Research Article A Study of Transverse Momentum...
Transcript of Research Article A Study of Transverse Momentum...
Research ArticleA Study of Transverse Momentum Distributions ofJets Produced in ๐-๐, ๐-๐, ๐-Au, Au-Au, and Pb-Pb Collisions atHigh Energies
Hua-Rong Wei and Fu-Hu Liu
Institute of Theoretical Physics, Shanxi University, Taiyuan, Shanxi 030006, China
Correspondence should be addressed to Fu-Hu Liu; [email protected]
Received 14 December 2014; Accepted 24 April 2015
Academic Editor: Elias C. Vagenas
Copyright ยฉ 2015 H.-R. Wei and F.-H. Liu. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited. The publication of this article was funded by SCOAP3.
The transverse momentum distributions of jets produced in ๐-๐, ๐-๐, ๐-Au, Au-Au, and Pb-Pb collisions at high energies withdifferent selected conditions are analyzed by using a multisource thermal model. The multicomponent (mostly two-component)Erlang distribution used in our description is in good agreement with the experimental data measured by the STAR, D0, CDF II,ALICE, ATLAS, andCMSCollaborations. Related parameters are extracted from the transversemomentumdistributions and someinformation on different interacting systems is obtained. In the two-component Erlang distribution, the first component has usuallytwo or more sources which are contributed by strong scattering interactions between two quarks or more quarks and gluons, whilethe second component has mostly two sources which are contributed by harder head-on scattering between two quarks.
1. Introduction
As a new state of matter, quark-gluon plasma (QGP) [1] isdifferent from common plasmas. Generally, the QGP cannotbe observed directly because its creation needs an extremelyhigh temperature and density. In order to study the propertiesof the QGP and the mechanisms of parton interactions,a lot of experiments of high energy heavy ion collisionshave been performed. Particularly, a high density and hightemperature location is formed at the Relativistic Heavy IonCollider (RHIC) and the Large Hadron Collider (LHC) tocreate the QGP and to produce multiple final-state particles.By investigating and analyzing these particles, one can obtainsome information on the QGP. Hadron jets are one typeof final-state particles. People study jets production processto learn the properties of the QGP and the mechanisms ofparton interactions both in theories and in experiments [2โ4].
The transverse momenta of particles carry importantinformation about the dynamics of particle productionsand the evolution process of interacting system formed innucleus-nucleus collisions [5]. The transverse momentum
(๐๐) distributions of final-state particles reflect the state of
the interacting system at the kinetic stage of freeze-out, whenhadrons are no longer interaction and their momenta donot change [6]. Comparing to the low-๐
๐hadrons which are
originated from strong interactions among gluons and seaquarks, high-๐
๐hadrons are produced due to harder head-
on scattering between valent quarks. To analyze high-๐๐
spectra of final-state particles is then important in studyingthe mechanisms of high energy collisions. In addition, themean transverse momentum of particles, which served as aprobe for the equation of state of the hadronic matter [7], canpartly reflect the effective temperature of interacting systemand the transverse excitation degree of emission source inhigh energy collisions [8].
Due to the hard-scattering of incident partons, partonicjets (including quark and gluon jets) materialize very earlyduring the collisions, which result in plenty of outgoinghigh-๐
๐partons. Soon afterwards, a parton fragments into
a leading hadron, a large number of which gather into acone of hadronic jets which are detected by various detectorssuch as STAR, D0, CDF II, ALICE, ATLAS, and CMS [9โ36].We are interested in analyzing the transversemomentum
Hindawi Publishing CorporationAdvances in High Energy PhysicsVolume 2015, Article ID 263135, 17 pageshttp://dx.doi.org/10.1155/2015/263135
2 Advances in High Energy Physics
distributions of various jets because they can reflect someinformation of early collisions of partons.
In this paper, we use the multicomponent (mostly two-component) Erlang distribution to describe the transversemomentum distributions of jets produced in ๐-๐, ๐-๐, ๐-Au, Au-Au, and Pb-Pb collisions at high energies, with theframework of a multisource thermal model [37โ39]. Thequoted data are at five energies, 0.2, 1.96, 2.76, 7, and 8 TeV pernucleon pair [9โ36], and were selected in different detectionchannels according to different conditions of cone radius,integrated luminosity, pseudorapidity (rapidity) range, andcentrality interval. The calculations are performed by usingthe Monte Carlo method.
2. The Model and Formulism
According to the multisource thermal model [37โ39], weassume that many emission sources are formed in highenergy collisions. These emission sources can be separatedinto a few groups due to different interacting mechanismsin the collisions and different event samples in experimentalmeasurements. Each emission source in the same grouphas the same transverse excitation degree, and the group isassumed to stay at a local equilibrium state. The total resultof a multigroup emission process contributes to the finaldistribution.
The transverse momentum distribution generated inthermodynamic system obeys an exponential distribution,which is the contribution of one emission source. We have
๐๐๐(๐๐ก๐๐) =
1
โจ๐๐ก๐๐โฉexp[โ
๐๐ก๐๐
โจ๐๐ก๐๐โฉ] , (1)
where ๐๐ก๐๐
is the transverse momentum contributed by the๐th source in the ๐th group and โจ๐
๐ก๐๐โฉ is the mean value of
different ๐๐ก๐๐. The folding result of ๐
๐sources in a given (the
๐th) group is an Erlang distribution; that is,
๐๐(๐๐) =
๐๐๐โ1
๐
(๐๐โ 1)! โจ๐
๐ก๐๐โฉ๐๐
exp[โ๐๐
โจ๐๐ก๐๐โฉ] , (2)
where ๐๐is the transverse momentum contributed by the๐
๐
sources. If the number of groups is ๐, the total contribution isthe multicomponent Erlang distribution expressed as
๐ (๐๐) =
๐
โ
๐=1
๐๐๐๐(๐๐) , (3)
where ๐๐is the weight contributed by the ๐th group, which
obeys the normalization โ๐๐= 1. To describe transverse
excitation degree of emission source in the present work, wedefine a new effective temperature parameter:
๐ โก
๐
โ
๐=1
๐๐โจ๐๐ก๐๐โฉ , (4)
which uses the inverse slope parameter โจ๐๐ก๐๐โฉ.
We will see from the following section that ๐๐distribu-
tions of jets analyzed in the present work can be mostly fittedby the two-component Erlang distribution. Generally, thefirst component corresponds to strong scattering interactionswhere two quarks or more quarks and gluons take part in theprocess, and the second one corresponds to harder head-onscattering where two quarks take part in the process. All thecalculations on ๐
๐distributions are performed by using the
Monte Carlo method. For the first component, we have
๐๐= โ โจ๐
๐ก๐1โฉ
๐1
โ
๐=1
ln๐ ๐, (5)
and, for the second component, we have
๐๐= โ โจ๐
๐ก๐2โฉ
๐2
โ
๐=1
ln๐ ๐, (6)
where ๐ ๐denote random numbers in [0, 1]. The statistics
based on weights ๐1and ๐
2(= 1 โ ๐
1) will give ๐
๐distri-
butions. In the case of using the three- or multicomponentErlang distribution, the calculation process of the MonteCarlo method is similar.
We would like to point out that the new effective temper-ature parameter defined in (4) is not the real temperature ofjets production source but the mean transverse momentumextracted from the model or experimental data. The realtemperature of jets production source should be a reflectionof purely thermal motion in the source. The effect of flowor blast wave should be excluded in the extraction of sourcetemperature. Generally, the effective temperature parameteris extracted from the transverse momentum distribution.It includes thermal motion and flow effect and should begreater than the source temperature. As the mean transversemomentum, the new effective temperature parameter isindependent of models.
