then attached to strings connected with partons producing jet. This endows correlation between jets and recoil partons, likely to be manifested as enhancement in soft hadronic yields at large angles to jet-axis. Finally, PYTHIA takes over and hadronization occurs by Lund string fragmentation mechanism.

Our simulation results are based on standard Jewel setup in a “recoil-on” mode, i.e, keeping record of recoil partons in the event information. As recoil partons in Jewel retain their thermal component, i.e, momentum before scattering, this essentially contributes to soft uncorrelated background specifically in the measurements of intra-jet observable and needed to be subtracted. Since Jewel does not simulate full event in A-A collisions, conventional background subtraction procedures are rendered not suitable. Instead, Jewel-compatible background subtraction techniques were proposed and tested over a variety jet-observables. We will use one of them, namely, the four momenta subtraction or 4MomSub [42].

For background subtraction in Jewel with 4MomSub, a set of neutral particles with very small momenta and positions corressponding to scattering centers, prior to interaction, are included in the final event information. These dummy particles together with others get clustured to a Jet. Then all the jet constituents pointing back to the scattering centers (background) are identified and their four momenta are added. Finally, background four momenta is subtracted vectorially from the four momenta of the reconstructed jets. This subtraction technique however, has certain limitations, for example, it is only applicable to full jets and can not be used for charged jets directly [42] .

About one million 0-10% central Pb-Pb and pp event sample were generated at $\sqrt{s_{NN}}=$ 2.76 TeV and 5.02 TeV. The initial conditions required to simulate the hydrodynamic background, such as thermalization time $\tau_{i}$ and initial temperature Ti are tabulated in TABLE 1. Jets are reconstructed with anti-kT [43] jet- reconstruction algorthim available in the FastJet package[44].

3 Results and Discussion

3.1 Jet nuclear modification factor (R${}_{AA}^{jet}$)

As a first step to characterize the effect of jet-medium interaction, we measure the nuclear modification factor for single inclusive jet spectrum, defined as

[TABLE]

where N${}^{jet}_{AA}$ and N${}_{pp}^{jet}$ are the number of jets in A-A and pp collisions, respectively and $\langle N_{coll}\rangle$ is the number of binary nucleon-nucleon collision averaged over a given collison centrality class. Figure 1 shows a comparison of $p_{T}$ dependence of $R_{AA}^{jet}$ calculated from Jewel with the recent measurements from ALICE[45, 46], ATLAS[47, 48] and CMS[49] for jet resolution parameter R = 0.4 at $\sqrt{s_{NN}}=$ 5.02 TeV [Fig.1(a)] and 2.76 TeV [Fig.1(b)].

Data-to-model comparison shows a reasonable agreement, although, uncertainties in some pT-bins in data are large. In A-A collisions, jets are usually reconstructed with small cone size (R) to avoid large underlying background. This may lead to additional suppression of jet cross sections because, partons scattered to large distances from jet-axis can not be recovered. This condition generally prevails when jets propagate through a medium. Energy and momentum transferred to medium by jets are carried away to larger distances by medium expansion. This can influence the effective jet energy loss, leading to a significant jet-cone size dependence. Also, the medium-stimulated radiations populating at large angles from the jet-axis can naturally account for additional reduction to jet energy. Expectedly, jets reconstructed in A-A collisions with smaller cone size will capture only a subset of the full parton shower causing stronger attenuation of jet spectrum relative to pp baseline. To illustrate the effect of R dependence of jet cross sections in pp and A-A, the ratio of jet-pT spectra at R = 0.2 with respect to different values of R are shown in Fig.2.

