Vector boson-tagged jet production in heavy ion collisions at the LHC
VVector boson-tagged jet production in heavy ion collisions at the LHC
Zhong-Bo Kang,
1, 2, 3, ∗ Ivan Vitev, † and Hongxi Xing
4, 5, ‡ Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA Mani L. Bhaumik Institute for Theoretical Physics,University of California, Los Angeles, California 90095, USA Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA High Energy Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA (Dated: October 12, 2018)Vector boson-tagged jet production in collisions of heavy nuclei opens new opportunities to studyparton shower formation and propagation in strongly interacting matter. It has been argued toprovide a golden channel that can constrain the energy loss of jets in the quark-gluon plasmacreated in heavy ion reactions. We present theoretical results for isolated photon-tagged and Z boson-tagged jet production in Pb+Pb collisions with √ s NN = 5 .
02 TeV at the LHC. Specifically,we evaluate the transverse momentum imbalance x JV distribution and nuclear modification factorI AA of tagged jets and compare our theoretical calculations to recent experimental measurements byATLAS and CMS collaborations. Our analysis, which includes both collisional and radiative energylosses, sheds light on their relative importance versus the strength of jet-medium interactions andhelps quantify the amount of out-of-cone radiation of predominantly prompt quark-initiated jets. I. INTRODUCTION
The production of a vector boson (either a photon γ or an electroweak boson such as the Z ) in association witha jet has been extensively studied in proton-proton collisions at the Large Hadron Collider (LHC), by both theATLAS [1–3] and CMS [4–7] collaborations. Such γ +jet and Z +jet processes are among the most powerful channelsthat can be used to test the fundamental properties of Quantum Chromodynamics (QCD). They also serve as crucialinputs for the precise determination of the parton densities in the proton, and can help improve the constraints on thegluon distribution function. It is, thus, not surprising that significant theoretical effort has been invested in preciselycomputing the differential cross sections for these processes [8–10].Vector boson-tagged jets are also particularly well suited to studying many-body QCD at high energies in heavy ioncollisions, where a deconfined quark-gluon plasma (QGP) is expected to be formed. On one hand, the tagging bosonsescape the region of the hot dense medium unscathed. This has been confirmed through the absence of significantmodification of both γ and Z boson production in Pb+Pb collisions relative to the binary collision-scaled proton-proton (p+p) baseline by both ATLAS and CMS collaborations [11–13]. On the other hand, the parton shower thatrecoils opposite the vector boson in heavy ion collisions gets modified, or quenched, due to the elastic and inelasticinteractions with the QCD medium. Since at leading order the vector boson and the jet are produced back-to-backin the azimuthal plane and have equal transverse momenta in the standard collinear factorization framework, it wasargued more than a decade ago [14] that a virtual photon that decays to dileptons ( γ ∗ → (cid:96) + (cid:96) − ) will provide verytight constraints on the energy of the away-side parton shower. Theoretical studies of cold nuclear matter effects haveshown that they don’t significantly affect vector boson-tagged jet distributions [15].However, only recently have measurements of approximately back-to-back isolated γ +jet and/or Z +jet finalstates, considered “golden channels” for the study of jet quenching and the extraction of the properties of the hotdense medium, become possible. It was also realized that higher order processes will alter the perfect transversemomentum balance p JT = p VT and lead to a distribution of recoiling jets [17]. A useful feature of this distribution forthe purpose of our study is that it is narrowly peaked and the shift of the peak will contain detailed information aboutjet energy loss. Furthermore, jets produced opposite to the isolated γ or Z bosons are much more likely to originatefrom quarks, while dijets usually involve significant quark and gluon fractions that vary strongly with transversemomentum. In this regard, vector boson-tagged jets can help constrain the flavor dependence of the jet quenchingmechanism. Previous studies of vector boson tagged jet production in heavy ion collisions have been carried outbased on a perturbative QCD framework [15, 18], a Boltzmann transport model [19], an event generator JEWEL [20], ∗ [email protected] † [email protected] ‡ [email protected] The so-called fragmentation contribution to Z -boson production is generally small even at the LHC energies [16]. a r X i v : . [ h e p - ph ] F e b and a hybrid strong/weak coupling model [21]. Photon-tagged heavy flavor jets have also been proposed as ways toincrease the fraction of prompt b quarks [22]. Last but not least, the substructure of γ -tagged jets was found to bemore sensitive to large angle radiation in comparison to inclusive jets [23].Isolated γ -tagged and Z -tagged jets in Pb+Pb collisions at the center-of-mass energy per nucleon pair √ s NN = 5 . JV distribution in both p+p and Pb+Pb collisions, where x JV = p JT /p VT with p JT and p VT thetransverse momentum of the jet and the vector boson, respectively. We also calculate the nuclear modification factorI AA and compare to the experimental findings. Within the theoretical model calculation we present our results for thetransverse momentum imbalance shift ∆ (cid:104) x JV (cid:105) and the relative contribution of radiative and collisional energy lossesof typical energy jets.The rest of our paper is organized as follows. In Sec. II, we present the evaluation of the differential cross sectionsfor isolated γ -tagged and Z -tagged jet production in p+p collisions using Pythia 8 [27] and determine the flavororigin of the recoil jet production for the proper implementation of the energy loss effects. In Sec. III, we provideinformation on how we implement the medium effects to obtain the modification of vector boson tagged jet productionin dense QCD matter. In Sec. IV, we present our phenomenological results and give detailed comparison with themost recent experimental measurements for the isolated γ and Z boson tagged jet production in heavy ion collisionsat the LHC. We summarize our paper in Sec. V. II. ISOLATED PHOTON-TAGGED AND Z -TAGGED JET PRODUCTION IN P+P COLLISIONS In this section we present the evaluation of the differential cross sections for isolated photon-tagged and Z -taggedjet production in p+p collisions using Pythia 8 [27]. Pythia 8 is a widely-used high energy phenomenology eventgenerator, which can describe well the main properties of the event structure. This event generator utilizes leading-order perturbative QCD matrix elements+parton shower, combined with the Lund string model for hadronization.The simulations presented in this paper are performed with the CTEQ6L1 parton distribution functions [28] andwith the anti- k T jet clustering algorithm [29]. In the p+p baseline simulations, we select the vector boson (isolated-photon and Z -boson) and jet according to the desired kinematics to match the experimental measurements, andwe have simulated around 10 events for both isolated photon-tagged and Z -tagged jets to reduce the statisticaluncertainties/fluctuations.Measurements of vector boson-tagged jet production in p+p collisions at different center-of-mass energies have beencarried out at both the Tevatron and the LHC. We present in Fig. 1 the comparisons to CMS measurements [6, 7]to show the validation of Pythia simulation against experimental data. The left panel in Fig. 1 is the differentialcross section dσ/dp JT as a function of leading jet transverse momentum p JT for Z +jet production in p+p collisionsat the LHC at √ s = 7 TeV. The right panel corresponds to the differential cross section dσ/dp γT as a function ofisolated-photon transverse momentum p γT for γ +jet production in p+p collisions at the LHC at √ s = 8 TeV. Inour simulations, the specific kinematic requirements are implemented to match the experimental measurements inselecting V+jet events. For details on the kinematic cuts, see Ref. [6] for Z +jet and Ref. [7] for γ +jet production.As can be seen in Fig. 1, the Pythia 8 event generator gives reasonably good description of the CMS experimentaldata.Before the implementation of energy loss effects through the medium-induced parton shower on vector boson-tagged jet production in Pb+Pb collisions at the LHC, we need the detailed baseline information for Z +jet and γ +jet production in p+p collisions for different partonic subprocesses. In our simulations, specific kinematic cuts forthe Z +jet and γ +jet event selections are applied as in Refs. [24] and [25], respectively. In particular, a minimumseparation of the azimuthal angle between the vector boson and the jet, ∆ φ JV > / π , is required to select back-to-back V+jet events. In each event of the Z +jet simulation, the Z -boson is required to have: the invariant mass ofthe decayed dileptons 70 < m (cid:96)(cid:96) <