3. Comparison with Experimental Data
Figure 1 presents ๐๐distributions of high tower (HT) trigger
jets in ๐-๐ collision (a), HT trigger jets in 0โ20% centralAu-Au collisions (b), jets from ๐-Au collisions (c), anduncorrected jets in ๐-๐ collision (d) at center-of-mass energyโ๐ ๐๐ = 0.2TeV, where for ๐-๐ collision โ๐ ๐๐ can besimplified as โ๐ . The symbols represent the experimentaldata of the STAR Collaboration [9โ11]. In Figures 1(a) and1(b), jet events were selected by an online HT trigger usingthe anti-๐
๐algorithm [12] with a cone radius ๐ = 0.4,
pseudorapidity range |๐| < 0.6, and ๐๐
> 2.0GeV/๐.The displayed uncertainty of the data is only systematicuncertainty. The data from Figure 1(c) were recorded duringRHIC run 8 (2007-2008) with ๐ = 0.4 and |๐| < 0.55.The error bars represent systematic uncertainty and statisticaluncertainty. Raw jets in Figure 1(d) were obtained under thecondition of ๐ = 0.7, โ0.7 < ๐ < 0.9, and jets ๐
๐>
5.0GeV/๐. In the figure, some error bars are not visible dueto their small values. In this case we regard the marker sizeas the errors in the calculation. The curves are our resultscalculated with the two-component Erlang distribution in
Advances in High Energy Physics 3
100
10โ2
10โ4
10 20 30 40
Reconstructed jet pT (GeV/c)
pjet,recT is calculated
only from constituentswith pT > 2GeV/c
p-p HT
(1/N
jet)(dN
jet/dp
jet,r
ecT
) ((G
eV/c)โ
1)
โsNN = 0.2TeV
(a)
100
10โ2
10โ4
10 20 30 40
pjet,recT is calculated
only from constituentswith pT > 2GeV/c
Au-Au HT, 0โ20%
Reconstructed jet pT (GeV/c)
(1/N
jet)(dN
jet/dp
jet,r
ecT
) ((G
eV/c)โ
1)
(b)
d-Auanti-kT, R = 0.4
|๐| < 0.55
15 20 25 30
Jet pT (GeV/c)
10โ5
10โ6
10โ7
(1/2๐N
evt)(d2N/dpTd๐
) ((G
eV/c)โ
1)
(c)
106
104
102
p-p
10 20 30 40 50
Uncorrected jet pT (GeV/c)
Cou
nts/
GeV
/c
(d)
Figure 1: Transverse momentum spectra of HT trigger jets in ๐-๐ collision (a), HT trigger jets in 0โ20% central Au-Au collisions (b), jetsfrom ๐-Au collisions (c), and uncorrected jets in ๐-๐ collision (d) at โ๐ ๐๐ = 0.2TeV. The symbols represent the experimental data of theSTAR Collaboration [9โ11] and the curves are our results calculated by using the two-component Erlang distribution in the framework of themultisource thermal model. All the calculations are performed by the Monte Carlo method.
the framework of the multisource thermal model by usingthe Monte Carlo method. The values of free parameters,defined effective temperature parameter ๐, and ๐2 per degreeof freedom (๐2/dof) or ๐2 are shown in Table 1, where ๐2 isused in the case of the number of data points being less than6 which is the number of free parameters and normalizationconstants. One can see that the multisource thermal modeldescribes the experimental data of the considered jets in๐-๐, ๐-Au, and Au-Au collisions at โ๐ ๐๐ = 0.2TeV. Thetransverse momentum distributions of mentioned jets areshown to obey the two-component Erlang distribution. ForFigures 1(a), 1(b), and 1(c), all the source numbers of thesecond groups are 2 and the values of mean excitation degree(defined effective temperature parameter) ๐ extracted fromthe spectra are close to each other. For the raw jets inFigure 1(d), the background interference leads to the numberof emission sources to increase and the mean excitationdegree to decrease.
Figure 2 shows ๐๐spectra of the leading jets (a)โ(c) and
all jets (d) that satisfy the event selection described below,
produced in ๐-๐ collision at โ๐ = 1.96TeV. The symbolsin (a) and (b) represent the experimental data collected bythe D0 Collaboration in run II with an integrated luminosityof 9.7fbโ1 [13], while (c) represents the same as (a) and(b) but for an integrated luminosity of 3.7fbโ1 [14], and (d)represents the experimental data collected by the CDF IICollaboration with a cone size of ๐ = 0.7, pseudorapidityrange of 0.1 < |๐| < 0.7, as well as an integrated luminosityof 6fbโ1 [15]. The data come from the ๐ bosons decaying topairs of leptons ๐๐ (a) or ๐๐ (b). The jets in Figure 2(c) arerequired to satisfy ๐
๐> 20GeV/๐ and rapidity |๐ฆ| < 3.2
with a cone radius ๐ = 0.5. The error bars in (a) and (b)represent the sum of statistical and systematic uncertainties,and those in (c) and (d) represent statistical and systematicuncertainties, respectively. In the figure, for the points withinvisible error bars, we measure the marker size as the errorsused in the calculation. The curves are our results calculatedwith the two-component Erlang distribution. The values offree parameters, defined ๐, and ๐2/dof in the calculation aregiven in Table 1. One can see that the two-component Erlang
4 Advances in High Energy Physics
Table 1: Values of free parameters, defined ๐, and ๐2/dof (๐2) corresponding to the curves in the figures, where ๐2 is given in bracket if thenumber of data points is less than 6 which is the number of free parameters and normalization constants. The errors of ๐
๐are estimated to
be 0.
Figure, type ๐1
๐๐ก๐1
(GeV/๐) ๐1
๐2
๐๐ก๐2
(GeV/๐) ๐ (GeV) ๐2/dof (๐2)
