Mesons and Glueballs, the Strong Effective Coupling within Analytic Confinement
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esons and Glueballs, the Strong Effective Coupling within Analytic Confinement Gurjav Ganbolda, b, * aBogoliubov
bInstitute
Laboratory of Theoretical Physics, JINR, Dubna, 141980 Russia of Physics and Technology, Mongolian Academy of Sciences, Ulaanbaatar, 13330 Mongolia *e-mail: [email protected] Received December 20, 2019; revised January 16, 2020; accepted January 29, 2020
Abstract—The phenomena of hadron mass generating, strong running coupling and radiative transitions of charmonium excited states have been studied in the framework of a relativistic field model with analytic confinement. A meson mass equation is derived and a specific new behavior of the mass-dependent strong coupling α s is revealed in the time-like region. A new infrared fixed point α s(0) = 1.032 has been found at origin. Independent and new estimates on the scalar glueball mass, radius and gluon condensate value have been performed. The spectrum of conventional mesons have been calculated by introducing a minimal set of parameters with relative errors less than 1.8 percent compared to the latest data. Accurate estimates of the leptonic decay constants of pseudoscalar and vector mesons have also been performed. Partial decay widths of the dominant radiative transitions of the charmonium orbital excitations have been estimated with reasonable accuracy. DOI: 10.1134/S1063779620040309
1. INTRODUCTION The low-energy region below ∼2 GeV becomes a testing ground, where much novel, interesting and challenging behavior is revealed in particle physics (see, e.g., [1]) while the inefficiency of the conventional perturbation theory in low-energy domain pushes particle physicists to develop and use different phenomenological and nonperturbative approaches. Any QCD-inspired theoretical model should be able to correctly describe hadron phenomena such as quark confinement, running strong coupling, generation of hadron mass etc. at large distances. The confinement conception explaining the nonobservation of color charged particles is a crucial feature of QCD and a great number of theoretical models have been suggested to explain the origin of confinement. A simple and reliable working tool implementing the confinement concept is still required. The strength of quark-gluon interaction g in QCD depends on the momentum transfer Q and this is described theoretically by the renormalization group equations. This dependence α s (Q) g 2 (4π) is determined well in experiments at relatively high energies [2] but the low-energy (or, infrared—IR) behavior of α s has not been well defined yet, it needs to be more specified. The hadron mass origin is one of the challenges to particle physics because the Standard Model intro-
duces only fundamental particles and does not explain the appearance of the multitude of observed massive hadrons. The calculation of hadron mass spectra in a quality comparable to precise experimental data still remains a key problem. Recently, the Particle Data Group [1] has reported that the treatment of the branching ratios of the charm
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