# PionpT Spectra in p+p Collisions as a Function of s and Event Multiplicity

Authors: Priyanka Sett; Prashant Shukla
Journal: Advances in High Energy Physics
 (2014)

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## Abstract

We study the charged pion transverse momentum(pT) spectra in p+p collisions as a function of collision energy s and event multiplicity using Tsallis distribution. This study gives an insight of the pion production process in p+p collisions. The study covers pion spectra measured in p+p collisions at SPS energies (6.27–17.27 GeV), RHIC energies (62.4 GeV and 200 GeV), and LHC energies (900 GeV, 2.76 TeV, and 7 TeV). The Tsallis parameters have been obtained and parameterized as a function of s. The study suggests that as we move to higher energy more and more hard processes contribute to the spectra. We also study the charged pion spectra for different event multiplicities in p+p collisions for LHC energies using Tsallis distribution. The variation of the Tsallis parameters as a function of event multiplicity has been obtained and their behavior is found to be independent of collision energy.


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## Body

## 1. Introduction

The particle spectra measured in hadronic collisions are of utmost interest because of their fundamental nature and simplicity, which allow verifying pQCD [1, 2] calculations and also help to make comprehensive phenomenological studies. The ratios of the particle yields obtained from the measured spectra allow getting the chemical freeze-out conditions, whereas the spectra themselves reflect the conditions at the kinetic freeze-out. The particle spectra provide useful information about the collision dynamics. The low pT region of the spectrum corresponds to the particles originating from low momentum transfer and multiscattering processes (nonperturbative QCD), whereas the high pT region comes from the hard-parton-scattering (pQCD) among the initial partons. The transition of this nonperturbative to perturbative dynamics has no sharp boundary, though one can have an estimate from the “xT-scaling” [3]. Extensive [4, 5] and nonextensive [6–10] statistical approaches have been used to characterize particle spectra in terms of thermodynamic variables. Extensive statistics assume thermal and chemical equilibrium of the system at hadronic phase which lead to an exponential distribution of the particle spectra. In experiments, the particle spectra show a power-law behavior at high pT. This behavior is reproduced by the nonextensive approach with an additional parameter. In recent times, the Tsallis [6] statistical approach is widely used to describe the particle spectra obtained in high-energy collisions with only two parameters, the temperature T and q, known as nonextensivity parameter which is a measure of temperature fluctuations or degree of nonequilibrium in the system.The Tsallis distribution gives an excellent description ofpT spectra of all identified mesons measured in p+p collisions at s=200 GeV [11]. In a recent work [12, 13], the Tsallis distribution has been used to describe the pT spectra of identified charged hadrons measured in p+p collisions at RHIC and at LHC energies. Such an approach has also been applied to the inclusive charged hadron p+p data in recent publications [14, 15]. It has been shown in [12, 16] that the functional form of the Tsallis distribution with thermodynamic origin is of the same form as the QCD-inspired Hagedorn formula [17, 18]. This could be the reason of success of Tsallis distribution in p+p collisions which is a power law typical of QCD hard scatterings. The hardness of the spectra is thus related to q and the parameter T governs the contribution from soft collisions.Using the Tsallis phenomenological function, we review and study the charged pion spectra inp+p collisions in a large energy regime, spanning from SPS [19] (6.27 GeV–17.27 GeV) and RHIC [20] (62.4 and 200 GeV) to LHC [21] (900 GeV, 2.76 TeV and 7 TeV) energies. The object of the present work is to study the behaviour of the Tsallis parameters as a function of collision energy. We also study the charged pion spectra for different event multiplicities in p+p collisions for LHC energies. Among all hadrons, pions are chosen because of their abundance in collisions, simple quark structure, and availability of the data at different energies.