110 GeV, p eT >
20 GeV, p µT >
10 GeV, | y e | < . | y µ | < .
4, and the transversemomentum of the Z boson p ZT >
60 GeV; the recoil jet is reconstructed using the anti- k T algorithm with a jet radiusparameter R = 0 . p JT >
30 GeV and | y | J < . γ +jet production, the photon is required tohave | y γ | < .
44. To minimize the fragmentation contribution to the photon, an isolation cut is applied where thesum of the transverse momenta of the generated particles in a cone of radius ∆ R = 0 . q + ¯ q → V + g and q (¯ q ) + g → V + q (¯ q ). We have checked that the g + g → V + g channel contributes to the crosssection only marginally and, thus, can be safely neglected. As can be seen in Fig. 2 (left), the cross section of Z +jet − − − − − Z+jet, √ s = 7 TeVR = 0 . , | y J | < . < m ℓℓ <
111 GeV | p ℓ T | >
20 GeV , | y ℓ | < . d σ / dp J T [ pb / G e V ] p JT CMSPYTHIA-8 p+p − − − γ +jet, √ s = 8 TeVR = 0 . , p JT >
30 GeV | y J | < . , | y γ | < . d σ / dp γ T [ pb / G e V ] p γ T CMSPYTHIA-8 p+p
FIG. 1. Comparison between Pythia 8 simulations and CMS measurements of V+jet production in p+p collisions at the LHC.Left: the Z +jet differential cross section at √ s = 7 TeV as a function of p JT . Right: the isolated photon+jet differential crosssection at √ s = 8 TeV as a function of p γT . The blue curves are from Pythia 8 simulations, the red data points are from theCMS collaboration [6, 7]. . . . . . , √ s = 5 .
02 TeV | y J | < . , p ZT >
60 GeV F r a c t i o n s p JT q + ¯ qq (¯ q )+g . . . . . γ + jet , √ s = 5 .
02 TeVp γ T >
60 GeV F r a c t i o n s p JT q + ¯ qq (¯ q )+g FIG. 2. The fractional contributions of different subprocesses to the Z +jet (left) and isolated- γ +jet (right) production crosssections in p+p collisions at √ s = 5 .
02 TeV. Kinematical cuts are implemented in our simulations as in CMS measurements,see Ref. [30] for Z +jet and Ref. [25] for isolated- γ +jet. production is dominated by q (¯ q ) + g → Z + q (¯ q ) channel (around 80%) for a wide p T range. In other words, theproduced jet predominantly originates from a light quark. The fraction for γ +jet production behaves similarly to thecase of Z +jet production, with even higher fractions from the q (¯ q ) + g → γ + q (¯ q ) channel. This implies that inheavy ion collisions at LHC energies, the medium modification of V+jet production is dominated by quark energyloss. We will present the detailed discussions about the medium effects on V+jet production in the next section. III. MODIFICATION OF TAGGED JET PRODUCTION IN DENSE QCD MATTER
In the presence of dense QCD matter, such as the QGP created in heavy-ion collisions, the vacuum parton showeris modified. Early investigations focused on non-Abelian energy loss processes [31–36]. The soft gluon emission limitwas subsequently relaxed to allow for a unified description of parton branching processes [37, 38]. In addition toradiative processes, collisional energy loss has also attracted a lot of attention [39–44] and was found to play a moresignificant role for lower parton energies.At present, the application of full in-medium splitting functions [45, 46] has not been combined with collisionalenergy loss processes. For this reason, we here follow the soft gluon emission radiative energy loss approximation.The benefit of this approach is that it allows us to consider multiple emissions. For a given impact parameter | b ⊥ | ,taken along the x -axis in the transverse plane of nucleus-nucleus collisions, we evaluate the cross sections as follows dσ AA ( | b ⊥ | ) dp VT dp JT = (cid:90) d s ⊥ T A (cid:18) s ⊥ − b ⊥ (cid:19) T A (cid:18) s ⊥ + b ⊥ (cid:19) (cid:88) q,g (cid:90) d(cid:15) P q,g ( (cid:15) ; s ⊥ , | b ⊥ | )1 − f loss q,g ( R ; s ⊥ , | b ⊥ | ) (cid:15) × dσ NNq,g (cid:0) p VT , p JT / { − f loss q,g ( R ; s ⊥ , | b ⊥ | ) (cid:15) } (cid:1) dp JT dp VT , (1)Let us now discuss Eq. (1). Hard processes in heavy ion collisions follow a binary collision density distribu-tion in the transverse plane at position s ⊥ . This means that the point-like large Q scattering is distributed ∝ T A ( s ⊥ − b ⊥ / T A ( s ⊥ + b ⊥ / T A ( s ⊥ ) = (cid:82) ∞−∞ ρ A ( s ⊥ , z ) dz . In our calculation we use an optical Glaubermodel and inelastic nucleon-nucleon scattering cross sections σ in = 70 mb to obtain average number of binary collisionsat √ s NN = 5 .
