Bottomonium spectroscopy using Coulomb plus linear (Cornell) potential

Abstract

The coulomb plus linear (Cornell) potential is used to investigate the mass spectrum of bottomonium. Gaussian wave function is used in position and momentum space to estimate values of potential and kinetic energies, respectively. Based on our calculations, we study newly observed Υ (10860) as an admixture of 43 S 1 with 4 3 D 1 , and Υ (10753) as an admixture of 6 3 S 1 with 4 3 D 1 also, we try to assign Υ(11020) as a pure 43 D 1 bottomonium state. We also study the Regge trajectories in the (J, M 2 ) and (n r , M 2 ) planes to help prove our association. We estimate the pseudoscalar and vector decay constants, the radiative (Electric and Magnetic Dipole) transition rates, and the annihilation decay width for bottomonium states. PACS. XX.XX.XX No PACS code given 1 Introduction Bottomonium (bb meson) was discovered as Υ, Υ ′ and Υ ′′ by the E288 Collaboration at Fermilab in 1977, and were substantially studied at various e + e − storage rings[1,2]. In 1982, χ bJ (2P ) states and in 1983, χ bJ (2P ), (J = 1, 2, 3) states were discovered in E1 transition from Υ ′′ [3,4] and Υ ′ [5,6], respectively. In 1984, Υ(4S), Υ(5S) and Υ(6S) states were observed [7,8]. In 2008, after three decade of discovery of Υ(nS) resonance, the BaBar Collaboration found η b , the pseudoscalar partner of the triplet state Υ(1S)[9]. In 2012, the Belle collaboration reported the first evidence of the η b (2S) with mass 9999 ± 3.5 +2.8 −1.9 ,M eV /c 2 using h b (2P ) → γη b (2S) transition and first observation of h b (1P ) → γη b (1S) and h b (2P ) → γη b (1S) with mass 9402 ± 1.5 ± 1.8 M eV /c 2 [10]. In 2004, CLEO Collaboration presented the first evidence for the production of Υ(1S)(1D) states in the fourphoton cascade, such as in a two-photon cascade starting from the Υ(3S) → γχ b (2P J ), χ b (2P J ) → γΥ(1D) and then select events with two more subsequent photon transitions, Υ(1D) → γχ b (1P J ), χ b (1P J ) → γΥ(1S), followed by the Υ(1S) annihilation into either e + e − or µ + µ − [11]. In 2010, the BABAR Collaboration reported the observation of the J = 2 state of Υ(1 3 D J ) in the hadronic π + π − Υ(1S) decay channel, with Υ(1S) → e + e − or µ + µ − [12]. In 2011, BABAR Collaboration reported evidence for the h b (1P ) state in the decay Υ(3S) → π0h b (1P ), with data sample corresponds to 28 f b −1 of integrated luminosity at a center of mass energy of 10.355 GeV, the mass of the Υ(3S) resonance and in the same year, the Belle Collaboration reported the first observation of the spin-singlet bottomonium states h b (1P ) and h b (2P ) produced via e + e − → h b (nP )π + π − transition corresponds to 121.4 f b −1 of integrated luminosity near the peak of the Υ(5S) resonance at a center-of-mass energy √ s ∼ 10.865 GeV[13]. Again in 2011, ATLAS Collaboration observed the χ b (nP ) states, recorded by the ATLAS detector during the proton-proton collisions at the LHC, run at a center-of-mass energy √ s ∼ 7 T eV and these states were reconstructed through their radiative decays to Υ(1S, 2S) with Υ → µ + µ − . In addition to the mass pea...

Mass spectra of $Ξ_{cc}$, $Ξ_{bc}$, $Ω_{cc}$, and $Ω_{bc}$ baryons in Regge Phenomenology

“…The Regge trajectories have been demonstrated to be nonlinear in several studies [34,35,36,37]. Generally the nonlinear behaviour of Regge trajectories are observed in quarkonia [38,39,40,41]. Although string-like or semi relativistic potential models may show a linear relationship between hadron mass squared and quantum numbers.…”