Figure 1(a) 2 1.70 ยฑ 0.20 0.860 ยฑ 0.030 2 3.25 ยฑ 0.10 1.917 ยฑ 0.205 0.328Figure 1(b) 2 1.60 ยฑ 0.20 0.900 ยฑ 0.030 2 3.55 ยฑ 0.20 1.795 ยฑ 0.215 0.189Figure 1(c) 2 1.82 ยฑ 0.07 0.994 ยฑ 0.002 2 5.00 ยฑ 0.50 1.839 ยฑ 0.070 0.038Figure 1(d) 11 1.25 ยฑ 0.05 0.890 ยฑ 0.020 8 2.47 ยฑ 0.05 1.384 ยฑ 0.071 (0.084)Figure 2(a) 2 8.80 ยฑ 0.80 0.830 ยฑ 0.030 2 22.80 ยฑ 1.50 11.180 ยฑ 1.022 0.132Figure 2(b) 2 8.80 ยฑ 0.70 0.840 ยฑ 0.030 2 23.00 ยฑ 1.50 11.072 ยฑ 0.974 0.191Figure 2(c) 2 10.20 ยฑ 1.00 0.900 ยฑ 0.030 2 26.60 ยฑ 2.00 11.840 ยฑ 1.257 0.393Figure 2(d) 2 12.00 ยฑ 8.00 0.996 ยฑ 0.001 2 34.00 ยฑ 0.50 12.088 ยฑ 7.968 0.186Figure 3(a) 2 5.20 ยฑ 0.04 0.900 ยฑ 0.020 2 11.20 ยฑ 0.40 5.800 ยฑ 0.253 0.044Figure 3(b) 2 5.50 ยฑ 0.03 0.950 ยฑ 0.010 2 12.70 ยฑ 0.40 5.860 ยฑ 0.143 0.097Figure 3(c) 2 5.50 ยฑ 0.02 0.950 ยฑ 0.010 2 12.80 ยฑ 0.50 5.865 ยฑ 0.143 0.011Figure 3(d) 2 5.60 ยฑ 0.03 0.960 ยฑ 0.010 2 12.70 ยฑ 0.80 5.884 ยฑ 0.145 0.054Figure 4(a), 1st 2 13.00 ยฑ 2.00 0.620 ยฑ 0.080 2 40.00 ยฑ 5.00 23.260 ยฑ 4.058 0.100Figure 4(a), 2nd 2 11.50 ยฑ 1.00 0.850 ยฑ 0.050 2 28.00 ยฑ 5.00 13.975 ยฑ 1.891 0.185Figure 4(b), lepton 2 28.00 ยฑ 2.00 0.907 ยฑ 0.010 2 100.00 ยฑ 30.00 30.160 ยฑ 2.377 0.019Figure 4(b), dilepton 2 25.00 ยฑ 2.00 0.850 ยฑ 0.050 2 47.00 ยฑ 5.00 28.300 ยฑ 3.246 0.055Figure 4(c), inclusive jets 2 42.00 ยฑ 2.00 0.998 ยฑ 0.001 2 115.00 ยฑ 10.00 42.164 ยฑ 2.000 0.619Figure 4(c), split jets 2 34.00 ยฑ 3.00 0.994 ยฑ 0.003 2 87.00 ยฑ 10.00 34.318 ยฑ 2.996 3.769Figure 4(d), lepton 2 21.90 ยฑ 2.00 0.890 ยฑ 0.090 2 40.50 ยฑ 10.00 23.946 ยฑ 4.642 0.095Figure 4(d), dilepton 2 22.50 ยฑ 2.00 0.880 ยฑ 0.100 2 47.00 ยฑ 10.00 25.440 ยฑ 5.629 0.392Figure 5(a) 2 13.50 ยฑ 1.00 0.910 ยฑ 0.050 2 50.00 ยฑ 20.00 16.785 ยฑ 3.282 0.303Figure 5(b) 2 11.20 ยฑ 1.00 0.820 ยฑ 0.100 2 28.00 ยฑ 10.00 14.224 ยฑ 3.606 0.312Figure 5(c) 2 18.00 ยฑ 2.00 0.810 ยฑ 0.100 2 29.00 ยฑ 5.00 20.090 ยฑ 3.896 0.067Figure 6(a) 4 12.70 ยฑ 0.90 0.900 ยฑ 0.020 2 44.00 ยฑ 4.00 15.830 ยฑ 1.286 0.187Figure 6(b) 6 11.50 ยฑ 1.00 0.710 ยฑ 0.100 2 80.00 ยฑ 30.00 31.365 ยฑ 11.896 0.661Figure 6(c) 4 18.80 ยฑ 1.00 0.960 ยฑ 0.010 2 92.00 ยฑ 10.00 21.728 ยฑ 1.401 0.181Figure 6(d) 5 15.20 ยฑ 0.80 0.770 ยฑ 0.080 2 42.00 ยฑ 5.00 21.364 ยฑ 3.804 0.173Figure 7, leading 7 14.00 ยฑ 1.00 0.610 ยฑ 0.050 2 58.00 ยฑ 2.00 31.160 ยฑ 3.143 (0.069)Figure 7, 2nd 7 9.60 ยฑ 0.08 0.740 ยฑ 0.050 2 42.00 ยฑ 2.00 18.024 ยฑ 2.217 (0.367)Figure 7, 3rd 7 6.10 ยฑ 0.50 0.620 ยฑ 0.050 2 23.00 ยฑ 1.00 12.522 ยฑ 1.287 (0.434)Figure 7, 4th 7 4.70 ยฑ 1.00 0.780 ยฑ 0.050 2 18.80 ยฑ 1.50 7.802 ยฑ 1.287 (0.281)Figure 7, 5th 7 4.00 ยฑ 0.70 0.820 ยฑ 0.040 2 15.00 ยฑ 1.50 5.980 ยฑ 0.888 (0.128)Figure 8(a) 5 22.00 ยฑ 2.00 0.820 ยฑ 0.030 2 82.00 ยฑ 4.00 32.800 ยฑ 3.114 0.177Figure 8(b) 6 17.60 ยฑ 1.00 0.880 ยฑ 0.030 2 79.00 ยฑ 5.00 24.968 ยฑ 2.651 0.619Figure 8(c) 5 23.00 ยฑ 3.00 0.580 ยฑ 0.050 2 81.00 ยฑ 5.00 47.360 ยฑ 5.016 0.408Figure 8(d) 6 18.00 ยฑ 1.00 0.820 ยฑ 0.040 2 100.00 ยฑ 10.00 32.760 ยฑ 4.520 0.799Figure 9(a) 4 24.90 ยฑ 2.00 0.880 ยฑ 0.040 2 89.00 ยฑ 7.00 32.592 ยฑ 4.180 1.022Figure 9(b) 6 36.50 ยฑ 1.00 0.850 ยฑ 0.030 2 132.00 ยฑ 8.00 50.825 ยฑ 4.364 0.112Figure 9(c) 6 18.50 ยฑ 1.00 0.880 ยฑ 0.050 2 120.00 ยฑ 50.00 30.680 ยฑ 8.581 0.427Figure 9(d) 6 19.10 ยฑ 1.00 0.930 ยฑ 0.030 2 160.00 ยฑ 50.00 28.963 ยฑ 6.040 0.453Figure 9(e) 7 16.00 ยฑ 1.00 0.870 ยฑ 0.050 2 109.00 ยฑ 15.00 28.090 ยฑ 5.908 0.815Figure 9(f) 9 11.60 ยฑ 1.00 0.750 ยฑ 0.050 2 180.00 ยฑ 100.00 53.700 ยฑ 26.588 0.731Figure 10(a) 9 11.00 ยฑ 0.70 0.700 ยฑ 0.070 4 41.00 ยฑ 3.00 20.000 ยฑ 3.143 0.196Figure 10(b) 9 10.90 ยฑ 0.70 0.710 ยฑ 0.050 4 40.00 ยฑ 2.00 19.339 ยฑ 2.209 0.138Figure 10(c) 5 15.20 ยฑ 2.00 0.540 ยฑ 0.100 2 69.00 ยฑ 10.00 39.948 ยฑ 8.500 0.137Figure 10(d) 5 5.80 ยฑ 1.00 0.580 ยฑ 0.100 2 26.00 ยฑ 5.00 14.284 ยฑ 3.441 0.298Figure 10(e) 2 25.30 ยฑ 2.00 0.830 ยฑ 0.030 2 61.00 ยฑ 3.00 31.369 ยฑ 2.634 0.053Figure 10(f) 2 12.50 ยฑ 0.50 0.970 ยฑ 0.003 2 47.00 ยฑ 2.00 12.877 ยฑ 0.507 0.295Figure 11(a) 4 45.80 ยฑ 4.00 0.969 ยฑ 0.010 2 118.00 ยฑ 5.00 48.038 ยฑ 4.080 0.392Figure 11(b) 6 3.00 ยฑ 0.10 0.760 ยฑ 0.020 2 19.00 ยฑ 1.00 6.840 ยฑ 0.460 0.062
Advances in High Energy Physics 5
Even
ts/5
GeV
/c
104
103
102
101
Leading jet pT (GeV/c)40 80 120 160 200
Z โ ee channel
p-p โs = 1.96TeV9.7fbโ1D0,
(a)
104
103
102
101
Leading jet pT (GeV/c)40 80 120 160 200
Even
ts/5
GeV
/c
Z โ ๐๐ channel9.7fbโ1D0,
(b)
Leading jet pT (GeV/c)
Even
ts/5
GeV
/c
105
103
101
60 120 180 240 300
3.7fbโ1D0,
(c)
Even
ts/10
GeV
/c
10โ1
10โ2
10โ3
R = 0.7, 0.1 < |๐| < 0.7
pT > 400GeV/c
420 480 540 600 660
Jets pT (GeV/c)
CDF II, 6fbโ1
(d)
Figure 2: Transverse momentum spectra for the leading jets (a)โ(c) and all the jet candidates (d) produced in ๐-๐ collision at โ๐ =1.96TeV. The symbols in Figures 2(a)โ2(c) and Figure 2(d) represent the experimental data of the D0 Collaboration [13, 14] and the CDFII Collaboration [15], respectively. The curves are our results calculated by using the two-component Erlang distribution.
distribution describes well the experimental data of the jetsproduced in๐-๐ collision atโ๐ = 1.96TeV. For the four cases,all the source numbers of the second groups are 2, and thevalues of ๐ extracted from the spectra are approximately thesame.
