Advances in High Energy Physics

Volume 2019, Article ID 8219567, 7 pages

https://doi.org/10.1155/2019/8219567

## Particle Transverse Momentum Distributions in p-p Collisions at TeV

^{1}Department of Physics, Islamic University of Science and Technology, Kashmir 192122, India^{2}Department of Physics, Jamia Millia Islamia (Central University), New Delhi 110025, India^{3}Research Lab., Govt. Degree College (Boys) Anantnag, J&K, India

Correspondence should be addressed to Inam-ul Bashir; moc.liamg@pehmani

Received 6 February 2019; Accepted 27 March 2019; Published 8 April 2019

Academic Editor: Takao Sakaguchi

Copyright © 2019 Inam-ul Bashir et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP^{3}.

#### Abstract

The midrapidity transverse momentum spectra of hadrons (p, K^{+}, , , , and ) and the available rapidity distributions of the strange hadrons (, , ) produced in p-p collisions at LHC energy = 0.9 TeV have been studied using a Unified Statistical Thermal Freeze-out Model (USTFM). The calculated results are found to be in good agreement with the experimental data. The theoretical fits of the transverse momentum spectra using the model calculations provide the thermal freeze-out conditions in terms of the temperature and collective flow parameters for different hadronic species. The study reveals the presence of a significant collective flow and a well-defined temperature in the system thus indicating the formation of a thermally equilibrated hydrodynamic system in p-p collisions at LHC. Moreover, the fits to the available experimental rapidity distributions data of strange hadrons show the effect of almost complete transparency in p-p collisions at LHC. The model incorporates longitudinal as well as a transverse hydrodynamic flow. The contributions from heavier decay resonances have also been taken into account. We have also imposed the criteria of exact strangeness conservation in the system.

#### 1. Introduction

Within the framework of the statistical hadronization model it is assumed that initially a fireball, i.e., a hot and dense matter of the partons (quarks and gluons), is formed over an extended region after the collision. The quarks and gluons in the fireball may be nearly free (deconfined) due to the ultra-violet freedom, i.e., in a quark gluon plasma (QGP) phase. This fireball undergoes a collective expansion accompanied by further particle production processes through the secondary collisions of quarks and gluons which consequently leads to a decrease in its temperature. Eventually the expansion reaches a point where quarks and gluons start interacting nonperturbatively leading to the confinement of quarks and gluons through the formation of hadrons, i.e., the so called hadronization process. In this hot matter which is in the form of a gas of hadronic resonances at high temperature and density, the hadrons continue to interact thereby producing more hadrons and the bulk matter expands further due to a collective hydrodynamic flow developed in the system. This consequently results in a further drop in the thermal temperature because a certain fraction of the available thermal energy is converted into directed (collective hydrodynamic) flow energy. As the mean free paths for different hadrons, due to expansion increases, the process of decoupling of the hadrons from the rest of the system takes place and the hadron spectra are frozen in time. The hadrons with smaller cross-sections stop interacting with the surrounding matter earlier and hence decouple earlier. Hence a so called sequential thermal/kinetic freeze-out of different hadronic species occurs. Following this, the hadrons freely stream out to the detectors. The freeze-out conditions of a given hadronic specie are thus directly reflected in its transverse momentum and rapidity spectra [1].

Within the framework of the statistical model, the system formed out of a heavy-ion collision is assumed to be in thermal and chemical equilibrium at the final freeze-out stage. The system at freeze-out can be described in terms of a nearly free gas of various hadronic resonances (HRG). The above assumptions are valid with or without the formation of a QGP at the initial stage. It is believed that the produced hadrons also carry information about the collision dynamics and the subsequent space-time evolution of the system. Hence precise measurements of the transverse momentum distributions of identified hadrons along with the rapidity spectra are essential for the understanding of the dynamics and properties of the created matter up to the final freeze-out [2]. The transverse momentum distributions are believed to be encoded with the information about the collective transverse and longitudinal expansions and the thermal temperature at freeze-out.

