论文标题
$ j^{pc} = 0^{++}，2^{++} $ in耦合$ d \ bar d $，$ d_s \ bar d_s $ sckaties in lattice in lattice，
Charmonium-like resonances with $J^{PC}=0^{++},2^{++}$ in coupled $D\bar D$, $D_s\bar D_s$ scattering on the lattice
论文作者
论文摘要
我们介绍了耦合通道$ d \ bar d $和$ d_s \ bar d_s $ scatting在$ j^{pc} = 0^{++} $和$ 2^{++} $ channels中的第一个晶格调查。部分波的散射矩阵$ l = 0,2 $和iSospin零是使用吕沙尔的形式主义使用多卷和惯性框架确定的。使用$m_π\ simeq280 $ mev，$ a \ simeq 0.09 $ fm和$ l/a = 24，〜32 $的晶格QCD合奏。产生的散射矩阵表明，在能量区域中存在$ j^{pc} = 0^{++} $的三个类似charmonium状态，范围从略低于$ 2M_D $至4.13 GEV。我们发现一个尚未观察到的$ d \ b d $绑定状态刚低于阈值，$ d \ bar d $共振可能与$χ_{c0}（3860）$有关，据信为$χ_{C0}（2p）$。此外，还有一个指示，有一个狭窄的$ 0^{++} $共振在$ d_s \ bar d_s $ threshold以下，大耦合到$ d_s \ bar d_s $，并且非常小的耦合到$ d \ bar d $。此共振可能与狭窄的$ x（3915）$/$χ_{c0}（3930）$在实验中观察到的$也略低于$ d_s \ bar d_s $。部分波$ l = 2 $具有与$χ_{C2}（3930）$有关的共振。我们使用几个假设，例如省略$ j/ψΩ$，$η_cη$和三粒子通道。仅量化统计不确定性，而对物理夸克大小和连续限制的外推是未来的挑战。
We present the first lattice investigation of coupled-channel $D\bar D$ and $D_s\bar D_s$ scattering in the $J^{PC}=0^{++}$ and $2^{++}$ channels. The scattering matrix for partial waves $l=0,2$ and isospin zero is determined using multiple volumes and inertial frames via Lüscher's formalism. Lattice QCD ensembles from the CLS consortium with $m_π\simeq280$ MeV, $a \simeq 0.09 $ fm and $L/a=24,~32$ are utilized. The resulting scattering matrix suggests the existence of three charmonium-like states with $J^{PC}=0^{++}$ in the energy region ranging from slightly below $2m_D$ up to 4.13 GeV. We find a so far unobserved $D\bar D$ bound state just below threshold and a $D\bar D$ resonance likely related to $χ_{c0}(3860)$, which is believed to be $χ_{c0}(2P)$. In addition, there is an indication for a narrow $0^{++}$ resonance just below the $D_s\bar D_s$ threshold with a large coupling to $D_s\bar D_s$ and a very small coupling to $D\bar D$. This resonance is possibly related to the narrow $X(3915)$/$χ_{c0}(3930)$ observed in experiment also just below $D_s\bar D_s$. The partial wave $l=2$ features a resonance likely related to $χ_{c2}(3930)$. We work with several assumptions, such as the omission of $J/ψω$, $η_cη$ and three-particle channels. Only statistical uncertainties are quantified, while the extrapolations to the physical quark-masses and the continuum limit are challenges for the future.