## 2. Formalism

The transverse momentum spectra of hadrons, obtained from different fixed and collider experiments, have shown that the highpT region of the spectra can be described successfully by the power law,
(1)Ed3Ndp3=CPpT-n,
where CP is the normalization constant and n is the power which determines the shape of the spectra at high pT. However, the low pT region of the particle spectra shows an exponential shape and can be described by the Boltzmann-Gibbs [22, 23] statistical approach,
(2)Ed3Ndp3=CBe-E/T,
where CB is the normalization constant, E is the particle energy, and T is the temperature of the system.In the early 80s, Hagedorn [17] proposed a phenomenological function which describes the particle spectra for both the higher and lower pT regions:
(3)Ed3Ndp3=A(1+pTp0)-n,
where A, p0, and n are the fit parameters. The above equation describes an exponential behavior for low pT and a power-law behavior for high pT. Consider
(4)(1+pTp0)-n≃exp⁡⁡(-npTp0),forpT⟶0≃(p0pT)n,forpT⟶∞.
The parameter n in this equation is often related to the “power” in the “QCD-inspired” quark interchange model [18].In the late 80s, Tsallis [6] introduced the idea of the nonextensive statistics in place of thermal Boltzmann-Gibbs statistics. This approach includes a parameter q, known as nonextensive parameter which quantifies the temperature fluctuation [24] in the system as q-1=Var⁡(1/T)/〈T〉2. The nonextensive statistics assume Boltzmann-Gibbs form in the limit q→1. In Tsallis approach, the Boltzmann-Gibbs distribution takes the form
(5)Ed3Ndp3=Cq(1+(q-1)ET)-1/(q-1),
where Cq is the normalization factor. One can use the relation E = mT at mid-rapidity and n=1/(q-1) in (5) to obtain
(6)Ed3Ndp3=Cn(1+mTnT)-n,
where Cn is the normalization factor. Equation (6) can be rewritten as
(7)12πpTd2NdpTdy=Cn(1+mTnT)-n,
The value of Cn can be obtained by integrating (7) over momentum space:
(8)Cn=dN/dy∫0∞‍(1+(mT/nT))-n2πpTdpT.
Here the quantity dN/dy is the pT integrated yield. Equation (6) with the normalization constant takes the form [11]
(9)Ed3Ndp3=12πdNdy(n-1)(n-2)(nT+m(n-1))(nT+m)×(nT+mTnT+m)-n.Larger values ofq correspond to smaller values of n which imply dominant hard QCD point-like scattering. Both n and q have been interchangeably used in Tsallis distribution [7, 11, 20, 25, 26]. The Tsallis interpretation of parameters T as temperature and q as nonextensivity parameter is more suited for heavy ion collisions while for p+p collisions Hagedorn interpretation in terms of power n and a parameter T=p0/n which controls soft physics processes is more meaningful. Phenomenological studies suggest that, for quark-quark point scattering, n~4 [27, 28] and when multiple scattering centers are involved, n grows larger.There are many other forms of (9), which are used often to describe particle spectra in literature; see, for example, [7, 20, 25, 26, 29–31].


## 3. Results and Discussions

All the studies are performed with (9) and the fit parameters n, T, and dN/dy are obtained. The different experiments, energies, rapidity ranges, and particles used in the analysis are summarized in Table 1. For SPS energies only available data is for π- measured by NA61 Collaboration [19]; for RHIC and LHC energies we use (π++π-)/2. All the data used are measured in mid-rapidity and are given for unit rapidity. The difference in rapidity range is not expected to affect the behaviour of the spectra. CMS experiment presented [21] transverse momentum spectra for different events classified on the basis of number of true tracks here referred to as track multiplicity of event or simply multiplicity. Each multiplicity class is represented by average number of tracks (〈Ntracks〉).Table 1
The center of mass energy and rapidity of the data used for the study.
Experiments
Center of massenergy (GeV)
Rapidity
Particles studied
SPS
6.27, 7.74, 8.76, 12.32, 17.27
0.0–0.2
π
-
RHIC
62.4, 200
|
y
|
<
0.35
π
+, π-
LHC
900, 2760, 700
|
y
|
<
1.0
π
+, π-


