Advances in High Energy Physics

Volume 2016 (2016), Article ID 6480926, 4 pages

http://dx.doi.org/10.1155/2016/6480926

## Calculating Masses of Pentaquarks Composed of Baryons and Mesons

Department of Physics, University of Kashan, Ghotb Ravandi Boulevard, Kashan 87317-51167, Iran

Received 24 December 2015; Accepted 10 May 2016

Academic Editor: Antonio Ereditato

Copyright © 2016 M. Monemzadeh 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

We consider an exotic baryon (pentaquark) as a bound state of two-body systems composed of a baryon (nucleon) and a meson. We used a baryon-meson picture to reduce a complicated five-body problem to simple two-body problems. The homogeneous Lippmann-Schwinger integral equation is solved in configuration space by using one-pion exchange potential. We calculate the masses of pentaquarks and .

#### 1. Introduction

There are two types of hadrons, baryons and mesons. Baryons are equivalent to the bound states of three quarks, and mesons are known to be the bound states of a quark and an antiquark. However, QCD describes mesons and baryons even with a more intricate structure. There are anomalous mesons such as , , and , as well as exotic baryons like , , and so forth. Pentaquarks are baryons with at least four quarks and one antiquark. In exotic pentaquarks, the antiquark has a flavor different from the other four quarks.

Exotic hadrons containing at least three valence quarks are being studied fairly extensively in modern physics. Although there are hundreds of ordinary hadrons, exotic ones have not been found stable yet. However, QCD does not reject their existence. Pentaquark , studied in photo production experiments [1, 2], is a prototype of exotic hadrons in light and strong quark sector. Theoretically, hadronic reactions contribute to production more vividly than other types of reactions.

The quark model is commonly used to describe hadrons. In this model, mesons are described as and baryons as three-quark composite particles. In a more microscopic view, QCD usually serves to describe the strong interaction. According to Lipkin [3, 4] and Gignoux et al. [5], among pentaquarks, the five-quark anticharmed baryons of and or similar antibeauty baryons are the most bound.

A lot of experimental evidence on the existence of exotic hadrons has been found since 2003. Exotic hadrons’ quantum numbers cannot be justified based on two- and three-quark bound states. Pentaquarks of form are examples of exotic baryon states. Conjugation quantity of charge is not an accurate quantum number for baryons, and all combinations of total spin and parity can exist. However, an exotic baryon combination can be readily identified by its electric charge and its strangeness . Some evidence has been reported during the last few years. For example, the pentaquark was proven to exist in Hermes experiment in Hamburg, Germany [6, 7].

For exotic baryons, we consider the following: : the existence of this exotic baryon was predicted in chiral solution model [8]. It has , , and . It is a narrow light-mass particle of 1540 MeV. These attributes initially made a subject of experimental observation by LEPS [9]. The most suitable hadronic decay mode to identify it is . and : the existence of the bound exotic hadron was predicted through bound Skyrmion approach. This particle has a mass of 2650 MeV and quantum numbers and . An experiment [10] showed a positive signal at a mass of about 3.1 GeV, but it was not confirmed later [11]. In strongly bound states, the decay mode is easy to identify. Likewise, the mass of with the same quantum numbers and was predicted to be 5207 MeV. The possible weak decay mode is . : it is the five-quark state with and . In a quark model which includes color-spin interaction, it can be bound and despite its strong decay, it becomes stable [12]. The mass dependent on the model parameters is predicted to be 2420 MeV. This state was traced in the Fermilab E791 experiment via mode [13] and mode [14].

Lippmann-Schwinger equation for two-body bound states is solved in Section 2. In Section 3, the procedure of the study is given and pentaquark masses are calculated.

#### 2. Lippmann-Schwinger Equation for Two-Body Bound States

In this part, the binding energy of the entire system (pentaquark) is calculated by numerical solution of homogeneous Lippmann-Schwinger equation for each subsystem of bound meson and baryon. Schrodinger equation for a two-body bound state with the potential runs as the following integral equation [16, 17]:where stands for the binding energy of the two-body bound system (meson + baryon). When the interaction potential is considered as function, (1) is of the following eigenvalue form

is the highest positive eigenvalue. The eigenvalue equation is solved through direct method [16–19] using a regularization method [20, 21]. To discretize the integrals, Gauss-Legendre method [22] is employed. 200 grid points are considered for and , whereas 100 mesh points are quite enough for . The kernel of integral equation is diagonized to find in the eigenvalue spectrum. The energy corresponding to will be the system’s binding energy.

#### 3. Numerical Results and Discussion

We consider a pentaquark as a bound state of a two-particle system formed by a baryon and a meson. The hadronic molecular structure consisting of a baryon and a meson is shown in Figure 1.