Quarkonia and quantum chromodynamics

The hidden-charm pentaquark and tetraquark states

“…They suggested this new resonance X(3823) as the 1 3 D 2 charmonium state with J PC = 2 −− . The mass and radiative decay behavior agree with the theoretical predictions for the 1 3 D 2 state [113,114,115,17,116,117]. Recently, the BESIII Collaboration confirmed the X(3823) resonance in the process of e + e − → π + π − X(3823) → π + π − γχ c1 at 6.2σ, with a mass (3821.7 ± 1.3 ± 0.7) MeV and width less than 16 MeV at the 90% C.L.…”

“…2.1.1.7, the X(3823) agrees with the theoretical predictions for the 1 3 D 2 state [113,114,115,17,116,117]. The 1 3 D 2 charmonium state with J PC = 2 −− is expected to be very narrow.…”

Bottom quark mass and αs from the ϒ system

“…1 The spectral function R (2) l (v) is known analytically and R (2) F (v) receives contributions from a two-particle cut with threshold at 2M which is known analytically and a four-particle cut with threshold at 4M which can be calculated numerically from a two-dimensional integral [30,31]. These results can be used to check the reliability of the Padé approximation for the moments.…”

“…However, the method of Padé approximants has been recently exploited to calculate Π (2) numerically, using available results at high energies (s → −∞), analytical results for the first seven moments M (2) i for i = 1, . .…”

“…The bottom quark mass is sufficiently heavy for a nonrelativistic description to be a good starting point to analyze the quark-antiquark forces. Thus, potential models -including relativistic corrections -have been successfully used to understand the spectroscopy of the corresponding mesonic bound states [1][2][3]. At the same time, the small size of the hadronic system makes possible to attempt a short-distance approach.…”