02 TeV.In heavy ion collisions a fraction (cid:15) of the energy of the parent parton can be redistributed through medium-induced bremsstrahlung. This process is independent on whether a jet is reconstructed or not, but reflects insteadthe parton energy, color charge, path length and medium properties dependence of the non-Abelian bremsstrahlung.The probability distribution P q,g ( (cid:15) ) of this energy fraction satisfies the following properties (cid:90) P q,g ( (cid:15) ) d(cid:15) = 1 , (cid:90) (cid:15)P q,g ( (cid:15) ) d(cid:15) = (cid:104) ∆ E rad q,g (cid:105) E q,g , (2)for every jet energy and every transverse position s ⊥ at a given impact parameter. To calculate this probability, wefirst need to evaluate the medium-induced gluon radiative spectrum dN gq,g ( ω, r ) dωdr ∝ C R α s (cid:90) ∞ d ∆ z λ g (∆ z ) (cid:20)(cid:90) d q (cid:18) σ el (∆ z ) dσ el (∆ z ) d q − δ ( q ) (cid:19)(cid:21) × k · qk ( k − q ) (cid:26) − cos (cid:20) ( k − q ) ω ∆ z (cid:21)(cid:27) (3)of parent quarks and gluons. Here, ω and r are the energy and angle of the radiated gluon and for small angles | k | = ωr . This calculation is performed to first order in opacity and the integral over ∆ z is along the path of the jetpropagation through the QGP medium from the hard collision point. In the soft gluon emission limit only the gluonscattering length λ g plays a role and quarks and gluons lose energy strictly proportional to their squared color charge.The Casimir C R in Eq. (3) is C F = 4 / C A = 3 for parent gluons. The momentum transfers q between the jet and the medium are distributed according to a normalized differential elastic scattering cross section,including a unitarizing forward scattering contribution.The spectrum is first averaged over the collision geometry, see for example the first line of Eq. (1). In the QGP weinclude an effective gluon mass via k → k + µ D (∆ z ). In this evaluation the exact leading power and sub-leadinglogarithmic dependence in the path length, density and coupling g between the jet and the medium is retained. Inthe gluon emission vertex the strong coupling is taken to run with the transverse gluon mass. In the application ofEq. (1) the point-by-point in collision geometry radiative gluon spectrum is unfolded to leading power in the pathlength, coupling g and gluon density, which goes as ∝ g (cid:82) d ∆ z ∆ z ρ g ( s ⊥ + n ⊥ ∆ z, τ + ∆ z ). Here n is the directionof jet propagation and we take the medium formation time τ = 0 . E we can then obtain dN gq,g ( ω ) dω = (cid:90) R max dr dN g ( ω, r ) dωdr , (cid:104) N gq,g (cid:105) = (cid:90) E dω dN g ( ω ) dω . (4)In Eq. (4) R max (cid:29) > R is a large radius chosen to capture the parton shower. In our calculation we use R max = 2.In the Poisson approximation the probability density for fractional energy loss (cid:15) = (cid:80) i ω i /E can be obtained as follows P q,g ( (cid:15) ) = ∞ (cid:88) n =0 P nq,g ( (cid:15) ) , P q,g ( (cid:15) ) = e − (cid:104) N gq,g (cid:105) δ ( (cid:15) ) , P n +1 q,g ( (cid:15) ) = 1 n + 1 (cid:90) E dω dN gq,g ( ω ) dω P nq,g (cid:16) (cid:15) − ωE (cid:17) . (5)For inclusive and tagged hadron production, unless one focuses on the p T region below 5 GeV, the fragmentationof radiated gluons does not contribute because they are typically soft. Since jets are defined by the amount of energyreconstructed inside the jet cone of radius parameter R , the evaluation of cross sections with jets in the final statecritically depends on the determination of how much of the energy of the medium-induced parton shower actually fallsoutside of the jet [47]. We here denote this fraction by f loss q,g ( R ), suppressing all other dependencies of this quantity.Let us first concentrate only on radiative processes. In this case we have f loss q,g ( R ; rad) = (cid:32)(cid:90) R max R dr (cid:90) E dω dN gq,g ( ω, r ) dωdr (cid:33) (cid:44) (cid:32)(cid:90) R max dr (cid:90) E dω dN gq,g ( ω, r ) dωdr (cid:33) . (6)The radiative out-of-cone energy loss is purely determined by the wide-angle medium-induced radiation pattern.Collisional interactions take energy away from the jet through the excitation of the QGP medium and dissipation ofthe energy away from the collision axis. The amplification of the collisional energy loss effects comes from the multipleemitted gluons [48]. In our simulation we assume that all of the energy is taken away from the jet. This is justifiedbecause we consider jets of small radius R (cid:28)