The ratio of cross sections exhibit a clear deviation from unity both in pp and Pb-Pb collisions, implying a large fraction of initial partonic energy can be recovered by reconstructing jets with large R. Interestingly, the ratio between R = 0.3 to R = 0.2 in pp and Pb-Pb are consistent with each other, suggesting redistribution of energy by jet quenching does not modify the jet structure from R = 0.2 to R = 0.3. This could be because at these two radii we only observe the unresolved hard-core of the entire jet. A significant difference between pp and Pb-Pb, beyond the statistical uncertainties, is however, observed from R = 0.2 to R = 0.4. The R dependence of nuclear suppression factor has been measured by the CMS collaborations[49] but given the current uncertainty in the measurements, suppression appears to be of R-independent. Instead, some model calculations predict a clear hierarchy of R${}_{AA}^{\mathrm{jet}}$ with R [50, 51]. For completeness, we also calculate R dependence of $R_{AA}^{jet}$ as function of pT, shown in Fig.3.

We observe the level of suppression at R = 0.2 and 0.3 is same, only difference is seen for R = 0.4, consistent with our calculation of jet cross section ratios in Fig.2. To be mentioned, ratios of RCP ( central-to-peripheral jet cross sections ratio), R${}_{CP}^{0.3}$/R${}_{CP}^{0.2}$, measured by the ATLAS collaboration [52] also show similar trend for p${}_{T}>$ 100 GeV/c (ratio is seen to be consistent with unity). For direct comparison of R-dependence of jet suppression to data, $R_{AA}^{jet}$ for R = 0.2 [Fig.4(a)] and R = 0.4 [Fig.4(b)] from Jewel are overlaid on the CMS measurement [49].

Jewel underestimates data for R = 0.2 but in case of R = 0.4, agreement with data is better. A similar trend in data was also reported by the the ALICE Collaboration for charged-jets in [46]. This may be because the recoil partons in Jewel are scattered out to larger angles than the physical expectation. Hence, when R is increased, recoil contributions are recovered leading to a better data-to-model agreement.

Besides the modification of inclusive jet yields from pp to A-A, jet-medium interactions also modify a number of intra-jet properties, like, the angular and momentum distributions of jet-constituents within the cone. Modifications of these intra-jet properties can be examined from the measurements jet fragmentation functions and jet shapes. These are reported in the sections to follow.

3.2 Fragmentation function distributions(FF)

As mentioned, the jet-quenching phenomena not only result in an overall jet energy loss but also modify the momentum distributions of particles within the jet. This modification can be quantified by measuring relative changes in the fragmentation functions from pp to A-A collisions at same energy and a given interval of jet-pT. The fragmentation function FF(z) [53], is generally defined as

[TABLE]

where z = $\frac{p_{T}\textrm{cos}\Delta R}{p_{T}^{jet}}$, refers to the longitudinal momentum fraction of particles relative to a jet of transverse momentum, p${}_{T}^{jet}$. The quantity Njet denotes the number of jets in a given momentum interval, and $\Delta R(=\sqrt{(\Delta\eta)^{2}+(\Delta\phi)^{2}})$ corressponds to pseudorapidity and azimuthal sepration of particles from the jet-axis.

Figure 5 shows FF(z) calculated within Jewel in pp and 0-10% central Pb-Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV in the p${}_{T}^{jet}$ interval of 126 to 158 GeV/c. Also shown in the same, a quantitative comparison with the ATLAS measurements from [53].

Furthermore, to quantify the modification of fragmentation functions in heavy ion collisons, ratios of FF(z) in Pb-Pb to that in pp collisions are shown in Fig.6 and compared with the ATLAS data for collision energies 5.02 TeV and 2.76 TeV [53, 54]. The shape of the distributions from the model calculation are similar to data, with following generic features: an enhancement at low and high z and a depletion at intermediate z. The enhancement at low z is interpreted as the softening of the fragmentation functions, i.e, an excess yield of low-pT particles within the jet-cone.

