Mass spectrum of charmonium is computed in the framework of potential non-relativistic quantum chromodynamics. \textit{O}$(1/m)$ and \textit{O}$(1/m^2)$ relativistic corrections to the Cornell potential and spin-dependent potential have been added, and is solved numerically. New experimentally observed and modified positive and negative parity states like ${{\boldsymbol \psi}{(4230)}}$, ${{\boldsymbol \psi}{(4260)}}$, ${{\boldsymbol \psi}{(4360)}}$, ${{\boldsymbol \psi}{(4390)}}$, ${{\boldsymbol \psi}{(4660)}}$, ${{\boldsymbol \chi}_{c1}{(4140)}}$ and ${{\boldsymbol \chi}_{c1}{(4274)}}$ near open-flavor threshold have also been studied. We explain them as admixtures of S-D wave states and P-wave states. Apart from these states, some other states like ${{\mathit X}{(3915)}}$, ${{\boldsymbol \chi}_{c1}{(3872)}}$, ${{\boldsymbol \psi}{(3770)}}$ and ${{\boldsymbol \psi}{(4160)}}$ have been identified as $2^3P_0$, $2^3P_1$, $1^3D_1$ and $2^3D_1$ states. Subsequently, the electromagnetic transition widths and $\gamma\gamma$, $e^+e^-$, light hadron and $\gamma\gamma\gamma$ decay widths of several states are calculated at various leading orders. All the calculated results are compared with experimental and results from various theoretical models.

中文翻译：

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由 pNRQCD 的一般特征激发的 Charmonium 光谱

Charmonium 的质谱是在潜在的非相对论量子色动力学框架下计算的。\textit{O}$(1/m)$ 和 \textit{O}$(1/m^2)$ 对康奈尔势和自旋相关势的相对论修正已被添加，并以数值方式解决。新的实验观察和修改的正负奇偶校验状态，如 ${{\boldsymbol \psi}{(4230)}}$, ${{\boldsymbol \psi}{(4260)}}$, ${{\boldsymbol \psi }{(4360)}}$, ${{\boldsymbol \psi}{(4390)}}$, ${{\boldsymbol \psi}{(4660)}}$, ${{\boldsymbol \chi}_ {c1}{(4140)}}$ 和 ${{\boldsymbol \chi}_{c1}{(4274)}}$ 接近开放风味阈值也进行了研究。我们将它们解释为 SD 波状态和 P 波状态的混合物。除了这些状态，其他一些状态如 ${{\mathit X}{(3915)}}$, ${{\boldsymbol \chi}_{c1}{(3872)}}$, ${{\boldsymbol \psi}{(3770)}}$ 和 ${{\boldsymbol \psi}{(4160)}}$ 已被识别为 $2^3P_0$、$2^3P_1$、$1^3D_1$ 和$2^3D_1$ 个州。随后，计算了几种状态的电磁跃迁宽度和$\gamma\gamma$、$e^+e^-$、光强子和$\gamma\gamma\gamma$ 衰变宽度在不同的领先阶数。所有计算结果都与实验和各种理论模型的结果进行了比较。