1, whereas Mach cones shockwaves propagate at angles θ M = arcsin c s .Thus, taking c s ≈ /
3, we find θ M ∼ (cid:104) ω q,g (cid:105) = (cid:104) ∆ E q,g (cid:105) / (cid:104) N gq,g (cid:105) . Parametrically, thecollisional energy loss rate to leading logarithmic accuracy goes as d ∆ E coll /d ∆ z ∝ C R g µ D ln( E/µ D ). In Ref. [48]we set a simulation of the collisional energy loss of the medium-induced shower as the parent parton propagatesthrough the medium and showers off gluons. The average number of gluons, rounded to an integer number, weredistributed along the path of jet propagation at positions z i and the net collisional energy loss obtained. Since thesofter medium-induced gluons thermalize first, for later convenience we can express this total collisional energy lossas an integral over the spectrum of the medium induced gluons∆ E coll q,g (tot . ) = N tot . partons q,g (cid:88) i =1 (cid:90) ∞ z i d ∆ E coll i d ∆ z d ∆ z , ∆ E coll q,g (tot . ) = (cid:90) ω min dω (cid:90) R max dr ω dN gq,g ( ω, r ) dωdr . (7)The collisional energy loss that Eq. (7) refers to is the one of the full medium induced parton shower. From theperspective of reconstructed jets, however, only the collisional energy loss of the medium-induced parton shower thatfalls inside the jet cone of radius R will modify the observed cross sections. Thus, when collisional energy losses areincluded the out-of-cone energy fraction of the medium-induced shower is f loss q,g ( R ; rad + coll) = 1 − (cid:32)(cid:90) R dr (cid:90) Eω min dω dN gq,g ( ω, r ) dωdr (cid:33) (cid:44) (cid:32)(cid:90) R max dr (cid:90) E dω dN gq,g ( ω, r ) dωdr (cid:33) . (8)Clearly, the expression above reduces to Eq. (6) when ω min = 0. This concludes the discussion of Eq. (1). IV. PHENOMENOLOGICAL RESULTS
In this section we present our phenomenological results and provide detailed comparison with the most recentexperimental measurements for the isolated γ -tagged and Z boson-tagged jet production in Pb+Pb collisions at √ s NN = 5 .
02 TeV at the LHC.In the absence of in-medium interactions one expects, to leading order in perturbative QCD, that the transversemomentum of the vector boson is balanced by the transverse momentum of the jet, p VT = p JT . Next-to-leading orderprocesses, and the development of parton showers in general, break this equality. Jet reconstruction algorithms,jet radius reconstruction choice, experimental cuts, and detector resolution effects can all affect the exact differentialdistribution of dσ/dp VT dp JT . Still, the downshift of this distribution to smaller values of p JT in general or the downshift ofthe peak in x JV = p JT /p VT space are currently the best proxies for jet energy loss. This so-called transverse momentumimbalance x JV distribution can be obtained from the double differential distribution of V+jet cross section dσd x JV = (cid:90) p J, max T p J, min T dp JT p JT x dσ ( p VT = p JT / x JV , p JT ) dp VT dp JT , (9)where p J, min T and p J, max T are matched to the desired cuts of the experimental measurements.In Fig. 3 we plot the normalized momentum imbalance distributions for the Z +jet channel (normalized by the Z boson cross section) in both p+p and Pb+Pb collisions at the LHC, and compare the calculations to the CMSmeasurements [24]. Here, the black dashed histogram shows the Pythia 8 simulation for the p+p baseline, and the . . . . . . . .
80 0 . . Z+jet √ s = 5 .
02 TeV σ Z d σ J Z d x J Z x JZ CMS p+pCMS Pb+Pb 0 − FIG. 3. The Z -tagged jet asymmetry distribution at √ s = 5 .
02 TeV in p+p (black) and Pb+Pb (red) collisions at theLHC. The jet radius parameter is R = 0 .
3, and the transverse momenta of the Z boson and the jet are p ZT >
60 GeV and p JT >
30 GeV, respectively. The p+p baseline is simulated by Pythia 8 and shown by the black dashed line. The theoreticalresults for Pb+Pb collisions with two different jet-medium coupling strength are shown by the green ( g = 2 .
