Advances in High Energy Physics

Volume 2016 (2016), Article ID 1402767, 9 pages

http://dx.doi.org/10.1155/2016/1402767

## Investigation of Pionic Contribution in the Lepton and Antilepton Production Cross Section in p-Cu and p-Pt Collision

Department of Physics, University of Mohaghegh Ardabili, Ardabil, Iran

Received 21 November 2015; Revised 28 March 2016; Accepted 3 April 2016

Academic Editor: Enrico Lunghi

Copyright © 2016 R. Rostami and F. Zolfagharpour. 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

For detailed explanation of the experimental results of lepton production cross section in hadronic collisions such as nucleon-nucleon or nucleon-nuclei, it is of great importance to use quarks and sea quarks distribution function inside free and bound nucleons. In this paper, the role of pion cloud inside the nucleus in the structure function of Cu and Pt nuclei and the EMC ratio of these nuclei were investigated by using harmonic oscillator model. Then, in the framework of the Drell-Yan process and conventional nuclear theory, GRV’s quarks distribution functions and pionic quarks distribution functions were used to calculate lepton and antilepton production cross section in p-Cu and p-Pt scattering. From the results and based on the mentioned model, by considering pionic contribution, the theoretical results are improved.

#### 1. Introduction

Nuclei are made up of protons and neutrons bounded by strong nuclear forces, with the binding energy much less than the rest mass of the nucleons. Therefore, it is expected that scattering cross section of the leptons from nucleus be obtained from noncoherent summation of scattering cross sections from individual bound nucleons [1–5]. Hence this impulse approximation seems to explain the experimental data obtained from relativistic lepton-nucleus or hadronic collision. However, in 1983, the experiment done by a group of European researchers confronted scientists with experimental results which demonstrated that the structure of free and bound nucleons was different [6–8]. It was therefore concluded that some phenomena existed which were responsible for the slight difference in the internal structure of nucleons and consequently in quarks distribution functions in the bound nucleons compared to free nucleons. This change in quark distribution functions, which alters the free nucleons structure functions, is known as the EMC effect. The researches done by many other groups, such as Thomas and his colleagues in the following years [1, 9, 10], showed that pure Fermi motion cannot explain the EMC effect and that binding energy plays an important role. Their effect is the result of nuclear interactions which play an important role in the deep inelastic scattering of leptons from nuclei. However it should be mentioned that the consideration of these phenomena alone is insufficient to explain the difference between quarks distribution functions inside bound and free nucleon. Ericson and Thomas [9] investigated the role of the pion field in the enhancement of the EMC effect in iron. Malace et al. [10] performed an overview of the EMC effect. In this paper, by using the works of mentioned authors and others [3, 9–13] to improve on previous results, the effect of Fermi motion and binding energy and pionic contribution was considered in extracting the quarks distribution functions inside the bound nucleon in the Cu and Pt nucleus, while other phenomena like shadowing effect and quark exchange were disregarded [9]. Therefore, the dileptons production cross section in scattering can be calculated by using the mentioned effects in the framework of conventional nuclear theory and Drell-Yan process. The used model is the harmonic oscillator model that is modified by considering different parameters for occupied nucleon energy state inside nucleus. This modification is done since nucleons in deferent state may be affected by different main field. In the case of less binding energy, better agreement between the theoretical results and experimental data can be achieved compared with the case when the nucleons are affected by fixed main field [14–17]. GRV’s quarks distribution functions for bound nucleons and pions are used for the calculation of quarks distribution inside nucleus [11]. In this work, to investigate the pionic contribution in the lepton and antilepton production cross section in p-Cu and p-Pt collision, by first considering the pionic contribution, the structure function of these nuclei and their corresponding EMC ratio were studied. Then their pionic contribution in quarks distribution functions was probed and finally the amount of this contribution in the dilepton production cross section in p-Cu and p-Pt scattering was computed.

#### 2. Calculation of the Structure Function and EMC Ratio of the ^{63}**Cu** and ^{195}**Pt** Nuclei

^{63}

**Cu**

The nucleus structure function by considering the pion cloud effect is defined as follows [12, 17]:where the first term indicates the pionic contribution and the next term indicates the nucleon contribution in the nucleus structure function. is the fraction of the total momentum of nucleus carried by nucleon in which is the nucleon momentum in the state , . is the momentum transferred from the lepton to the nucleon and is the energy transferred from the lepton to the nucleon. is the Bjorken scaling variable, where is the square of the four-momentum transfer from the lepton. is the pion structure function and is the structure function of free nucleons in which and refer to neutron and proton, respectively. is the distribution function of pion inside the nucleus that is given as follows [17]:where , , is the pion mass, and is the coupling constant. The cut-off parameter plays the most substantial role that shows changes in nuclear environments. When the nucleon is embedded in a nucleus, several modifications, such as the polarization of nuclear medium, occur. These may be expressed by an effective change of . By considering pions and ignoring the contribution made by virtual particles like particle and heavy mesons, the momentum sum rule can be written as follows:where and are the momentum carried by the nucleons and pions, respectively, and are defined as follows:where and represent the mass of nucleus and the mass of nucleons, respectively. In the second term of (1), the first sum is related to the total number of neutrons and protons and the second is related to the quantum number of each energy state. is the occupation number of energy state such that, for protons, and, for neutrons, . Function , which is calculated by the wave functions of harmonic oscillator, describes energy and momentum distribution of nucleons inside the nucleus as follows [12, 13]:where is the mean one nucleon separation energy or, from the other point of view, is the average removal energy that has been considered the same for nucleons in different levels [13]. In this study, was considered to be different for nucleons in different levels.

should satisfy the normalization rule: Taking into consideration the sea quarks and gluons contributions, the structure function of nucleons satisfies the sum rules:In the harmonic oscillator, in the neutral unit could be expressed as follows:where is the mean square radius of state , and its unit is Fermi. The EMC ratio as the ratio of the structure function of nucleus to the deuterium structure function is defined as follows:

#### 3. Drell-Yan Process

In 1970, initial studies of lepton pair production in Hadron-Hadron collision was reported by Christenson et al. [21] as follows:The process of which is shown in Figure 1. The dilepton production cross section is decreased by increasing the dilepton mass. Drell and Yan [22] suggested that, in Hadron-Hadron collision, leptons with opposite sign are produced. In the first stage, a quark of a hadron is annihilated with an antiquark of other hadrons and a virtual photon is generated. The generated photon is converted into lepton pairs with opposite sign like and . This is an electromagnetic process which can be calculated. Many research groups such as Jung and Miller have investigated deep inelastic scattering for different purposes in the framework of the Drell-Yan process [23]. The role of different phenomena, including Fermi motion and binding energy, together with the pionic contribution in nuclear Drell-Yan process has been probed by various case studies [24–26]. In this paper, in order to improve on previous results, the pionic contribution in the dilepton production cross section in the framework of the Drell-Yan process and conventional nuclear theory [3, 9–13] was calculated by using harmonic oscillator model. In order to predict the differential cross section of lepton pairs production in an interaction like Figure 1, an idea of the quarks and antiquarks distribution functions inside and hadrons was necessary. The lepton production cross section in the collision of two hadrons in terms of quarks and antiquarks distribution functions is calculated as follows [27]:where , is the Hadron-Hadron c.m. energy, and is the mass of dileptons. is the correction coefficient known as factor that is considered in order to provide an agreement between the experimental and the theoretical results. is the fractional electric charge of quark . is the th antiquark distribution function inside bound hadron and is th quark distribution function inside the bound hadron , which is defined as follows [28]:where and are the distribution functions of quarks inside the free hadrons [11] and free pions [29].