Charmonium resonances with JPC=1−− and 3−−

Abstract

We present a lattice QCD study of charmonium resonances and bound states with J P C = 1 −− and 3 −− near the open-charm threshold, taking into account their strong transitions toDD. Vector charmonia are the most abundant in the experimentally established charmonium spectrum, while recently LHCb reported also the first discovery of a charmonium with likely spin three. TheDD scattering amplitudes for partial waves l = 1 and l = 3 are extracted on the lattice by means of the Lüscher formalism, using multiple volumes and inertial frames. Parameterizations of the scattering amplitudes provide masses and widths of the resonances, as well as the masses of bound states. CLS ensembles with 2+1 dynamical flavors of non-perturbatively O(a) improved Wilson quarks are employed with mπ 280 MeV, a single lattice spacing of a 0.086 fm and two lattice spatial extents of L = 24 and 32. Two values of the charm quark mass are considered to examine the influence of the position of theDD threshold on the hadron masses. For the lighter charm quark mass we find the vector resonance ψ(3770) with mass m = 3780(7) MeV and coupling g = 16.0( +2.1 −0.2 ) (related to the width), both consistent with their experimental values. The vector ψ(2S) appears as a bound state with m = 3666(10) MeV. The charmonium resonance with J P C = 3 −− is found at m = 3831( +10 −16 ) MeV, consistent with the X(3842) recently discovered by LHCb. At our heavier charm-quark mass the ψ(2S) as well as the ψ(3770) are bound states and the X(3842) remains a resonance. We stress that all quoted uncertainties are only statistical, while lattice spacing effects and the approach to the physical point still need to be explored. This study of conventional charmonia sets the stage for more challenging future studies of unconventional charmonium-like states.

Charmonium-like resonances with JPC = 0++, 2++ in coupled $$ \mathrm{D}\overline{\mathrm{D}} $$, $$ {\mathrm{D}}_{\mathrm{s}}{\overline{\mathrm{D}}}_{\mathrm{s}} $$ scattering on the lattice

“…Two lattice volumes are employed for the charmonium system at rest and in flight. This analysis uses the same lattice setup as our previous article on the identification of the spin and parity of the single hadron spectrum [24] and the investigation of single channel DD scattering for J P C = 1 −− and 3 −− [25]. While the present study represents a significant improvement on previous work, some simplifications remain and a comparison of the results for the masses and widths with experiment is qualitative.…”

Hadron Spectroscopy

“…The added difficulty for a lattice calculation to extract a state is that multiple partial waves, namely, = 1 and 3 must be determined. A first study of this system [43] has presented encouraging results.…”

Lattice spectroscopy (focus on exotics)

“…Five excited Ω * c : css LHCb [14] discovered five excited Ω * c and Belle recently confirmed four of them [15]. All these states were predicted by lattice QCD already in 2013 [13]: there are indeed five states in the energy region between 3.0 − 3.2 GeV in Fig 3a. This lattice study predicted their quantum numbers to be 1/ Charmonia with J PC = 3 −− and 1 −− :cc Charmonium resonances with J PC = 3 −− and 1 −− have been extracted from lattice QCD by simulating DD scattering in partial waves l = 3, 1 [17], as described in Section 2. The resonance with J PC = 3 −− was found at a mass that is in agreement with the very recent LHCb discovery of a first charmonium X(3842) with spin three [18] (Fig.…”

“…The resonance masses of charmonia with J PC = 3 −− and 1 −− , extracted from lattice[17] and compared to experiment[18].P c pentaquarks:ccuud The LHCb experiment confirmed/discovered three P c pentaquarks near Σ + cD ( * ) thresholds in 2019…”