0) and magenta( g = 2 .
2) histograms. The data is from the CMS collaboration [24]. black solid points represent the CMS results. One can see that the x JZ distribution from Pythia 8 simulation isnarrower than the one measured by the CMS experiment for the p+p reference. We anticipate that this is mainlydue to detector resolution effects that have not been unfolded in the data analysis . The results of our theoreticalcalculations in Pb+Pb collisions are shown in green and magenta histograms, which correspond to jet-medium couplingstrengths g = 2 . g = 2 .
2, respectively. These values have worked well in describing the single inclusive hadron[49, 50], heavy flavor mesons [51], and jet suppression data [46] at the LHC. In the implementation of energy losseffects, we have included both medium-induced radiative energy loss and energy dissipation of parton showers throughcollisional interactions between the jet and the medium, detailed description of these two energy loss effects can befound in the last section. By comparing Pb+Pb to p+p results, one can clearly see the downshift of x JV , as shown inFig. 3, which agrees with the data quantitatively in terms of the difference between p+p and Pb+Pb. This downshiftcan be easily explained by the nature of energy loss effects. The Z -boson escapes out of the medium unscathed, whilepart of the energy of away-side parton shower is redistributed outside of the jet cone. This reduces the jet transversemomentum and results in the downshift of the x JV distribution in Pb+Pb collisions.To further quantify the downshift of the x JV distribution, we define the mean value of x JV , (cid:104) x JV (cid:105) = (cid:18)(cid:90) d x JV x JV dσd x JV (cid:19)(cid:30) (cid:18)(cid:90) d x JV dσd x JV (cid:19) . (10)In Table I we show the difference for (cid:104) x JV (cid:105) in p+p and Pb+Pb collisions, i.e.,∆ (cid:104) x JV (cid:105) = (cid:104) x JV (cid:105) pp − (cid:104) x JV (cid:105) PbPb . (11)The positive values of ∆ (cid:104) x JV (cid:105) represent downshifts of the x JV distribution, and they are consistent with the exper-imental data within the measurement uncertainties for different p ZT cuts. From our theoretical results, we can seethe p ZT cut dependence of ∆ (cid:104) x JV (cid:105) , it gets larger with the increase of p ZT cut. However, this can’t be clearly identifiedwithin the current experimental error bars.We also evaluated the cross section for isolated- γ -tagged jet production in p+p and Pb+Pb collisions at the LHC.The comparisons to CMS and ATLAS measurements are shown in Figs. 4 and 5, respectively. Notice that the recoiljet is reconstructed with the anti- k T algorithm with R = 0 . − − J γ distributions in p+p and Pb+Pb are quite compatible with what is seen in experimental data. One exception isthat we didn’t see as significant nuclear modifications in semi-central (30 − (cid:104) x J γ (cid:105) and the numerical values are given in Table II for By applying the same smearing functions, as those that experiments apply to Monte Carlo simulations, to our calculated 3-D p T distributions for p+p and Pb+Pb collisions, we expect to get broader x JZ distributions which would bring the curves for both p+p andPb+Pb closer to the data points. TABLE I. Theoretical results for the difference of the average x JZ between p+p and Pb+Pb central collisions (0 − √ s = 5 .
02 TeV, the transverse momentum cut for the recoil jet is p JT >
30 GeV.∆ (cid:104) x JZ (cid:105) p ZT (GeV) 40 −
50 50 −
60 60 −
80 80 − ± ± ± ± g = 2 . g = 2 . . . . . . . . .
80 0 . . γ + jet √ s = 5 .
02 TeV0 − σ γ d σ J γ d x J γ x J γ CMS p+p prel.CMS Pb+Pb prel. 0 − . . . . . . . .
80 0 . . γ + jet √ s = 5 .