### 3.1. Tsallis Parameters as a Function ofs in p+p System

In this analysis all the Tsallis parameters are obtained for charged pion spectra as a function ofs in p+p system for SPS [19], RHIC [20], and LHC [21] energies. Similar study is available in [12] using RHIC and LHC data and in [13] for SPS and LHC data.The pionpT spectra measured in p+p collisions at different s are shown in Figure 1 along with with Tsallis fits (9) shown by solid lines. The spectra are scaled by arbitrary factors (given in figure) for visual clarity. In case of RHIC data, we restrict the pT range to 1.7 GeV/c2 to have similar pT range at all energies. It can be noticed that the spectra become harder with increase in s which is depictive of occurrence of harder scatterings at higher collision energy. The χ2 per degree of freedom χ2/NDF values for all the fits are given in Table 2. The χ2/NDF values are ≲ 1, which is indicative of good fit quality.Table 2
Values of theχ2/NDF for Tsallis fits of pion spectra at different s.
s
χ
2
/
NDF
6.27 GeV
6.31/12
7.74 GeV
5.80/12
8.76 GeV
10.68/12
12.32 GeV
9.25/12
17.27 GeV
2.65/12
62 GeV
0.74/11
200 GeV
0.48/11
900 GeV
24.33/19
2.76 TeV
5.59/19
7.00 TeV
13.11/19Figure 1
The invariant yield spectra of charged pions as a function of (mT-m) for SPS [19] energies 6.27 GeV, 7.74 GeV, 8.76 GeV, 12.32 GeV, and 17.27 GeV, RHIC [20] energies 62.4 GeV and 200 GeV, and LHC [21] energies 900 GeV, 2.76 TeV, and 7 TeV. The solid lines are the Tsallis function (9). The negative pion yields are plotted for SPS energies and for all other energies; average yield for positive and negative pion is plotted.The parametersn and T obtained from this analysis are shown in Figures 2 and 3, respectively, as a function of s. The variation of dN/dy as a function of s is shown in Figure 4. The parameter n decreases with increasing s and starts saturating at LHC energies. The value of T also reduces slowly from SPS energies to LHC energies. The integrated yield dN/dy increases 10 times when going from SPS to highest LHC energy.Figure 2
The variation of the Tsallis parametern for charged pions as a function of s. The solid curve represents the parameterization (a+(s)-α)b.Figure 3
The variation of the Tsallis parameterT for charged pions as a function of s. The solid curve represents the parameterization (a+(s)-α)b.Figure 4
The variation of the integrated yielddN/dy for charged pions as a function of s. The solid curve represents the parameterization (a+(s)-α)b.Larger value ofn (also larger value of T) suggests that the spectra have contribution from processes involving small momentum transfer arising due to the rescattering, recombination of partons, fragmentation from strings, and so forth, whereas smaller values of n are indicative of harder processes being involved in particle production. Thus the spectra at SPS energies have large softer contribution and as the collision energy increases more and more contribution from hard processes is added.All the three parameters can be parametrized by a function of type(10)f(s)=(a+(s)-α)b.
Here a=1.33±0.08, α=0.22±0.06, and b=4.36±0.24 for n(s), a=2.63±0.62, α=0.04±0.02, and b=3.76±0.49 for T(s), and a=0.65±0.01, α=0.22±0.01, and b=-4.78±0.03 for dN(s)/dy. Using the parameterizations for n by (10) we get n~3.46 in the limit s→∞. The extrapolated values for n, T and dN/dy for s=14 TeV are n~5.09, T~90.33 MeV, and dN/dy~3.44.


