Combined analysis of midrapidity transverse momentum spectra of the charged pions and kaons, protons and antiprotons in p+p and Pb+Pb collisions at (snn)1/2 = 2.76 and 5.02 TeV at the LHC
Abstract:The experimental transverse momentum spectra of the charged pions and kaons, protons and antiprotons, produced at midrapidity in [Formula: see text] collisions at [Formula: see text] and 5.02 TeV, central (0–5%) and peripheral (60–80%) Pb[Formula: see text]+[Formula: see text]Pb collisions at [Formula: see text] TeV, central (0–5%), semicentral (40–50%) and peripheral (80–90%) Pb[Formula: see text]+[Formula: see text]Pb collisions at [Formula: see text] TeV, measured by ALICE collaboration, were analyzed using… Show more
“…This simple form of the equation having a few parameters, is very powerful tool to compare different collisions with a small number of parameters. The Hagedorn function has reproduced the spectra described in 18 , 32 , 33 with physical parameters. We can re-arrange these terms in our current analysis as follows, …”
Section: Methods and Modelsmentioning
confidence: 89%
“…The n and in the equation are two free parameters of the function. Moreover, the Tsallis function 15 – 18 can excellently describe the and invariant distribution measured in pp collisions at high energies. There are several version of the Tsallis function that can give good fit results to the spectra, however, the following expression is a simple version of the Tsallis function 22 that describes the invariant spectra of particles in terms of the effective temperature and non-extensivity parameter q which accounts for the deviation of the spectra from the usual Boltzmann–Gibbs exponential distribution function.…”
Section: Methods and Modelsmentioning
confidence: 99%
“…These modifications have been discussed in 18 , 33 , 34 and have successfully calculated the average transverse flow velocity and , and the equation is now known as the Hagedorn equation with embedded transverse flow velocity 35 : where C is the normalization constant and is to be normalized to 1. = and is the average transverse flow velocity.…”
Section: Methods and Modelsmentioning
confidence: 99%
“…The temperature at the kinetic freeze-out stage ( ), the effective temperature ( ) and the average transverse flow velocity ( ) are extracted by fitting the data with these statistical functions. and are obtained by using a modified Hagedorn function with embedded transverse flow velocity 15 – 18 . In addition, is extracted by using the Tsallis distribution function 19 – 23 .…”
The measured charged particle $$p_T$$
p
T
spectra in proton-proton collisions obtained by the CMS experiment at CERN is compared with the simulation results of EPOS–LHC and Pythia8.24 models at 7 TeV center-of-mass energy. The Pythia8.24 model describes the experimental data very well, particularly in the high $$p_T$$
p
T
region. The model also predicts the $$p_T$$
p
T
spectra for $$|$$
|
$$\eta $$
η
$$|$$
|
< 2.4 at 0 $$\le $$
≤
$$p_T$$
p
T
$$\le $$
≤
6 $$\text {GeV/}c$$
GeV/
c
. The EPOS–LHC model underpredicts the $$p_T$$
p
T
spectra from 0.1 to 2 $$\text {GeV/}c$$
GeV/
c
in all $$\eta $$
η
bins for about 20% and the $$p_T$$
p
T
spectrum from 0.1 to 4.2 $$\text {GeV/}c$$
GeV/
c
for $$|$$
|
$$\eta $$
η
$$|$$
|
< 2.4 by about 15% while reasonably predicts well for $$p_T$$
p
T
> 4.2 $$\text {GeV/}c$$
GeV/
c
within the experimental errors. Furthermore, to get information about collective properties of the hadronic matter, modified Hagedorn function with embedded transverse flow velocity and thermodynamically consistent Tsallis distribution functions are used to fit the experimental data and simulated results. The values of $$\chi ^2/ndf$$
χ
2
/
n
d
f
show that the functions fit the data and simulation results well. The parameter extracted by the functions: $$\beta _T$$
β
T
, $$T_0$$
T
0
, and $$T_{eff}$$
T
eff
decreases with increasing $$\eta $$
η
. The decrease in $$\beta _T$$
β
T
with increasing $$\eta $$
η
is due to the large energy deposition in lower rapidity bins producing rapid expansion due to large pressure gradient resulting quick expansion of the fireball. Similarly, large energy transfer in the lower pseudo-rapidity bin results in higher degree of excitation of the system which results larger values of $$T_0$$
T
0
and $$T_{eff}$$
T
eff
. The values of the fit constant $$N_0$$
N
0
increase with $$\eta $$
η
where the values of $$N_0$$
N
0
extracted from Pythia8.24 are closer to the data than the EPOS–LHC model. The Pythia8.24 model has better prediction than the EPOS–LHC model which might be connected to its flow-like features and color re-connections resulting from different Parton interactions in the initial and final state.