02 TeV30 − σ γ d σ J γ d x J γ x J γ CMS p+p prel.CMS Pb+Pb prel. 30 − FIG. 4. The isolated photon-tagged jet asymmetry distributions are shown and compared to CMS data in central (left)and semi-central (right) collisions [25]. The transverse momenta for the isolated photon and the jet are p γT >
60 GeV and p JT >
30 GeV, respectively. The jet radius parameter is R = 0 .
3. The p+p baseline, simulated by Pythia 8, is shown in theblack dashed line. The theoretical results for Pb+Pb collisions with two different jet-medium coupling strengths are shown bygreen ( g = 2 .
0) and magenta ( g = 2 .
2) lines. . . . . . . . .
80 0 . . γ + jet √ s = 5 .
02 TeV0 − σ γ d σ J γ d x J γ x J γ ATLAS p+p prel.ATLAS Pb+Pb prel. 0 − . . . . . . . .
80 0 . . γ + jet √ s = 5 .
02 TeV30 − σ γ d σ J γ d x J γ x J γ ATLAS p+p prel.ATLAS Pb+Pb prel. 30 − FIG. 5. Same as in Fig. 4, but for comparison to ATLAS data with jet radius R = 0 . different cuts on p γT . We see similar behavior in the x J γ distribution for isolated γ +jet production as in the x JZ distribution for Z +jet production. This is expected, as both processes are dominated by Compton scattering, whichleads to similar energy loss effects.Another classical observable to quantify nuclear modification effects in V+jet systems is I AA , which is defined asratio of the tagged differential cross section in A+A collisions to the binary collision scaled p+p result,I AA = 1 (cid:104) N bin (cid:105) dσ AA [ p VT ] dp JT (cid:30) dσ pp [ p VT ] dp JT , (12) TABLE II. Theoretical results for the difference of averaged x J γ between p+p and Pb+Pb central collisions (0 − √ s = 5 .
02 TeV, the transverse momentum cuts for the recoil jet is p JT >
30 GeV.∆ (cid:104) x J γ (cid:105) p γT (GeV) 40 −
50 50 −
60 60 −
80 80 −
100 100 − ± ± ± ± ± g = 2 . g = 2 . . .
52 50 100 150 200 250 γ + jet , √ s = 5 .
02 TeVR = 0 . , | y J | < . , | y γ | < . < p γ T <
50 GeV
50 100 150 200 250 < p γ T <
60 GeV
50 100 150 200 250 < p γ T <
80 GeV
50 100 150 200 250 < p γ T <
100 GeV I AA p JT (GeV) CMS prel. 0-30% p JT (GeV) Rad. E-loss g=2.0Rad. and Coll. E-loss g=2.0Rad. E-loss g=2.2Rad. and Coll. E-loss g=2.2 p JT (GeV) p JT (GeV) FIG. 6. The transverse momentum cuts dependence of I AA are shown comparing to CMS data. We have chosen four differentsetups of energy loss effects: with and without collisional energy loss for both g = 2 . g = 2 . where (cid:104) N bin (cid:105) is the average number of binary nucleon-nucleon collisions for a given centrality. In this notation weimply that the transverse momentum of the vector boson is integrated in the appropriate range dσ [ p VT ] dp JT ≡ (cid:90) p V,maxT p V,minT dσdp VT dp JT . (13)Our theoretical calculations for I AA in isolated γ +jet production in 0 −
30% Pb+Pb collisions are shown in Fig. 6, andcompared to CMS experimental data. We find that our results agree with data for a wide kinematic range. In each p γT window, the energy loss effects are shown in four curves with different colors, which correspond to a combinationof two different jet-medium coupling strength, g = 2 . g = 2 .
2, as well as the situations where we either includeor exclude the collisional energy loss effects in our calculations. As one has expected, the energy loss effect is morepronounced when we include collisional energy loss and a larger jet-medium coupling strength. One can see clearly inFig. 6 that there is a sensitive kinematical dependence of I AA . The largest suppression is observed along the diagonalregion of the transverse momenta of the trigger γ and the recoil jet: p γT ≈ p JT . This arises from the steeper fallingcross section in the transverse momenta diagonal region. As we expect, the cross section in the region p JT > p γT issuppressed, and enhanced in p JT < p γT . This is characteristic of in-medium tagged-jet dynamics. We further presenttheoretical predictions on the nuclear modification factor I AA for Z +jet in Fig. 7, which show similar p ZT and p JT dependence as those observed in γ +jet process.Taking into account the observables that we have investigated, the x JV momentum imbalance distributions, themean x JV shift, and the tagged jet modification I AA we find that data favors coupling strengths between the jet andthe medium in the range g = 2 . g = 2 . α s = 0 .