While some model calculations attribute this excess to multiple soft gluon emissions, in Jewel, enhancement is mainly from the jet-induced medium response. It is realized, because of the momentum conservation, jet-energy deposited into the medium will have a component along the jet direction ( unless completely thermalized ). As a result, particles produced from the medium in the vicinity of jets will be endowed with kinematic focussing along the jet-axis. These particles being reconstructed as a part of a jet will soften the momentum distributions of hadronic fragments of jets in a medium than in vacuum. Quantitatively, Jewel calculation overshoots the data at low-z. This discrepency may be related to the fact that recoil partons in Jewel suffer only single interaction. Therefore, the degree of correlation between jet and soft recoils could be larger than expected in a physical scenario where recoils suffer multiple interactions and tend to thermalize. Here we would like to mention that the background subtraction in Jewel is done at the inclusive level and not at the track level this might contribute to the discrepency between data and Jewel at the level of a few percent [42].

On the other hand, observed enhancement at high-z is attributed to hardening and narrowing of jets because of the energy loss. A possible explanation to this was offered by the apparent similarity in the fragmentation functions of quenched jets with the jets initiated by quarks in vacuum. A quark-initiated jet is in general, harder and more collimated [55] .

Similar enhancement at high-z is also expected from the color coherence effect[56, 57]. Partonic fragments with transverse spread less than the coherent length scale of the medium, remain unresolved and shielded against the medium modification. As a consequence, although a quenched jet has a overall energy less than the jet in vacuum at same pT but it may have originated from a more energetic parton. Since a sizeable fraction of the total jet energy is concentrated within the unresolved hard core, despite the energy loss, modification to intra-jet structures are negligible. This may actually bias an ensemble of quenched jets in A-A collisions to higher virtuality relative to pp when compared at same jet-pT. In Jewel a similar situation may have been mimicked because the re-scatterings of shower partons with medium are ordered according to virtuality. Thus, a scattering harder than the virtuality of the shower parton would result in a medium-induced radiation. Since the re-scatterings are softer than the orginal scale of the parton shower, hard inner core remain unmodified, leading to the observed enhancement in fragmentation function ratios at high-z.

To further determine how the modification of fragmentation functions depends on p${}_{T}^{jet}$, ratios of fragmentation functions in three jet-pT intervals: 40 <p${}_{T}^{jet}$ <100 GeV/c, 126 <p${}_{T}^{jet}$ <158 GeV/c and 316 <p${}_{T}^{jet}$ <398 GeV/c are compared in Fig.7. A clear excess of soft particles is observed in all jet-pT intervals together with an ordering. While low-z excess is maximum in the lowest p${}_{T}^{jet}$ interval, the high-z enhancement in the same p${}_{T}^{jet}$ range is seen to be least. This might indicate a significant modification to jet substructures at this low p${}_{T}^{jet}$ interval. With high statistics data being available from the LHC Run II, such predictions can be tested to achieve insight on the transverse resolution scale of the medium at the LHC kinematics.

Next we move to study a classic jet shape observable that has been designed to analyse the radial distribution of the jet transverse momentum from the jet axis.

3.3 Radial distribution of transverse momentum density

The radial distribution of transverse momentum density, dpT**sum/dr, within a jet is measured as a function of the distance r = $\sqrt{(\Delta\eta)^{2}+(\Delta\phi)^{2}}$ radially outword from the jet axis. The momentum density

[TABLE]

is calculated by taking scalar sum of the transverse momentum, p${}_{T}^{sum}$, of all particles that falls within the annular regions of width $\Delta$r at radius r [58].

Figure 8 shows the modification in jet shape distribution in 0-10% central Pb-Pb collisions relative to pp baseline. The ratio of jet shape distribution functions in A-A to pp collision is seen to have depletion at intermediate r and an enhancement at large r. However, at small r, jets with p${}_{T}^{jet}$ >100 GeV/c modification factor is consistent with unity, implying that jet core remains unmodified or negligibly modified.

While some model calculations attribute this enhancement at large-r to wide-angle medium induced gluon radiation and/or momentum broadening [23], but, in Jewel, enhancement at large-r can only be accounted on inclusion of the recoil partons. Interestingly, in the jet-pT range 40 to 100 GeV/c, depletion persists down to very small r. This is consistent with what we inferred from the modification of fragmentation functions of jets <100 GeV/c. That is, low momentum jets, preferably <100 GeV/c at LHC energies might have their inner core modified by the jet-medium interaction.