In Figure 3, we give charged jet ๐๐spectra produced in
Pb-Pb collisions at โ๐ ๐๐ = 2.76TeV in different centralityintervals of 0โ10% (a), 10โ30% (b), 30โ50% (c), and 50โ80%(d). The experimental data represented by the symbols weremeasured with a cone radius ๐ = 0.2, |๐| < 0.5, anti-๐๐jet algorithm [12], charged track ๐
๐> 0.15GeV/๐, and
leading charged track ๐๐> 10GeV/๐ by the ALICE Col-
laboration [16]. The error bars include the total uncertainty.The curves are our fitted results with the two-componentErlang distribution.The values of free parameters, defined ๐,and ๐2/dof in the calculation are displayed in Table 1. Oncemore, the two-component Erlang distribution describes wellthe experimental data of the charged jets produced in Pb-Pb collisions at โ๐ ๐๐ = 2.76TeV with different centralityintervals. The fitted source numbers of the second groups arealso 2, and the effective temperature parameter ๐ extracted
from the spectra slightly increases with increase of thecentrality percentage ๐ถ, or ๐ has no obvious change withincrease of ๐ถ in the error range. The figure display of thedependence of ๐ on ๐ถ will be discussed in the last part ofthis section.
Figure 4 displays jet ๐๐spectra produced in ๐-๐ collision
at โ๐ = 7TeV for different conditions. The symbols in (a)and (b) represent the experimental data recorded by the CMSCollaboration [17], and those in (c) and (d) represent theATLAS Collaboration [18, 19]. The first [the black squaresin Figure 4(a)] and the second leading jets [the red circlesin Figure 4(a)], as well as the lepton + jets channel jetswith ๐
๐> 35GeV/๐ [the black squares in Figure 4(b)]
and the dilepton channel jets with ๐๐> 30GeV/๐ [the
red circles in Figure 4(b)], were selected corresponding toa total integrated luminosity of 5.0fbโ1. In Figure 4(c), theselected data for the Cambridge-Aachen algorithm jet eventswhere the number of reconstructed primary vertices (๐PV)composed of at least five tracks is exactly one correspondingto an integrated luminosity of 2 pbโ1, ๐ = 1.2, and |๐ฆ| < 2.The jets shown by the red circles in Figure 4(c) were split and
6 Advances in High Energy Physics
(106/N
coll)
(1/N
evt)(d2N
chje
t/dpTd๐
jet)
((G
eV/c)โ
1)
100
10โ1
10โ2
10โ3
10โ4
25 50 75 100
pT,ch jet (GeV/c)
anti-kT, R = 0.2, |๐jet| < 0.5
0โ10%
Pb-Pb โsNN = 2.76 TeV
(a)
(106/N
coll)
(1/N
evt)(d2N
chje
t/dpTd๐
jet)
((G
eV/c)โ
1)
100
10โ1
10โ2
10โ3
10โ4
25 50 75 100
pT,ch jet (GeV/c)
ptrackT > 0.15GeV/c
Leading track pT > 10GeV/c10โ30%
(b)
(106/N
coll)
(1/N
evt)(d2N
chje
t/dpTd๐
jet)
((G
eV/c)โ
1)
100
10โ1
10โ2
10โ3
25 50 75 100
Charged jets
pT,ch jet (GeV/c)
30โ50%
(c)
(106/N
coll)
(1/N
evt)(d2N
chje
t/dpTd๐
jet)
((G
eV/c)โ
1)
100
10โ1
10โ2
10โ3
Charged jets
25 50 75 100
pT,ch jet (GeV/c)
50โ80%
(d)
Figure 3: Charged jet ๐๐spectra produced in Pb-Pb collisions atโ๐ ๐๐ = 2.76TeV in different centrality intervals of 0โ10% (a), 10โ30% (b),
30โ50% (c), and 50โ80% (d). The symbols represent the experimental data of the ALICE Collaboration [16] and the curves are our resultscalculated by using the two-component Erlang distribution.
filtered from those jets with ๐๐> 200GeV/๐ represented
by the black squares in the same panel. The data for ๐-quark jets (๐-jets) displayed in Figure 4(d) were collectedwith an integrated luminosity of 1.8fbโ1 for the single-leptonchannels by the black squares and for the dilepton channelsby the red circles. The error bars on the data points indicatethe statistical uncertainty in Figures 4(a)โ4(c) and systematicuncertainty in Figure 4(d). For some data points in whichthe error bars are invisible in the figure, we use the markersize instead of the real error values in our calculation. Thecurves are our fitted results by the two-component Erlangdistribution. The relevant parameter values with ๐2/dof inthe calculation are presented in Table 1. The two-componentErlang distribution with๐
2= 2 provides a good description
on the data. As can be seen, the value of ๐ extracted fromthe 1st leading jet spectra is significantly larger than thatextracted from the 2nd one. In the error range, ๐ extracted
from the single-lepton channel jet spectra is approximatelyin agreement with that from the dilepton one.
The transverse momentum distributions for the sublead-ing ๐-jets after the ๐ + 2๐-jets selection corresponding toan integrated luminosity of 5.0fbโ1, the soft-muon tagging(SMT) jets for opposite-sign and same-sign (OS-SS) eventsin ๐ + 1, 2 jets samples in electron channels with anintegrated luminosity of 4.6fbโ1, and the light-quark jetsproduced in the same condition as that in Figure 4(d) in๐-๐ collision at โ๐ = 7TeV are shown in Figures 5(a)โ5(c), respectively. The experimental data represented by thesymbols were recorded by the CMS Collaboration [20] andthe ATLAS Collaboration [19, 21]. The error bars indicate thetotal uncertainty. In Figure 5(c), the error bars of the pointsin high-๐
๐area present the marker size of the points from
[19], in which the linear coordinate is used.The curves are ourresults calculated by the two-component Erlang distribution.
Advances in High Energy Physics 7
1st leading additional reconstructed jets2nd leading additional reconstructed jets
Jets pT (GeV/c)
50 100 150 200
Jets/
10G
eV/c
103
102
101
100
10โ1
p-p โs = 7TeV
โซLdt = 5.0fbโ1
(a)
Lepton + jets combinedDilepton combined
Jets pT (GeV/c)
50 100 150 200 250
Jets/
10G
eV/c
105
103
101
โซLdt = 5.0fbโ1
(b)
Inclusive jetsSplit/filtered jets with Rqq > 0.3
Jets pT (GeV/c)200 400 600 800 1000
Cambridge-AachenR = 1.2
NPV = 1, |๐| < 2
Jets/
100
GeV
/c
104
101
10โ2
โซLdt = 2.0pbโ1
(c)
Single-lepton channelDilepton channel
b-jets pT (GeV/c)
80 160 240 320
Jets/
10G
eV/c
103
101
10โ1
โซLdt = 1.8fbโ1
(d)
Figure 4: Jet ๐๐spectra produced in ๐-๐ collision atโ๐ = 7TeV for different situations shown in the panels and text. The symbols shown in
Figures 4(a)-4(b) and Figures 4(c)-4(d) represent the experimental data of the CMS Collaboration [17] and the ATLAS Collaboration [18, 19],respectively. The curves are our modelling results.
The parameter values and the defined ๐ in the calculationare shown in Table 1 with values of ๐2/dof. One can see thatthe experimental data are in good agreement with the two-component Erlang distribution with ๐
2= 2. In the error
range, the three effective temperatures extracted from thethree distributions are approximately equal to each other.
Figure 6 shows some other jet ๐๐distributions in ๐-๐
collision at โ๐ = 7TeV. The symbols in (a)โ(d) representthe experimental data which were recorded with the ATLASdetector corresponding to an integrated luminosity of 37 pbโ1[22], the CMS detector corresponding to an integratedluminosity of 5.0fbโ1 for the leading ๐-tagged jets in the๐ + 2๐-jets sample [20], the ATLAS detector correspondingto an integrated luminosity of 4.6fbโ1 for the leading ๐-tagged jets in ๐ + jets channels [23], and the ATLAS detectorcorresponding to an integrated luminosity of 4.6fbโ1 for theleading ๐-tagged jets in ๐ + jets channels [23], respectively.
The statistical or systematic uncertainties are included inthe error bars. For some data points with no error bars, weuse the marker size as their errors in the calculation. TheMonte Carlo results calculated by using the two-componentErlang distribution are indicated by the curves, and thecorresponding parameters, defined ๐, and ๐2/dof are listedin Table 1. The fitting distributions are in agreement withthe experimental data. All the source numbers of the secondcomponents are 2.The values of ๐ extracted from the leadingjets in Figures 6(b)โ6(d) are larger than that extracted frominclusive jets in Figure 6(a). In addition, for the leading ๐-tagged jets, ๐ from ๐ + jets channels is in agreement with thatfrom ๐ + jets channels within uncertainties.