32 to α s = 0 .
39 at tree level). While theasymmetry distributions prefer the larger values of the coupling strength g , the I AA distributions prefer smaller valuesof g . Due to the complexity of the physics involved in heavy ion collisions, every theoretical calculation is bound tohave model dependence. However, the amount of out-of-cone energy redistribution due to radiative and collisionalprocesses needed for modification comparable to experimental measurements is relatively robust since it only dependson the differential transverse momentum distribution of the recoiling jet and the proper inclusion of the Jacobianfactor that accounts for the energy loss in Eq. (1). We present in Table III the results for the mean out-of-cone energyloss of prompt quark-initiated and prompt gluon-initiated 100 GeV jets of small radius R = 0 . . .
52 40 50 60 70 80 90 100 110 120
Z + jet , √ s = 5 .
02 TeVR = 0 . , | y J | < . < p ZT <
50 GeV
40 50 60 70 80 90 100 110 120 < p ZT <
60 GeV
40 50 60 70 80 90 100 110 120 < p ZT <
80 GeV
40 50 60 70 80 90 100 110 120 < p ZT <
100 GeV I AA p JT (GeV) p JT (GeV) Rad. E-loss g=2.0Rad. and Coll. E-loss g=2.0Rad. E-loss g=2.2Rad. and Coll. E-loss g=2.2 p JT (GeV) p JT (GeV) FIG. 7. The predicted transverse momentum cuts dependence of I AA for Z +jet in central (0 − √ s NN = 5 .
02 TeV. The jet radius parameter is R = 0 . R = 0 . −
10% Pb+Pb collisions at √ s NN = 5 .
02 TeV are considered. (cid:104) ∆ E out q,g (cid:105) = E jet q,g (cid:104) (cid:15) (cid:105) f loss q,g ( R )Type of E-loss Rad. g=2.0 Rad.+Col. g=2.0 Rad. g=2.2 Rad.+Col. g=2.2Prompt quark-initiated jet 7 GeV 8 GeV 10 GeV 14 GeVPrompt gluon-initiated jet 15 GeV 18 GeV 21 GeV 29 GeV Pb+Pb collisions at √ s NN = 5 .
02 TeV. One caveat that we must point out is that these numbers represent the upperlimits. The reason for that is that multi-gluon fluctuations lead to effective energy losses smaller than the mean. Wefind that radiative energy losses dominate, however collisional energy loss can be as large as 40% correction to theradiative energy loss. This effect arises from the high gluon multiplicity in the medium-induced parton shower, whichamplifies collisional energy losses. This can be clearly seen by comparing the two different couplings g between thejet and the medium. The fractional growth of the out-of-cone radiation when we include collisional energy loss islarger for g = 2 . g = 2 . (cid:104) ∆ E out q,g (cid:105) . V. CONCLUSIONS
In summary, in this paper we presented a new study of vector boson-tagged (either isolated γ or Z ) jet production inPb+Pb collisions at a center-of-mass energy per nucleon pair of 5.02 TeV. This work is timely since new experimentalresults on these final states from the LHC experiments are becoming available. Within the traditional energy lossapproach, by including both collisional and radiative energy loss effects, we evaluated several experimentally relevantobservables: the so-called transverse momentum imbalance x JV distribution modification in going from p+p to Pb+Pbcollisions, the related mean momentum imbalance shift ∆ (cid:104) x JV (cid:105) , and the tagged jet nuclear modification factor I AA .While some tension remains between the baseline Pythia simulations and the experimental measurements, which atpresent are not unfolded for detector resolution effects, we found good agreement between the theoretical simulationsof the modification of these observables for coupling strengths between the jet and the medium g = 2 . g = 2 . γ -tagged and Z -tagged jets are very effective in selectingprompt quark-initiated jets and can provide valuable information on the flavor dependence of parton energy loss. Wefurther found that while for small radius jets radiative energy loss gives the dominant contribution, collisional energyloss may play a significant role, especially for larger coupling strengths of the interaction between the jet and themedium. We conclude by emphasizing that the substructure modification of γ -tagged and Z -tagged jets can differ0quite substantially from the substructure modification of inclusive jets and future experimental measurements of suchobservables can add significantly to our understanding of in-medium QCD dynamics. ACKNOWLEDGMENTS
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