### 3.2. Tsallis Parameters as a Function of Multiplicity (〈Ntracks〉) for LHC Energies

The Tsallis parameters for charged pion spectra are studied as a function of event multiplicity for different LHC energies 900 GeV and 2.76 and 7 TeV. The event multiplicity data was also studied in a recent work [10] but our analysis and interpretations are different.The invariant yield spectra corresponding to different multiplicities are fitted with (9) and are shown by the solid black lines in Figure 5 for 900 GeV, in Figure 6 for 2.76 TeV, and in Figure 7 for 7 TeV center of mass energy. The spectra are scaled up for distinctness. The Tsallis distribution describes all the spectra well, shown by the χ2/NDF values given in Table 3. The χ2/NDF values are little higher for some of the lower multiplicities due to the deviation of first data point in pT spectra with the curve.Table 3
Values of theχ2/NDF for the Tsallis fits in different event multiplicities.
〈
N
tracks
〉
χ
2
/
NDF values for
900 GeV
2.76 TeV
7.0 TeV
7
48.89/18
57.66/18
48.10/18
16
25.21/18
26.38/18
27.76/18
28
9.97/18
11.47/18
22.83/18
40
7.20/18
6.91/18
19.25/18
52
8.00/18
6.08/18
22.52/18
63
9.18/18
6.44/18
26.30/18
75
15.01/18
9.05/18
21.30/18
86
8.16/18
19.24/18
98
11.91/18
23.59/18
109
20.82/18
120
16.85/18
131
19.77/18Figure 5
The invariant yield spectra of(π++π-)/2 [21], as a function of mT-m for p+p collisions at s = 900 GeV. The yields are shown for 〈Ntracks〉 7, 16, 28, 40, 52, 63, and 75. The spectra are scaled up for clarity by a factor of 6i, where i=0,1,2,3,4,5, and 6. The solid lines show the Tsallis fits.Figure 6
The invariant yield spectra of(π++π-)/2 [21], as a function of mT-m for p+p collisions at s = 2.76 TeV. The yields are shown for 〈Ntracks〉 7, 16, 28, 40, 52, 63, 75, 86, and 98. The spectra are scaled up for clarity by a factor of 3i, where i=0,1,2,3,4,5,6,7, and 8. The solid lines show the Tsallis fits.Figure 7
The invariant yield spectra of(π++π-)/2 [21], as a function of mT-m for p+p collisions at s = 7.00 TeV. The yields are shown for 〈Ntracks〉 7, 16, 28, 40, 52, 63, 75, 86, 98, 109, 120, and 131. The spectra are scaled up for clarity by a factor of 3i, where i=0,1,2,3,4,5,6,7,8,9,10, and 11. The solid lines show the Tsallis fits.The parametersn and T obtained from the fits are shown in Figures 8 and 9, respectively, as a function of 〈Ntracks〉. The circles, squares, and triangles correspond to the parameter values obtained from data at 900 GeV, 2.76 TeV, and 7 TeV, respectively. It is seen that both the parameters n and T decrease rapidly and then start saturating with the increase of 〈Ntracks〉 for all three energies. This variation (of n and T) is very similar to the variation which we find as a function of s. It means that events with higher multiplicity have larger contribution from hard processes. The value of n for high multiplicity events at 7 TeV is ~4 which is depictive of production from point quark-quark scattering. The variation of n and T as a function of 〈Ntracks〉 can be described by the same curve given in the figure for all three energies and are parameterized by
(11)f(〈Ntracks〉)=(a+(〈Ntracks〉)-α)b.
Here a=1.13±0.01, α=0.81±0.04, and b=10.32±0.76 for n(〈Ntracks〉) and a=2.20±0.06, α=0.56±0.08, and b=5.33±0.23 for T(〈Ntracks〉).Figure 8
The variation of the Tsallis parametern for charged pions as a function of 〈Ntracks〉. The variation is shown for 900 GeV by black circles, 2.76 TeV by red squares, and 7.00 TeV by green triangles. The dashed curve represents the parameterization (a+(〈Ntracks〉)-α)b.Figure 9
The variation of the Tsallis parameterT for charged pions as a function of 〈Ntracks〉. The variation is shown for 900 GeV by black circles, 2.76 TeV by red squares, and 7.00 TeV by green triangles. The dashed curve represents the parameterization (a+(〈Ntracks〉)-α)b.ThepT integrated pion yield distribution in different multiplicity classes is shown in Figure 10 for the three LHC energies. The total pT integrated pion yield for each energy can be obtained by integrating the above distributions over all multiplicity classes. It is noticed that as the energy increases more and more high mutliplicity events are added in the sample with mean of the distribution shifting towards higher 〈Ntracks〉.Figure 10
The variation of the integrated yielddN/dy for charged pions as a function of 〈Ntracks〉. The variation is shown for 900 GeV by black circles, 2.76 TeV by red squares, and 7.00 TeV by green triangles.


