Spectroscopy and Regge trajectories of heavy quarkonia in the relativistic quark model
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ELEMENTARY PARTICLES AND FIELDS Theory
Spectroscopy and Regge Trajectories of Heavy Quarkonia in the Relativistic Quark Model∗ D. Ebert1), R. N. Faustov2), and V. O. Galkin2) Received April 3, 2012
Abstract—The mass spectra of charmonia and bottomonia are calculated in the framework of the relativistic quark model up to high orbital and radial excitations. The Regge trajectories of heavy quarkonia are constructed both in the (J, M 2 ) and (nr , M 2 ) planes, where J is the total angular momentum and nr is the radial quantum number. All daughter trajectories turn out to be almost linear and parallel, while parent trajectories exhibit some nonlinearity. Such nonlinearity occurs only in the vicinity of ground states and few lowest excitations and is more pronounced for bottomonia, while it is only marginal for charmonia. The obtained results are compared with available experimental data, and a possible interpretation of the new charmonium-like states above open charm production threshold is discussed. DOI: 10.1134/S1063778813110057
1. INTRODUCTION At present a vast amount of experimental data on the heavy quarkonium spectroscopy have been accumulated [1]. The number of known states is constantly increasing. Thus, in the last eight years more than ten new charmonium-like states have been discovered [2]. The total number of charmonium states, listed in the Particle Data Group Listings [1], is 25 at present. Some of the new states (such as ηc (2S), hc , χc2(2P ), etc.) are the long-awaited ones, expected by quark models many years ago, while some others, with masses higher than the threshold of the open charm production, have narrow widths and unexpected decay properties [2]. There are theoretical indications that some of these new states could be the first manifestation of the existence of exotic hadrons (tetraquarks, molecules, hybrids, etc.), which are expected to exist in QCD [3]. In order to explore such options, a comprehensive understanding of the heavy quarkonium spectroscopy up to rather high orbital and radial excitations is required. The LHCb Collaboration at the Large Hadron Collider (LHC) plans to search for the bottom counterparts of the newly discovered charmonium-like states [4]. At present, the experimentally known bottomonium spectrum consists of 14 states [1]. Therefore, the investigation of the masses of the excited heavy quarkonium states represents an important and interesting problem. To ∗
The text was submitted by the authors in English. ¨ Physik, Humboldt–Universitat ¨ zu Berlin, GerInstitut fur many. 2) Dorodnicyn Computing Centre, Russian Academy of Sciences, Moscow. 1)
achieve this goal one should treat the quark dynamics in mesons completely relativistically. Here, we extend the approach previously used for the investigations of light meson spectroscopy [5] to heavy quarkonia. In order to improve our description, leading radiative corrections to the heavy quark potential [6] are also taken into account. Such corrections are suppressed by additional powers of αs , which are rather small for
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