Hunting for states in the recent LHCb di-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>J</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:mi>ψ</mml:mi></mml:math> invariant mass spectrum
Ze-Rui Liang, Xiao-Yi Wu, De-Liang Yao
Abstract
Partial wave analysis is performed, with effective potentials as dynamical inputs, to scrutinize the recent LHCb data on the di-$J/\ensuremath{\psi}$ invariant mass spectrum. Coupled-channel effects are incorporated in the production amplitude via final state interactions. The LHCb data can be well described. A dynamically generated pole structure, which can be identified as the $X(6900)$ state, is found. Our analysis also provides hints for the existence of three other possible states: a bound state $X(6200)$, a broad resonant state $X(6680)$ and a narrow resonant state $X(7200)$. The ${J}^{PC}$ quantum numbers of the $X(6680)$ and $X(6900)$ states should be ${2}^{++}$, while the $X(6200)$ and $X(7200)$ states prefer ${0}^{++}$. To determine the above states more precisely, more experimental data for the channels, such as $J/\ensuremath{\psi}\ensuremath{\psi}(2S)$, $J/\ensuremath{\psi}\ensuremath{\psi}(3770)$, di-$\ensuremath{\psi}(2S)$, are required.