## 3.1. Tsallis Parameters as a Function ofs in p+p System

In this analysis all the Tsallis parameters are obtained for charged pion spectra as a function ofs in p+p system for SPS [19], RHIC [20], and LHC [21] energies. Similar study is available in [12] using RHIC and LHC data and in [13] for SPS and LHC data.The pionpT spectra measured in p+p collisions at different s are shown in Figure 1 along with with Tsallis fits (9) shown by solid lines. The spectra are scaled by arbitrary factors (given in figure) for visual clarity. In case of RHIC data, we restrict the pT range to 1.7 GeV/c2 to have similar pT range at all energies. It can be noticed that the spectra become harder with increase in s which is depictive of occurrence of harder scatterings at higher collision energy. The χ2 per degree of freedom χ2/NDF values for all the fits are given in Table 2. The χ2/NDF values are ≲ 1, which is indicative of good fit quality.Table 2
Values of theχ2/NDF for Tsallis fits of pion spectra at different s.
s
χ
2
/
NDF
6.27 GeV
6.31/12
7.74 GeV
5.80/12
8.76 GeV
10.68/12
12.32 GeV
9.25/12
17.27 GeV
2.65/12
62 GeV
0.74/11
200 GeV
0.48/11
900 GeV
24.33/19
2.76 TeV
5.59/19
7.00 TeV
13.11/19Figure 1
The invariant yield spectra of charged pions as a function of (mT-m) for SPS [19] energies 6.27 GeV, 7.74 GeV, 8.76 GeV, 12.32 GeV, and 17.27 GeV, RHIC [20] energies 62.4 GeV and 200 GeV, and LHC [21] energies 900 GeV, 2.76 TeV, and 7 TeV. The solid lines are the Tsallis function (9). The negative pion yields are plotted for SPS energies and for all other energies; average yield for positive and negative pion is plotted.The parametersn and T obtained from this analysis are shown in Figures 2 and 3, respectively, as a function of s. The variation of dN/dy as a function of s is shown in Figure 4. The parameter n decreases with increasing s and starts saturating at LHC energies. The value of T also reduces slowly from SPS energies to LHC energies. The integrated yield dN/dy increases 10 times when going from SPS to highest LHC energy.Figure 2
The variation of the Tsallis parametern for charged pions as a function of s. The solid curve represents the parameterization (a+(s)-α)b.Figure 3
The variation of the Tsallis parameterT for charged pions as a function of s. The solid curve represents the parameterization (a+(s)-α)b.Figure 4
The variation of the integrated yielddN/dy for charged pions as a function of s. The solid curve represents the parameterization (a+(s)-α)b.Larger value ofn (also larger value of T) suggests that the spectra have contribution from processes involving small momentum transfer arising due to the rescattering, recombination of partons, fragmentation from strings, and so forth, whereas smaller values of n are indicative of harder processes being involved in particle production. Thus the spectra at SPS energies have large softer contribution and as the collision energy increases more and more contribution from hard processes is added.All the three parameters can be parametrized by a function of type(10)f(s)=(a+(s)-α)b.
Here a=1.33±0.08, α=0.22±0.06, and b=4.36±0.24 for n(s), a=2.63±0.62, α=0.04±0.02, and b=3.76±0.49 for T(s), and a=0.65±0.01, α=0.22±0.01, and b=-4.78±0.03 for dN(s)/dy. Using the parameterizations for n by (10) we get n~3.46 in the limit s→∞. The extrapolated values for n, T and dN/dy for s=14 TeV are n~5.09, T~90.33 MeV, and dN/dy~3.44.