The particle production in p-p collisions is very important as these can serve as a baseline for understanding the particle production mechanism and extraction of the signals of QGP formation in heavy ion collisions [3]. The value of chemical potential is always lower in p-p collisions than in heavy ion collisions due to the lower stopping power in p-p collisions [4]. At lower energies like SPS and RHIC, the transparency effects are not much prominent and instead nuclear stopping takes place. As one goes to LHC energies, the stopping reduces much further giving rise to nearly zero net baryon density at midrapidity and thus the value of the chemical potential at midrapidity essentially reduces to zero. Thus at LHC, we believe the p-p collisions to be completely transparent.

The p-p collisions at lower energies (SPS and RHIC) were successfully described in the past by using statistical hadronization model [5, 6]. Naively, the p-p collisions are not expected to form QGP or a system with collective hydrodynamic effects. An absence of radial flow in p-p collisions at = 200 GeV and 540 GeV was found in a recent work [7]. However, there have been speculations [8–11] about the possibility of the formation of such a system but of smaller size in the p-p collisions. The occurrence of the high energy density events in high multiplicity p- collisions [12, 13] at CERN-SPS motivated searches for hadronic deconfinement in these collisions at = 0.54 TeV at SPS [8] and at = 1.8 TeV [9, 10] at the Tevatron, Fermilab. A common radial flow velocity for meson and antibaryon found from the analysis of the transverse momentum data of the Tevatron [9] had been attributed to as an evidence for collectivity due to the formation of QGP. [14]

Keeping in view the above facts, we in our present analysis will address the collective flow effect signatures in the p-p collisions at LHC, particularly in terms of transverse flow parameter while attempting to reproduce the transverse momentum distributions of various hadrons produced in p-p collisions at LHC. We will also address the effect of nuclear transparency by studying the rapidity distributions of the hadrons at LHC. We have employed the earlier proposed Unified Statistical Thermal Freeze-out Model (USTFM) which assumes the system at freeze-out to be in a state of local thermochemical equilibrium. We have incorporated the effects of transverse as well as longitudinal hydrodynamic flow in the produced system. A detailed description of our model is available in the references [2, 15–20]. We have employed the strangeness conservation criteria such that the net strangeness in the system is zero.

#### 2. Rapidity Spectra

In Figure 1, we have shown the rapidity distributions of some strange particles like , , and produced in p-p collisions at LHC energy = 0.9 TeV. The available data is taken from the CMS experiment at CERN LHC [21] and is shown by red colored filled shapes in Figure 1. The best fit of the model calculations with the experimental data is obtained by minimizing the distribution of given by [22]where is the measured value of the yield with its statistical uncertainty and is the value from the model calculations. In this analysis, we have taken only the statistical errors into consideration. for fitting the rapidity spectra are minimized with respect to the model variables* a*,* b* and whereas the values of T,* n* and are first obtained by fitting the corresponding distributions. The model parameter defines the chemical potential at midrapidity and the parameter gives the variation of the chemical potential along the rapidity axis in accordance with the equation [15–17, 19, 20]Equation (2) is the outcome of the nuclear transparency effect where in is the baryon chemical potential and =* c*z is the rapidity of the expanding hadronic fluid element along the rapidity axis (z-axis),* c* being the constant of proportionality. The transverse velocity component of the hadronic fireball, , is assumed to vary with the transverse coordinate in accordance with the Blast Wave model aswhere is an index which determines the profile of and is the hadronic fluid surface transverse expansion velocity and is fixed in the model by using the following parameterization [15–17, 19, 20]In the present model, the transverse radius of the fireball formed in the most central collisions is assumed to decrease monotonically along the rapidity axis and is therefore written aswhere the parameter fixes the* transverse* size of the expanding hadronic matter at the freeze-out and *σ* represents the width of the matter distribution.