Charmonium spectroscopy motivated by general features of pNRQCD

New puzzle in charmonium decays

“…The partial width of η c (2S) → γγ of (2.21 +0.88 −0.64 ) keV is a first model-independent evaluation, to be compared with various calculations compiled in Ref. [22]. It is worth to point out that the ratio of the branching fractions of η c (2S) and η c → γγ agrees fairly well with the Q P = 1 rule:…”

“…The partial width of η c → γγ, (5.43 +0.41 −0.38 ) keV, is about one standard deviation higher than the world average [10] and is lower than the lattice QCD calculation of Γ ηc→γγ = (6.51 ± 0.20) keV [21] by 2.5 standard deviations. Further measurements and refined calculations are needed to clarify the tension and to develop other model calculations [22].…”

Calculation of the One-loop Box Integral at Finite Temperature and Density

“…The instanton effects are also studied in another model with six parameters [6]. The mass spectrum was calculated in the framework of non-relativistic QCD, with seven parameters [7]. The charmonium properties were studied by solving the Schrödinger equation with the discrete variable representation method [8].…”

Mass Spectrum and Decay Constants of Heavy Quarkonia

“…The thresholds for the charmonium and bottomunium systems are approximately 3.71 and 10.50 GeV, respectively [2]. Many charmonium and bottomonium states below thresholds have been experimentally observed and theoretically studied through various relativistic and non-relativistic potential models [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and approaches like chiral perturbation theory [20], heavy quark effective field theory, lattice QCD [21][22][23][24][25][26][27][28][29][30][31], QCD sum rules [32][33][34][35][36][37][38], NRQCD [39][40][41], and dynamical equations based approaches like Bethe Salpeter and Dyson-Schwinger equations [41][42][43][44]. The heavy quarkonia were observed so far, still have many puzzles [17].…”