## 3.2. Tsallis Parameters as a Function of Multiplicity (〈Ntracks〉) for LHC Energies

The Tsallis parameters for charged pion spectra are studied as a function of event multiplicity for different LHC energies 900 GeV and 2.76 and 7 TeV. The event multiplicity data was also studied in a recent work [10] but our analysis and interpretations are different.The invariant yield spectra corresponding to different multiplicities are fitted with (9) and are shown by the solid black lines in Figure 5 for 900 GeV, in Figure 6 for 2.76 TeV, and in Figure 7 for 7 TeV center of mass energy. The spectra are scaled up for distinctness. The Tsallis distribution describes all the spectra well, shown by the χ2/NDF values given in Table 3. The χ2/NDF values are little higher for some of the lower multiplicities due to the deviation of first data point in pT spectra with the curve.Table 3
Values of theχ2/NDF for the Tsallis fits in different event multiplicities.
〈
N
tracks
〉
χ
2
/
NDF values for
900 GeV
2.76 TeV
7.0 TeV
7
48.89/18
57.66/18
48.10/18
16
25.21/18
26.38/18
27.76/18
28
9.97/18
11.47/18
22.83/18
40
7.20/18
6.91/18
19.25/18
52
8.00/18
6.08/18
22.52/18
63
9.18/18
6.44/18
26.30/18
75
15.01/18
9.05/18
21.30/18
86
8.16/18
19.24/18
98
11.91/18
23.59/18
109
20.82/18
120
16.85/18
131
19.77/18Figure 5
The invariant yield spectra of(π++π-)/2 [21], as a function of mT-m for p+p collisions at s = 900 GeV. The yields are shown for 〈Ntracks〉 7, 16, 28, 40, 52, 63, and 75. The spectra are scaled up for clarity by a factor of 6i, where i=0,1,2,3,4,5, and 6. The solid lines show the Tsallis fits.Figure 6
The invariant yield spectra of(π++π-)/2 [21], as a function of mT-m for p+p collisions at s = 2.76 TeV. The yields are shown for 〈Ntracks〉 7, 16, 28, 40, 52, 63, 75, 86, and 98. The spectra are scaled up for clarity by a factor of 3i, where i=0,1,2,3,4,5,6,7, and 8. The solid lines show the Tsallis fits.Figure 7
The invariant yield spectra of(π++π-)/2 [21], as a function of mT-m for p+p collisions at s = 7.00 TeV. The yields are shown for 〈Ntracks〉 7, 16, 28, 40, 52, 63, 75, 86, 98, 109, 120, and 131. The spectra are scaled up for clarity by a factor of 3i, where i=0,1,2,3,4,5,6,7,8,9,10, and 11. The solid lines show the Tsallis fits.The parametersn and T obtained from the fits are shown in Figures 8 and 9, respectively, as a function of 〈Ntracks〉. The circles, squares, and triangles correspond to the parameter values obtained from data at 900 GeV, 2.76 TeV, and 7 TeV, respectively. It is seen that both the parameters n and T decrease rapidly and then start saturating with the increase of 〈Ntracks〉 for all three energies. This variation (of n and T) is very similar to the variation which we find as a function of s. It means that events with higher multiplicity have larger contribution from hard processes. The value of n for high multiplicity events at 7 TeV is ~4 which is depictive of production from point quark-quark scattering. The variation of n and T as a function of 〈Ntracks〉 can be described by the same curve given in the figure for all three energies and are parameterized by
(11)f(〈Ntracks〉)=(a+(〈Ntracks〉)-α)b.
Here a=1.13±0.01, α=0.81±0.04, and b=10.32±0.76 for n(〈Ntracks〉) and a=2.20±0.06, α=0.56±0.08, and b=5.33±0.23 for T(〈Ntracks〉).Figure 8
The variation of the Tsallis parametern for charged pions as a function of 〈Ntracks〉. The variation is shown for 900 GeV by black circles, 2.76 TeV by red squares, and 7.00 TeV by green triangles. The dashed curve represents the parameterization (a+(〈Ntracks〉)-α)b.Figure 9
The variation of the Tsallis parameterT for charged pions as a function of 〈Ntracks〉. The variation is shown for 900 GeV by black circles, 2.76 TeV by red squares, and 7.00 TeV by green triangles. The dashed curve represents the parameterization (a+(〈Ntracks〉)-α)b.ThepT integrated pion yield distribution in different multiplicity classes is shown in Figure 10 for the three LHC energies. The total pT integrated pion yield for each energy can be obtained by integrating the above distributions over all multiplicity classes. It is noticed that as the energy increases more and more high mutliplicity events are added in the sample with mean of the distribution shifting towards higher 〈Ntracks〉.Figure 10
The variation of the integrated yielddN/dy for charged pions as a function of 〈Ntracks〉. The variation is shown for 900 GeV by black circles, 2.76 TeV by red squares, and 7.00 TeV by green triangles.


## 4. Conclusion

This work presented the study of the transverse momentum spectra of the charged pions for different collisional energies and also for different event multiplicities (at LHC energies) using Tsallis distribution. The Tsallis parametern decreases with increasing s and starts saturating at LHC energies. The value of T also reduces slowly from SPS energies to LHC energies. It means that the spectra at SPS energies have large softer contribution and as the collision energy increases more and more contribution from hard processes is added. The pT integrated pion yield increases with increasing s and becomes 10 times when going from SPS to highest LHC energy. The Tsallis parameters are also obtained as a function of event multiplicity for all three LHC energies which can be described by the same curve. The variation of n and T as a function of multiplicity is very similar to the variation which we find as a function of s. It means that events with higher multiplicity have larger contribution from hard processes. The value of n for high multiplicity events at 7 TeV is ~4 which is depictive of production from point quark-quark scattering. The pT integrated pion yield distribution for the three LHC energies shows that as the energy increases, more and more high mutliplicity events are added in the sample with mean of the distribution shifting towards higher multiplicity.



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*Source: 896037-2014-09-02.xml*