“…This simple form of the equation having a few parameters, is very powerful tool to compare different collisions with a small number of parameters. The Hagedorn function has reproduced the spectra described in 18 , 32 , 33 with physical parameters. We can re-arrange these terms in our current analysis as follows, …”
Section: Methods and Modelsmentioning
confidence: 89%
“…The n and in the equation are two free parameters of the function. Moreover, the Tsallis function 15 – 18 can excellently describe the and invariant distribution measured in pp collisions at high energies. There are several version of the Tsallis function that can give good fit results to the spectra, however, the following expression is a simple version of the Tsallis function 22 that describes the invariant spectra of particles in terms of the effective temperature and non-extensivity parameter q which accounts for the deviation of the spectra from the usual Boltzmann–Gibbs exponential distribution function.…”
Section: Methods and Modelsmentioning
confidence: 99%
“…These modifications have been discussed in 18 , 33 , 34 and have successfully calculated the average transverse flow velocity and , and the equation is now known as the Hagedorn equation with embedded transverse flow velocity 35 : where C is the normalization constant and is to be normalized to 1. = and is the average transverse flow velocity.…”
Section: Methods and Modelsmentioning
confidence: 99%
“…The temperature at the kinetic freeze-out stage ( ), the effective temperature ( ) and the average transverse flow velocity ( ) are extracted by fitting the data with these statistical functions. and are obtained by using a modified Hagedorn function with embedded transverse flow velocity 15 – 18 . In addition, is extracted by using the Tsallis distribution function 19 – 23 .…”
The measured charged particle $$p_T$$
p
T
spectra in proton-proton collisions obtained by the CMS experiment at CERN is compared with the simulation results of EPOS–LHC and Pythia8.24 models at 7 TeV center-of-mass energy. The Pythia8.24 model describes the experimental data very well, particularly in the high $$p_T$$
p
T
region. The model also predicts the $$p_T$$
p
T
spectra for $$|$$
|
$$\eta $$
η
$$|$$
|
< 2.4 at 0 $$\le $$
≤
$$p_T$$
p
T
$$\le $$
≤
6 $$\text {GeV/}c$$
GeV/
c
. The EPOS–LHC model underpredicts the $$p_T$$
p
T
spectra from 0.1 to 2 $$\text {GeV/}c$$
GeV/
c
in all $$\eta $$
η
bins for about 20% and the $$p_T$$
p
T
spectrum from 0.1 to 4.2 $$\text {GeV/}c$$
GeV/
c
for $$|$$
|
$$\eta $$
η
$$|$$
|
< 2.4 by about 15% while reasonably predicts well for $$p_T$$
p
T
> 4.2 $$\text {GeV/}c$$
GeV/
c
within the experimental errors. Furthermore, to get information about collective properties of the hadronic matter, modified Hagedorn function with embedded transverse flow velocity and thermodynamically consistent Tsallis distribution functions are used to fit the experimental data and simulated results. The values of $$\chi ^2/ndf$$
χ
2
/
n
d
f
show that the functions fit the data and simulation results well. The parameter extracted by the functions: $$\beta _T$$
β
T
, $$T_0$$
T
0
, and $$T_{eff}$$
T
eff
decreases with increasing $$\eta $$
η
. The decrease in $$\beta _T$$
β
T
with increasing $$\eta $$
η
is due to the large energy deposition in lower rapidity bins producing rapid expansion due to large pressure gradient resulting quick expansion of the fireball. Similarly, large energy transfer in the lower pseudo-rapidity bin results in higher degree of excitation of the system which results larger values of $$T_0$$
T
0
and $$T_{eff}$$
T
eff
. The values of the fit constant $$N_0$$
N
0
increase with $$\eta $$
η
where the values of $$N_0$$
N
0
extracted from Pythia8.24 are closer to the data than the EPOS–LHC model. The Pythia8.24 model has better prediction than the EPOS–LHC model which might be connected to its flow-like features and color re-connections resulting from different Parton interactions in the initial and final state.
“…The extraction of final-state temperature T 0 is more complex than that of the initial temperature T i . Generally, one may introduce the transverse flow velocity β T in the considered function and obtain T 0 and β T simultaneously [49][50][51][52][53][54][55][56][57], in which the effective temperature T no longer appears. Alternatively, the intercept in T versus m 0 is assumed to be T 0 [50,[58][59][60][61][62][63], and the slope in hp T i versus m is assumed to be β T [62][63][64][65][66], where m denotes the average energy.…”
Section: The Initial-and Final-state Temperatures According Tomentioning
The differential cross-section in squared momentum transfer of
ρ
,
ρ
0
,
ω
,
ϕ
,
f
0
980
,
f
1
1285
,
f
0
1370
,
f
1
1420
,
f
0
1500
, and
J
/
ψ
produced in high-energy virtual photon-proton (
γ
∗
p
), photon-proton (
γ
p
), and proton-proton (
p
p
) collisions measured by the H1, ZEUS, and WA102 Collaborations is analyzed by the Monte Carlo calculations. In the calculations, the Erlang distribution, Tsallis distribution, and Hagedorn function are separately used to describe the transverse momentum spectra of the emitted particles. Our results show that the initial- and final-state temperatures increase from lower squared photon virtuality to a higher one and decrease with the increase of center-of-mass energy.
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