Status of quarkonia-like negative and positive parity states in a relativistic confinement scheme

Abstract

Properties of quarkonia-like states in the charm and bottom sector have been studied in the frame work of relativistic Dirac formalism with a linear confinement potential. We have computed the mass spectroscopy and decay properties (vector decay constant and leptonic decay width) of several quarkonia-like states. The present study is also intended to identify some of the unexplained states as mixed P-wave and mixed S-D-wave states of charmonia and bottomonia. The results indicate that the X(4140) state can be an admixture of two P states of charmonium. And the charmoniumlike states X(4630) and X(4660) are the admixed state of S-D-waves. Similarly, the X (10610) state recently reported by Belle II can be mixed P-states of bottomonium. In the relativistic framework we have computed the vector decay constant and the leptonic decay width for S wave charmonium and bottomonium. The leptonic decay widths for the J PC = 1 −− mixed states are also predicted. Further, both the masses and the leptonic decay width are considered for the identification of the quarkonia-like states.

Importance of confinement in instanton induced potential for bottomonium spectroscopy

“…For the masses of P and D waves, we have incorporated the contribution of the spin-orbit and tensor part of the confined one gluon exchange potential (COGEP) of the form given by [77,78,93,[110][111][112]…”

“…For mesons λ i .λ j qq = − 4 3 [115]. Expression for the confined gluon propagators are taken from [77,93] as,…”

“…where, α 1 = 1.035, α 2 = 0.3977 GeV, c 0 = 0.3418 GeV, γ = 0.8639 and c 2 = 0.4123 GeV are used here as the same as used in previous study of quarkonium states [93].…”

Spectroscopy and decay properties of charmonium

“…[60] suggest that X(4274) can be a good candidate for the conventional χ c1 (3 3 P 1 ) state. Study of charmonium in relativistic Dirac formalism with linear confinement potential indicate that the X(4140) state can be admixture of two P states whereas X(4630) and X(4660) are the admixed of S-D wave state [61].…”

Masses of tetraquark states in the hidden charm sector above D − D⁎ threshold

“…The diquark -diantiquark picture for tetraquark configuration is one of the most promising approach to understand the structure of many exotic mesonic states as the diquark-diantiquark structure is a strongly correlated system [16]. The confinement masses of quarks and antiquarks are obtained through a mean-field linear potential of the form [17],…”