arXiv 2205.040752022-05-09hep-phnucl-th

光阵面夸克模型中1 S和2S态重介子的混合效应

Mixing effects on 1S and 2S state heavy mesons in the light-front quark model

Ahmad Jafar Arifi, Ho-Meoyng Choi, Chueng-Ryong ji, Yongseok Oh

备注：: 17 pages, 8 figures, 6 tables. Comments are welcome
发表信息：: Phys.Rev.D 106 (2022) 014009
DOI：: 10.1103/PhysRevD.106.014009

摘要：

在光阵面夸克模型下，分析了$1S$态和$2S$态重赝标（$P$）和矢量（$V$）介子的质量谱和波函数。在我们的质量谱和波函数的分析中采用的重要的经验约束是实验质量间隙关系，$ΔM_P > ΔM_V$，其中$ΔM_{P(V)}=M^{2S}_{P(V)}-M^{1S}_{P(V)}$和$1S$和$2S$介子状态之间的衰变常数，$f_{1S}>f_{2S}$的层次。在库仑加限制势的哈密顿量变分计算中，我们保持了$1S$和$2S$态试探波函数的正交性，并根据重夸克的对称性，对重-重和重-轻$P$和$V$介子的超精细相互作用作微扰处理.考虑到不混合$1S$和$2S$态就不能满足经验约束，我们求出了$1S$和$2S$态之间混合角$θ$的下界为$θ_c = {\rm cot}^{-1}(2\sqrt{6})/2\simeq 6^{\circ}$，并得到了$12^\circ$附近混合角的最佳值，以同时覆盖重夸克的粲味和底味.发现混合效应对$2S$态介子比对$1S$态介子更显著。计算了$1S$和$2S$态介子的质量谱、衰变常数、扭转2分布振幅和电磁形状因子。我们的结果被发现是在一个很好的协议与现有的数据和晶格模拟。特别地，$2S$态赝标$D_s$介子被预测为具有$2600$ MeV的质量，这非常接近LHCb协作组新发现的$D_{s0}(2590)^+$介子的质量。这支持的解释所观察到的状态作为径向激发的$D^+_s$介子。

英文摘要：

The mass spectra and wave functions of both $1S$ and $2S$ state heavy pseudoscalar ($P$) and vector ($V$) mesons are analyzed within the light-front quark model. Important empirical constraints employed in our analysis of the mass spectra and wave functions are the experimental mass-gap relation, $ΔM_P > ΔM_V$, where $ΔM_{P(V)}=M^{2S}_{P(V)}-M^{1S}_{P(V)}$ and the hierarchy of the decay constants, $f_{1S}>f_{2S}$, between $1S$ and $2S$ meson states. We maintain the orthogonality of the trial wave functions of the $1S$ and $2S$ states in our variational calculation of the Hamiltonian with the Coulomb plus confining potentials and treat the hyperfine interaction perturbatively for the heavy-heavy and heavy-light $P$ and $V$ mesons due to the nature of the heavy quark symmetry. Realizing that the empirical constraints cannot be satisfied without mixing of the $1S$ and $2S$ states, we find the lower bound of the mixing angle $θ$ between $1S$ and $2S$ states as $θ_c = {\rm cot}^{-1}(2\sqrt{6})/2\simeq 6^{\circ}$ and obtain the optimum value of the mixing angle around $12^\circ$ to cover both the charm and bottom flavors of the heavy quark. The mixing effects are found to be more significant to the $2S$ state mesons than to the $1S$ state mesons. The properties of $1S$ and $2S$ state mesons including the mass spectra, decay constants, twist-2 distribution amplitudes, and electromagnetic form factors are computed. Our results are found to be in a good agreement with the available data and lattice simulations. In particular, the $2S$ state pseudoscalar $D_s$ meson is predicted to have a mass of $2600$ MeV, which is very close to the mass of the newly discovered $D_{s0}(2590)^+$ meson by the LHCb Collaboration. This supports the interpretation of the observed state as a radial excitation of the $D^+_s$ meson.

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