Calculation of masses of heavy pentaquark using the NU Method
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ORIGINAL PAPER
Calculation of masses of heavy pentaquark using the NU Method P Sadeghi Alavijeh, N Tazimi* and M Monemzadeh Department of Physics, University of Kashan, Kashan, Iran Received: 13 September 2019 / Accepted: 18 March 2020
Abstract: In this paper, the bound states of pentaquark systems are studied by solving the Schrodinger equation containing Van der Waals potential via Nikiforov–Uvarov method. The binding energies, wave functions and the masses of heavy pentaquarks are calculated. The results are in agreement with the existing ones in the literature. Keywords: Binding energy; Pentaquark bound states; Schrodinger equation; Nikiforov–Uvarov method
1. Introduction In quark model, composite particles may conventionally be mesons consisting of quark–antiquark pairs or baryons consisting of three quarks. Particles not consistent with this model are referred to as exotic hadrons. Murray Gell-Mann and George Zweig proposed the quark model in their independent works in 1964, and they also mentioned the possibility of exotic hadrons such as pentaquarks, but their existence was demonstrated experimentally half a century later. Despite the arguments against pentaquark states, the LHCb collaboration reported the Pc ð4450Þþ and in July 2015. Pc ð4380Þþ pentaquark structures ðuudccÞ Their experiment showed the existence of these heavy pentaquarks contributing to the Kb 0 ! J=w p K decay. Both of these pentaquarks are resonant-energy states of the particle and are thus known as proton and the J=wðccÞ ‘‘charmonium pentaquarks.’’ LHCb team speculate that the pentaquark could be a tightly bound (spherical) system of all five quarks (Fig. 1 left) or a molecular system composed of a weakly bound baryon and a meson (Fig. 1 right) [1]. In the pentaquark case, the LHCb team analyzed data from the decay of Kb 0 ðbudÞ particle (which is formed of three quarks) into three quark-containing particles: a J=w, a proton, and a charged kaon. They discovered that sometimes, when Kb decays, it changes into an intermediate state consisting of a five-quark particle and a kaon.
LHCb collaboration has recently discovered the new particle Pc ð4312Þþ , which accounts for the pentaquark structure reported earlier. This particle decays into a proton and a J=w particle comprising a charm and an anti-charm quark. This observation had a statistical significance of 7:3r (r refers to standard deviation). This exceeds the limit of 5r required to claim the discovery of a new particle. The new particle is lighter compared to Pc ð4450Þþ and Pc ð4380Þþ pentaquark structures. The existence of Pc ð4312Þþ sheds some light into the fundamental nature of the entire family. A very recent analysis at the Rencontres de Moriond QCD conference in March 2019 revealed the structure of Pc ð4450Þþ as consisting of two narrow overlapping peaks, Pc ð4440Þþ and Pc ð4457Þþ , with the twopeak structure. There are a number of works which have studied pentaquark states during the last few years. Santopinto et al. [2] used the constituent quark model to study the
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