The reconstructed jet๐๐spectra for the leading (squares),
2nd (circles), 3rd (triangles), 4th (stars), and 5th order jets(diamonds) in the electron (๐ + jets) channels producedin ๐-๐ collision at โ๐ = 7TeV are indicated in Figure 7.
8 Advances in High Energy Physics
Even
ts/10
GeV
/c
102
101
b-subleading jet pT (GeV/c)50 100 150
p-p โs = 7TeV
โซLdt = 5.0fbโ1
(a)O
S-SS
even
ts/5
GeV
/c
103
102
SMT jet pT (GeV/c)50 100
electron channelโซLdt = 4.6fbโ1
(b)
Jets/
10G
eV/c
103
102
101
100
Light jet pT (GeV/c)100 200
โซLdt = 1.8fbโ1
(c)
Figure 5: Transverse momentum spectra for the subleading ๐-jets (a), the SMT jets (b), and the light-quark jets (c) produced in ๐-๐ collisionatโ๐ = 7TeV.The symbols represent the experimental data of the CMS Collaboration [20] and the ATLAS Collaboration [19, 21].The curvesare our modelling results.
The symbols represent the experimental data collected bythe ATLAS Collaboration corresponding to an integratedluminosity of 4.6fbโ1 and a radius parameter of 0.4 withinthe pseudorapidity range |๐| < 2.5 using anti-๐
๐jet algorithm
[12] for ๐๐> 25GeV/๐ jets [24]. In the figure, all the data
have invisible error bars (statistical uncertainty only), so wemeasure the marker size as the errors used in the calculation.The curves are our fitted results with the two-componentErlang distribution, and the related parameter values with๐2 are given in Table 1. From the figure one can see that
the fitted results are in agreement with the observed jet ๐๐
distributions. For different jet orders, we have ๐1= 7 and
๐2= 2.The value of๐ decreases with increase of the jet order
๐. The figure display of the dependence of ๐ on ๐ will bediscussed in the last part of this section.
In Figure 8, the leading jet ๐๐distributions in (a) the 4-jet
๐ก๐ก, (b) preselection, (c)๐ boson + jets, and (d) 5-jet ๐ก๐ก withan integrated luminosity of 4.7fbโ1 in ๐-๐ collision at โ๐ =7TeV are shown. The symbols represent the experimentaldata recorded by the ATLAS Collaboration [25]. The error
Advances in High Energy Physics 9
Jets pT (GeV/c)
Even
ts/G
eV/c
104
103
100 200 300
p-p โs = 7TeV
โซLdt = 37pbโ1
(a)
Even
ts/10
GeV
/c
102
101
100
Leading b-jet pT (GeV/c)100 200
โซLdt = 5.0fbโ1
(b)
Even
ts/G
eV/c
102
101
100
e + jets channel
Leading b-jet pT (GeV/c)100 200 300
โซLdt = 4.6fbโ1
(c)
Even
ts/G
eV/c
102
100
Leading b-jet pT (GeV/c)100 200 300
๐ + jets channelโซLdt = 4.6fbโ1
(d)
Figure 6: Some other jet ๐๐spectra in ๐-๐ collision atโ๐ = 7TeV for different situations shown in the panels and text.The symbols shown in
Figures 6(a), 6(b), and 6(c)-6(d) represent the experimental data of the ATLAS [22], CMS [20], and ATLAS Collaborations [23], respectively.The curves are our modelling results.
Even
ts/G
eV/c
103
102
101
100
Jet pT (GeV/c)103102
anti-kT, R = 0.4, |๐| < 2.5
e + jets channel
Leading jet2nd jet3rd jet
4th jet5th jet
โซLdt = 4.6fbโ1p-p โs = 7TeV,
Figure 7: The transverse momentum spectra for the leading, 2nd, 3rd, 4th, and 5th order jets in the electron (๐ + jets) channels produced in๐-๐ collision atโ๐ = 7TeV.The symbols represent the experimental data of the ATLAS Collaboration [24] and the curves are our modellingresults.
10 Advances in High Energy Physics
Even
ts/40
GeV
/c
104
103
102
101
100
Leading jet pT (GeV/c)200 400 600 800
โซLdt = 4.7fbโ1
4-jet tt control region
p-p โs = 7TeV
(a)
Leading jet pT (GeV/c)200 400 600 800
Even
ts/40
GeV
/c
105
104
103
102
101
โซLdt = 4.7fbโ1
preselection region
(b)
Leading jet pT (GeV/c)200 400 600 800
Even
ts/40
GeV
/c
104
103
102
101
100
โซLdt = 4.7fbโ1
W boson + jetscontrol region
(c)
Leading jet pT (GeV/c)200 400 600 800
Even
ts/40
GeV
/c
103
102
101
100
โซLdt = 4.7fbโ1
5-jet ttcontrol region
(d)
Figure 8:The leading jet ๐๐distributions in (a) the 4-jet ๐ก๐ก, (b) preselection, (c)๐ boson + jets, and (d) 5-jet ๐ก๐กwith an integrated luminosity
of 4.7fbโ1 in ๐-๐ collision at โ๐ = 7TeV. The symbols represent the experimental data of the ATLAS Collaboration [25] and the curves areour modelling results.
bars indicate the total uncertainty. The curves indicate thefitted results by the two-component Erlang distribution, andthe corresponding values of free parameters, defined ๐,and ๐2/dof are listed in Table 1. One can see that the two-component Erlang distribution with ๐
2= 2 describes the
data of the leading jet ๐๐spectra, and the extracted effective
temperature parameters have a smaller difference.Figures 9(a) and 9(b) display ๐
๐distributions of the
leading and fat jets in๐-๐ collision atโ๐ = 7TeV, respectively,where the results are in the lepton plus jets channels usingan integrated luminosity of 2.05fbโ1. Figures 9(c)โ9(f) give๐๐distributions of the leading jets in the same collision,
and the corresponding integrated luminosity and lepton plusjets channels are shown in the panels. The symbols representthe experimental data of the ATLAS Collaboration [26โ30]. The error bars indicate the experimental uncertainty.Our calculated results by using the two-component Erlangdistribution are presented by the curves in the figure. Thevalues of free parameters, defined ๐, and ๐2/dof are givenin Table 1. One can see that the mentioned ๐
๐spectra for
the leading and fat jets are fitted by the two-componentErlang distribution with ๐
2= 2 and relatively larger ๐. In
addition, in the error range,๐ extracted from the jet spectra in๐+ jets channels is in agreement with that in ๐+ jets channels.
The transverse momentum distributions of the leadingjets produced in ๐-๐ collision at โ๐ = 8TeV with an inte-grated luminosity of 14.3fbโ1 in the ๐ + jets and an integratedluminosity of 14.2fbโ1 in the ๐ + jets, after the resolvedselection, are shown in Figures 10(a) and 10(b), respectively.The experimental data (the squares) were recorded by theATLAS Collaboration [31]. Meanwhile, the data (the squares)of the leading light jet ๐
๐distribution and the second leading
light jet ๐๐distribution from ๐-๐ collision at โ๐ = 8TeV
corresponding to a total integrated luminosity of 19.5fbโ1measured by the CMS Collaboration [32] are presented inFigures 10(c) and 10(d), respectively. Moreover, the leadingjet ๐๐distribution and the subleading jet ๐
๐distribution in
the dijet system using ๐-๐ collision at โ๐ = 8TeV with anintegrated luminosity of 20.3fbโ1 are displayed in Figures10(e) and 10(f), respectively, where the squares represent the
Advances in High Energy Physics 11
Leading jet pT (GeV/c)500250 750 1000
Even
ts/20
GeV
/c
104
102
100
โซLdt = 2.05fbโ1
l + jets channel
p-p โs = 7TeV
(a)
Fat jet pT (GeV/c)500250 750 1000
Even
ts/G
eV/c
101
100
10โ1
10โ2
โซLdt = 2.05fbโ1
R = 1.0
l + jets channel
(b)
Leading jet pT (GeV/c)200100 300 400 500
Even
ts/20
GeV
/c
104
103
102
101
โซLdt = 4.7fbโ1
e + jets channel
(c)
Leading jet pT (GeV/c)200100 300 400 500
Even
ts/20
GeV
/c104
103
102
โซLdt = 4.7fbโ1
๐ + jets channel
(d)
Leading jet pT (GeV/c)200 400 600 800
Even
ts/25
GeV
/c
103
102
101
100
โซLdt = 200pbโ1
l + jets channel
(e)
Leading jet pT (GeV/c)100 200 300 400
Cand
idat
e eve
nts/
GeV
102
101
100
l + jets channelโซLdt = 33pbโ1
(f)
Figure 9: Transverse momentum distributions of the leading and fat jets produced in ๐-๐ collision at โ๐ = 7TeV with different channelsand integrated luminosities shown in the panels and text. The symbols represent the experimental data of the ATLAS Collaboration [26โ30]and the curves are our modelling results.