We further decompose the excess at large-r into different ranges of constituent particle’s pT inside the jet cone. Here in Fig.9, we note that the excess is more pronounced in the lowest pT range, 1 <pT <2 GeV/c, which is consistent with the enhancement seen in the measurements of jet-track correlations in [59]. This certainly suggests that a sizeable fraction of total jet-energy is carried out to large relative angles from the jet axes and concentrated in the low pT ranges of the overall spectrum.

4 Summary

Manifestations of jet-medium interactions are not only limited to the suppression of single inclusive jet spectrum but also reflected in the modifications of it’s transverse and longitudinal energy or momentum profile. In this work we have investigated the effect of jet energy loss on the single inclusive jet yields and intra-jet properties, namely, the jet fragmentation functions and jet shapes, within a dynamical framework of jet-medium interaction, Jewel, at LHC energies. Jewel calculations with appropriately chosen parameters (constrained to describe bulk obsevables in high energy heavy ion collisions) can reasonably describe the pT dependence of jet yield modification in data when evaluated at jet resolution parameter, R = 0.4, as shown in Fig.1. We have repeated the same exercise for smaller values of R, as jet-medium interactions are likely to redistribute the jet energy over a wide angular spread. Therefore, one may expect stronger suppression of jet spectrum when calculated at smaller values of R. Indeed such an effect has been observed in Fig.2 where the jet cross-section ratios, $\sigma(\textit{R}=0.2)/\sigma(\textit{R}=0.3)$ in Pb-Pb and pp are seen to deviate from unity but their magnitudes are consistent. A significant difference between Pb-Pb and pp is however, noticed for $\sigma(\textit{R}=0.2)/\sigma(\textit{R}=0.4)$. This essentially suggests that dynamics of jet-medium interaction in Jewel is able to capture the large angle transport of jet energy in medium which is a key feature responsible for the jet energy loss. Same conclusion can also be drawn from Fig.3 and Fig.4 where jet suppression factor is seen to exhibit observable difference when evaluated at small (0.2) and large (0.4) R.

Further details on the jet-medium interactions can be extracted from measurements of jet fragmentation functions and jet shapes. We observe quenched jets have a harder fragmentation pattern than jets in vacuum when compared in the same jet-pT interval. In addition a pT-dependent modification to these fragmentation functions are also observed. Modification quantified by the ratios of the fragmentation functions in A-A collisions to those in pp exhibit large enhancement at low and high z ($\sim$ pT) as shown in Fig.7. This excess yield of soft fragments is generally attributed to wide angle emission of medium-induced soft gluons but in Jewel soft excess could only be achieved on inclusion of recoil contributions. The enhancement of hard fragments (jet-constituents with relatively large transverse momentum and generally aligned to the jet axis), on the other hand, could be because of quark-like fragmentation pattern on top-of the hardening of the initial energy spectrum of quenched jets when compared to vacuum-jets in the same jet-pT interval. It is worthy to note that in the jet-$p_{T}$ range 40 to 100 GeV/c, enhancement at high-z drops significantly. This may be because at this jet-pT interval, jet-medium interactions are strong enough to resolve the inner hard core of jets. Similar conclusions has been reached from the measurements complementary to the fragmentation functions i.e jet shapes, presented in Fig.8.

Acknowledgement

Significant part of computation for this work was carried out using the computing server facility at CAPSS, Bose Insititute, Kolkata. RB is supported by DST sponsored project SR/MF/PS-01/2014-BI. SC acknowledges financial support granted under SERB (DST) sponsored “Ramanujan Fellowship“ of Dr. Saikat Biswas (D.O. no. SR/S2/RJN-02/2012). RB and SC would like to acknowledge fruitful discussions with Raghav Kunnawalkam Elayavalli on background subtraction in Jewel.