12 Advances in High Energy Physics
Even
ts/G
eV/c
103
102
101
โซLdt = 14.3fbโ1
e + jets channelresolved
Leading jet pT (GeV/c)100 200 300 400 500
p-p โs = 8TeV
(a)
Even
ts/G
eV/c
103
102
101
100
โซLdt = 14.2fbโ1
๐ + jets channelresolved
Leading jet pT (GeV/c)100 200 300 400 500
(b)
Even
ts/14.2
GeV
/c
103
102
101
100
โซLdt = 19.5fbโ1
Leading light jet pT (GeV/c)0 150 300 450 600
(c)
Even
ts/6.75
GeV
/c
103
102
101
โซLdt = 19.5fbโ1
Second leading light jet pT (GeV/c)60 120 180 240
(d)
Nob
s/20
GeV
/c
105
104
103
102
โซLdt = 20.3fbโ1
Leading jet pT (GeV/c)100 200 300 400
(e)
Nob
s/20
GeV
/c
105
104
103
102
101
โซLdt = 20.3fbโ1
Subleading jet pT (GeV/c)100 200 300 400
(f)
Figure 10: Transverse momentum distributions of different types of jets produced in ๐-๐ collision at โ๐ = 8TeV with different selectedconditions shown in the panels and text. The symbols shown in Figures 10(a)-10(b), 10(c)-10(d), and 10(e)-10(f) represent the experimentaldata of the ATLAS [31], CMS [32], and ATLAS Collaborations [33], respectively. The curves are our modelling results.
data of the ATLAS Collaboration [33]. In the figure, the errorbars reflect the statistical uncertainty, and the curves areour results calculated by using the two-component Erlangdistribution. The relevant parameter values with ๐2/dof inour calculation are presented in Table 1. From the figure,one can see that the modelling results are in agreement
with the data. Comparing with the leading jet spectra,the defined ๐ extracted from the subleading jet spectraexhibits a quick decrease. The defined ๐ extracted from thelight jet spectra shows relatively a little larger value thanthat from the nontagged jets spectra, or the two situationsare approximately the same in the error range. Moreover,
Advances in High Energy Physics 13
dN
jets/dpT
((G
eV/c)โ
1)
104
102
100
10โ2
โซLdt = 10.7fbโ1
Inclusive jet pT (GeV/c)500 1000 1500 2000 2500
p-p โs = 8TeV
(a)Ev
ents/
1.25
GeV
/c 105
104
โซLdt = 19.8fbโ1
Jets pT (GeV/c)20 40 60 80 100
Z โ ๐๐
(b)
Even
ts/30
GeV
/c
103
102
101
100
โซLdt = 20fbโ1
Large-R jet pT (GeV/c)200 400 600 800 1000
(c)
Figure 11: (a) and (b) Inclusive jet ๐๐spectra and (c) the large-๐ jet ๐
๐spectrum produced in ๐-๐ collision atโ๐ = 8TeV.The symbols shown
in Figures 11(a)-11(b) and 11(c) represent the experimental data of the CMS [34, 35] and ATLAS Collaborations [36], respectively. The curvesare our modelling results, where the two-component Erlang distribution is used for Figures 11(a) and 11(b), and the three-component Erlangdistribution is used for Figure 11(c).
the defined ๐ corresponding to the leading jets from ๐ + jetsand ๐ + jets channels in Figures 10(a) and 10(b) is nearly thesame.
The inclusive jet ๐๐distributions and the large-๐ jet
๐๐distribution produced in ๐-๐ collision at โ๐ = 8TeV
are presented in Figure 11. The data (squares) in Figure 11(a)were collected with the CMS detector corresponding to anintegrated luminosity of 10.7fbโ1 from a high-level trig-ger that accepted events containing at least one jet with๐๐> 320GeV/๐ [34]. The data (squares) in Figure 11(b)
for ๐ โ ๐๐ events were selected from the full 2012 runand amounted to a total integrated luminosity of 19.8fbโ1[35]. The data (squares) in Figure 11(c) were collected bythe ATLAS Collaboration corresponding to an integratedluminosity of 20fbโ1 with an uncertainty of 2.8% [36]. Inthe figure, the curves indicate our fitted results. One can seethat the modelling results are in good agreement with theexperimental data. The related parameter values for Figures11(a) and 11(b) are given in Table 1, where the number ofcomponents is two and the source numbers of the second
14 Advances in High Energy Physics
T(G
eV)
6
5.8
5.6
Pb-Pb 2.76TeV
C (%)0 25 50 75
Charged jetsFitted function
(a)
T(G
eV)
30
15
0
O
1st 2nd 3rd 4th 5th
p-p 7TeV
Leading jetsFitted function
(b)
Figure 12: Dependences of defined effective temperature parameter ๐ on centrality percentage ๐ถ in Pb-Pb collisions at โ๐ ๐๐ = 2.76TeV(a) and on jet order ๐ in ๐-๐ collision at โ๐ = 7TeV (b). The symbols represent ๐ values obtained from Figures 3 and 7 (listed in Table 1),respectively, and the curves are our fitted results which are presented in (7) and (8), respectively.
components are ๐2= 2. For Figure 11(c), we have to use
the three-component Erlang distribution with ๐1= 29,
๐๐ก๐1= (6.65 ยฑ 0.60)GeV/๐, ๐
1= 0.396 ยฑ 0.036, ๐
2= 14,
๐๐ก๐2= (19.50 ยฑ 1.00)GeV/๐, ๐
2= 0.204 ยฑ 0.036, ๐
3= 2,
๐๐ก๐3= (111.00 ยฑ 10.00)GeV/๐, ๐ = 51.011 ยฑ 11.853GeV, and
๐2/dof = 0.377.To see clearly the dependence of the effective temperature
parameter ๐ on the centrality percentage ๐ถ in Pb-Pb colli-sions at โ๐ ๐๐ = 2.76TeV, we present the relation ๐ โ ๐ถ inFigure 12(a). The circles represent the effective temperaturevalues obtained from Figure 3 and listed in Table 1, and thecurve is our fitted result by an exponential function of
๐ = (โ0.125 ยฑ 0.020) exp [โ ๐ถ
(10.500 ยฑ 3.000)]
+ (5.878 ยฑ 0.010)
(7)
with ๐2/dof = 0.0002, where ๐ is in the units of GeV and ๐ถis in %. One can see that ๐ slightly increases with increaseof ๐ถ, and a saturation effect quickly appears in semicentralcollisions, or ๐ has no obvious change in the error range withincrease of ๐ถ. In addition, to see clearly the dependence ofthe effective temperature parameter ๐ on the jet order ๐ in๐-๐ collision at โ๐ = 7TeV, we present the relation ๐ โ ๐ inFigure 12(b). The circles represent the effective temperaturevalues obtained from Figure 7 and listed in Table 1, and thecurve is our fitted result by an exponential function of
๐ = (54.30 ยฑ 3.00) exp [โ ๐
(1.43 ยฑ 0.10)]
+ (4.55 ยฑ 1.00)
(8)
with ๐2 = 0.129, where ๐ is in the units of GeV. One can seethat ๐ decreases with increase of ๐.
The dependences of the effective temperature parameter๐ on other factors such as ๐ and di-๐ channels (a), ๐(๐๐) and๐(๐๐) channels (b), leading and subleading jets (c), and size of
interacting system (d) are displayed in Figure 13, where thesymbols represent the effective temperature values obtainedfrom the above figures and listed in Table 1. One can seethat a high center-of-mass energy results in a high effectivetemperature, different lepton channels show approximatelythe same effective temperature in the error range, andthe leading jets correspond to a high effective temperaturecomparing with the subleading jets. At the same time, ๐slightly decreases with increase of the size of interactingsystem, or ๐ is approximately not related to the size in theerror range.The former case can be explained by the influenceof jet quenching effect (quick energy loss) which exists in Au-Au collisions and does not exist in ๐-๐ collision.
4. Conclusions
From the above discussions, we obtain following conclusions.(a) The transverse momentum distributions, of various
jets produced in ๐-๐, ๐-๐, ๐-Au, Au-Au, and Pb-Pb collisionsover an energy range from 0.2 to 8 TeV in different additionalselection conditions, are described by using the multicompo-nent Erlang distribution in the framework of the multisourcethermalmodel which reflects the reaction types in interactingsystem and multiple temperatures emission. The calculatedresults are in good agreement with the experimental datameasured by the STAR, D0, CDF II, ALICE, ATLAS, andCMS Collaborations.
(b) Except for one group data in Figure 11(c) which isdescribed by the three-component Erlang distribution, thedata of ๐
๐spectra for mentioned jets are fitted by the two-
component Erlang distribution. The source numbers of thefirst components are greater than or equal to 2, while thesource numbers of the second components are mostly 2. In๐๐distribution, the first component in charge of low-๐
๐jets
indicates strong scattering interactions between two quarksor among more quarks and gluons and accounted for a largerproportion, and the second component for high-๐
๐region
means harder head-on scattering between two quarks.
Advances in High Energy Physics 15
T(G
eV)
30
24
l channel di-l channel
b-jetsInclusive jets
p-p โs = 7TeV
(a)
T(G
eV)
30
15
๐(๐๐) channel e(ee) channel
b-leading p-p 7TeVLeading p-p 7TeV
Leading p-p 8TeVLeading p-p 1.96TeV
(b)
T(G
eV) 30
15
Leading Subleading
b-jets (p-p 7TeV)Inclusive jets (p-p 7TeV)
Light jets (p-p 8TeV)Inclusive jets (p-p 8TeV)
(c)
T(G
eV)
1.9
1.8
p-p d-Au Au-Au
โsNN = 0.2TeV
(d)
Figure 13: Dependences of ๐ on ๐ and di-๐ channels (a), ๐(๐๐) and ๐(๐๐) channels (b), leading and subleading jets (c), and size of interactingsystem (d). The symbols represent ๐ values obtained from related figures and listed in Table 1.
(c)The effective temperature parameter๐ is higher, whichmeans that the transverse excitation of emission source isvery violent. From our study, ๐ depends on the center-of-mass energy, system size, centrality interval, jet type, jetorder, channel of detection system, and origination. Gen-erally, ๐ increases with increase of center-of-mass energy,which renders the fact that the larger the center-of-massenergy is, the more violent the transverse excitation of theinteracting system is. Besides, at the same center-of-massenergy, there is a slightly negative correlation between ๐
and the system size, or ๐ is approximately independent ofthe size in the error range. The former case reflects that, inrelatively complex collision system, there is a jet quenchingeffect (quick energy loss) in the case of high energy quark andgluon jets penetrating through the dense deconfined matter.
(d) From ๐๐
distributions of charged jets producedin Pb-Pb collisions at โ๐ ๐๐ = 2.76TeV with differentcentrality intervals analyzed by using the two-component
Erlang distribution, we know that ๐ slightly increases withincrease of the centrality percentage ๐ถ and quickly saturatesin semicentral collisions, or ๐ has no obvious change in theerror range with increase of ๐ถ. In addition, as expected, theextracted effective temperature from the reconstructed jets๐๐spectra produced in electron channels in ๐-๐ collisions
at โ๐ = 7TeV decreases with increase of the jet order fromthe 1st to 5th.
(e)At the same energy, the effective temperature extractedfrom the leading jets is much higher than that from thesubleading jets.This is a natural result because the leading jetsare produced through more violent scattering. The effectivetemperature extracted from tagged jets (such as light-quarkjets and ๐-quark jets) seems to be higher than that fromnontagged jets, which reveals that the hadron jets originatedfrom quark jets carry more energy and the leading jets pri-marily originate from quark jets. The effective temperaturesextracted from different lepton and dilepton channel jets are
16 Advances in High Energy Physics
approximately the same in the error range, which reflects thecommon property in these jets.
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper.
Acknowledgments
One of the authors (Fu-HuLiu) thanks Prof. Dr. Charles Gale,Prof. Dr. Sangyong Jeon, and the members of the PhysicsDepartment of McGill University, Canada, for their hospital-ity, where this work was partly finished. The authorsโ workwas supported by theNational Natural Science Foundation ofChina under Grant no. 10975095, the Open Research Subjectof the Chinese Academy of Sciences Large-Scale ScientificFacility under Grant no. 2060205, the Shanxi ProvincialNatural Science Foundation under Grant no. 2013021006,and the Foundation of Shanxi Scholarship Council of Chinaunder Grant no. 2012-012.
References
[1] D. H. Rischke, โThe quarkโgluon plasma in equilibrium,โProgress in Particle and Nuclear Physics, vol. 52, no. 1, pp. 197โ296, 2004.
[2] D. H. Rischke, โRemarks on the extraction of freeze-outparameters,โ Nuclear Physics A, vol. 698, no. 1โ4, pp. 153โ163,2002.
[3] D. dโEnterria, โJet quenching,โ in Landolt-Boernstein, vol. 1โ23A, Springer, 2011, http://arxiv.org/abs/0902.2011.
[4] I. Arsene, I. G. Bearden, D. Beavis et al., โQuark-gluon plasmaand color glass condensate at RHIC? The perspective from theBRAHMS experiment,โ Nuclear Physics A, vol. 757, no. 1-2, pp.1โ27, 2005.
[5] S. Domdey, B. Z. Kopeliovich, and H. J. Pirner, โJet-evolutionin the quark-gluon plasma from RHIC to the LHC,โ NuclearPhysics A, vol. 856, no. 1, pp. 134โ153, 2011.
[6] N. Gupta,A Study of Fluctuations inMultiplicity Distributions atUltra-Relativistic Heavy Ion Interactions, University of Jammu,2008.
[7] L. van Hove, โMultiplicity dependence of ๐๐กspectrum as a
possible signal for a phase transition in hadronic collisions,โPhysics Letters B, vol. 118, no. 1โ3, pp. 138โ140, 1982.
[8] H.-R. Wei, Y.-H. Chen, L.-N. Gao, and F.-H. Liu, โComparingmulticomponent erlang distribution and levy distribution ofparticle transverse momentums,โ Advances in High EnergyPhysics, vol. 2014, Article ID 782631, 2014.
[9] L. Adamczyk, J. K. Adkins, G. Agakishiev et al., โJet-Hadroncorrelations in โ๐ ๐๐ = 200 GeV ๐ + ๐ and central Au+Aucollisions,โ Physical Review Letters, vol. 112, no. 12, Article ID122301, 2014.
[10] J. Kapitan and The STAR Collaboration, โJets in 200GeV p+ pand d +Au collisions from the STAR experiment at RHIC,โJournal of Physics: Conference Series, vol. 270, no. 1, Article ID012015, 2011.
[11] L. Adamczyk, G. Agakishiev,M.M. Aggarwal et al., โLongitudi-nal and transverse spin asymmetries for inclusive jet production
at mid-rapidity in polarized ๐ + ๐ collisions at โ๐ = 200GeV,โhttp://arxiv.org/abs/1205.2735.
[12] M. Cacciari, G. P. Salam, and G. Soyez, โThe anti-kt jetclustering algorithm,โ Journal of High Energy Physics, vol. 2008,no. 4, article 063, 2008.
[13] V. M. Abazov, B. Abbott, B. S. Acharya et al., โMeasurementof the ratio of differential cross sections ๐(๐๐ โ ๐ + ๐jet )/
๐(๐๐ โ ๐ + jet) in ๐๐ collisions at โ๐ = 1.96TeV,โ PhysicalReview D, vol. 87, no. 9, Article ID 092010, 2013.
[14] V. M. Abazov, B. Abbott, B. C. Acharya et al., โStudies of Wboson plus jets production in ๐๐ collisions at โ๐ = 1.96TeV,โPhysical Review D, vol. 88, no. 9, Article ID 092001, 2013.
[15] CDF II Collaboration, โThe substructure of high transversemomentum jets observed by CDF II,โ CDF Note CDF-PUB-JET-PUBLIC-10199, 2011.
[16] B. Abelev, J. Adam,D. Adamova et al., โMeasurement of chargedjet suppression in Pb-Pb collisions atโ๐ ๐๐ = 2.76 TeV,โ Journalof High Energy Physics, vol. 2014, no. 4, article 013, 2014.
[17] S. Chatrchyan, V. Khachatryan, A. M. Sirunyan et al., โMea-surement of jet multiplicity distributions in ๐ก๐ก production in ๐๐collisions at โ๐ = 7TeV,โThe European Physical Journal C, vol.74, article 3014, 2014.
[18] G. Aad, B. Abbott, J. Abdallah et al., โJet mass and substructureof inclusive jets in โ๐ = 7TeV pp collisions with the ATLASexperiment,โ Journal of High Energy Physics, vol. 2012, no. 5,article 128, 2012.
[19] G. Aad, T. Abajyan, B. Abbott et al., โMeasurement of jet shapesin top-quark pair events at โ๐ = 7 TeV using the ATLASdetector,โ The European Physical Journal C, vol. 73, Article ID2676, 2013.
[20] S. Chatrchyan, V. Khachatryan, A.M. Sirunyan et al., โMeasure-ment of the production cross sections for a Z boson and oneor more b jets in pp collisions at โ๐ = 7 TeV,โ Journal of HighEnergy Physics, vol. 2014, no. 6, article 120, 2014.
[21] G. Aad, T. Abajyan, B. Abbott et al., โMeasurement of theproduction of aW boson in association with a charm quark inpp collisions at โ๐ = 7TeV with the ATLAS detector,โ Journalof High Energy Physics, vol. 2014, no. 5, article 68, 2014.
[22] G. Aad, E. Abat, J. Abdallah et al., โDynamics of isolated-photonplus jet production in ๐๐ collisions at โ๐ = 7 TeV with theATLAS detector,โNuclear Physics B, vol. 875, no. 3, pp. 483โ535,2013.
[23] G. Aad, T. Abajyan, B. Abbott et al., โMeasurements of normal-ized differential cross sections for ๐ก๐ก production in ๐๐ collisionsat โ๐ = 7TeV using the ATLAS detector,โ Physical Review D,vol. 90, no. 7, Article ID 072004, 2014.
[24] G. Aad, B. Abbott, J. Abdallah et al., โMeasurement of the ๐ก๐กproduction cross-section as a function of jet multiplicity and jettransverse momentum in 7 TeV proton-proton collisions withthe ATLAS detector,โ Journal of High Energy Physics, vol. 2015,no. 1, article 020, 2015.
[25] G. Aad, T. Abajyan, B. Abbott et al., โSearch for resonant topquark plus jet production in ๐ก๐ก + jets events with the ATLASdetector in ๐๐ collisions at โ๐ = 7TeV,โ Physical Review D, vol.86, no. 9, Article ID 091103, 2012.
[26] G. Aad, B. Abbott, J. Abdallah et al., โA search for tt resonanceswith the ATLAS detector in 2.05fbโ1 of proton-proton colli-sions at โ๐ = 7TeV,โ The European Physical Journal C, vol. 72,Article ID 2083, 2012.
[27] G. Aad, T. Abajyan, B. Abbott et al., โA search for ๐ก๐ก resonancesin lepton+jets events with highly boosted top quarks collected
Advances in High Energy Physics 17
in pp collisions atโ๐ = 7 TeVwith the ATLAS detector,โ Journalof High Energy Physics, vol. 2012, no. 9, article 041, 2012.
[28] G. Aad, T. Abajyan, B. Abbott et al., โSearch for ๐ก๐ก resonancesin the lepton plus jets final state with ATLAS using 4.7fbโ1 of๐๐ collisions at โ๐ = 7 TeV,โ Physical Review D, vol. 88, no. 1,Article ID 012004, 2013.
[29] The ATLAS Collaboration, โA search for ๐ก๐ก resonances in thelepton plus jets channel using 200 pbโ1of๐๐ collisions atโ๐ = 7TeV,โ Tech. Rep. ATLAS-CONF-2011-087, 2011.
[30] The ATLAS Collaboration, โA search for new high-mass phe-nomena producing top quarks with the ATLAS experiment,โTech. Rep. ATLAS-CONF-2011-070, 2011.
[31] ATLAS Collaboration, โA search for resonance in the leptonplus jets channel with ATLAS using 14fbโ1 of proton-protoncollisions atโ๐ = 8TeV,โEPJWeb of Conferences, vol. 60, ArticleID 20044, 2013, ATLAS NOTE ATLAS-CONF-2013-052.
[32] The CMS Collaboration, โSearch for pair production of reso-nances decaying to a top quark plus a jet in final states with twoleptons,โ Tech. Rep. CMS-PAS-B2G-12-008, 2013.
[33] G. Aad, T. Abajyan, B. Abbott et al., โMeasurement of theelectroweak production of dijets in association with a Z-bosonand distributions sensitive to vector boson fusion in proton-proton collisions at โ๐ = 8TeV using the ATLAS detector,โJournal of High Energy Physics, vol. 2014, no. 4, article 31, 2014.
[34] V. Khachatryan, A. M. Sirunyan, A. Tumasyan et al., โSearchfor jet extinction in the inclusive jet-๐
๐spectrum from proton-
proton collisions atโ๐ = 8 TeV,โ Physical Review D, vol. 90, no.3, Article ID 032005, 2014.
[35] The CMS Collaboration, โPileup jet identification,โ Tech. Rep.CMS-PAS-JME-13-005, 2013.
[36] G. Aad, B. Abbott, J. Abdallah et al., โSearch for top squarkpair production in final states with one isolated lepton, jets, andmissing transversemomentum inโ๐ = 8TeV pp collisions withthe ATLAS detector,โ Journal of High Energy Physics, vol. 2014,no. 11, article 118, 2014.
[37] F.-H. Liu, N. N. Abd Allah, and B. K. Singh, โDependence ofblack fragment azimuthal and projected angular distributionson polar angle in silicon-emulsion collisions at 4.5AGeV/c,โPhysical Review C, vol. 69, no. 5, Article ID 057601, 2004.
[38] F.-H. Liu, โDependence of charged particle pseudorapiditydistributions on centrality and energy in ๐(๐)๐ด collisions athigh energies,โ Physical Review C, vol. 78, no. 1, Article ID014902, 2008.
[39] F.-H. Liu, โUnified description of multiplicity distributions offinal-state particles produced in collisions at high energies,โNuclear Physics A, vol. 810, no. 1โ4, pp. 159โ172, 2008.
Submit your manuscripts athttp://www.hindawi.com
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
FluidsJournal of
Atomic and Molecular Physics
Journal of
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
Advances in Condensed Matter Physics
OpticsInternational Journal of
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
AstronomyAdvances in
International Journal of
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
Superconductivity
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
Statistical MechanicsInternational Journal of
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
GravityJournal of
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
AstrophysicsJournal of
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
Physics Research International
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
Solid State PhysicsJournal of
โComputationalโโMethodsโinโPhysics
Journal of
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
Soft MatterJournal of
Hindawi Publishing Corporationhttp://www.hindawi.com
AerodynamicsJournal of
Volume 2014
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
PhotonicsJournal of
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
Journal of
Biophysics
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
ThermodynamicsJournal of