在先前开发的幺正和解析耦合通道形式主义的框架中研究了双介子跃迁$Υ(10860)\toπ^+π^-Υ(nS)$（$n=1,2,3$），用于分析底偶态$Z_b(10610)$和$Z_b(10650)$的实验数据[Phys. Rev. D 98，074023（2018）]并预测其自旋伙伴的性质[Phys. Rev. D 99，094013（2019）]。在这项工作中，我们使用一个相对简单，但现实的版本，这种方法，其中的散射和生产振幅的构造只采用短程之间的相互作用的开放和隐藏的味道通道符合重夸克自旋对称性的约束，扩展分析的实验线的形状。特别地，从$Υ(10860)$到之前已经研究过的最终状态$ππh_b(mP)$（$m=1,2$）和$πB^{(*)}\bar B^* $的转变现在被$Υ(10860)\toπ^+π^-Υ(nS)$最终状态（$n=1,2,3$）增强。这是通过采用色散理论来解释$ππ$子系统的终态相互作用，包括其与$K\bar K$通道的耦合来实现的。对$π^+π^-Υ$最终状态的二维Dalitz图进行拟合。调整两个实减法常数以实现对每个PDMATHAMBMX $(n=1,2,3)$的Dalitz图的最佳描述，同时与PDMATHAMBMZ的性质相关的所有参数从先前的研究中保持固定。在这项工作中实现的所有$Υ(10860)\toπ^+π^-Υ(nS)$通道的数据的一个很好的整体描述提供了额外的强有力的支持$Z_b$状态的分子解释。
英文摘要：
The dipion transitions $Υ(10860)\toπ^+π^-Υ(nS)$ ($n=1,2,3$) are studied in the framework of a unitary and analytic coupled-channel formalism previously developed for analysing experimental data on the bottomoniumlike states $Z_b(10610)$ and $Z_b(10650)$ [Phys. Rev. D 98, 074023 (2018)] and predicting the properties of their spin partners [Phys. Rev. D 99, 094013 (2019)]. In this work we use a relatively simple but realistic version of this approach, where the scattering and production amplitudes are constructed employing only short-ranged interactions between the open- and hidden-flavour channels consistent with the constraints from heavy quark spin symmetry, for an extended analysis of the experimental line shapes. In particular, the transitions from the $Υ(10860)$ to the final states $ππh_b(mP)$ ($m=1,2$) and $πB^{(*)}\bar B^* $ already studied before, are now augmented by the $Υ(10860)\toπ^+π^-Υ(nS)$ final states ($n=1,2,3$). This is achieved by employing dispersion theory to account for the final state interaction of the $ππ$ subsystem including its coupling to the $K\bar K$ channel. Fits to the two-dimensional Dalitz plots for the $π^+π^-Υ$ final states were performed. Two real subtraction constants are adjusted to achieve the best description of the Dalitz plot for each $Υ(nS)$ $(n=1,2,3)$ while all the parameters related to the properties of the $Z_b$'s are kept fixed from the previous study. A good overall description of the data for all $Υ(10860)\toπ^+π^-Υ(nS)$ channels achieved in this work provides additional strong support for the molecular interpretation of the $Z_b$ states.
Dipion transitions from $X(3872)$ to $χ_{cJ}\ (J=0,1,2)$
School of Physics, Henan Normal University（河南师范大学物理学院）；School of Physics, Southeast University（东南大学物理学院）；Lanzhou Center for Theoretical Physics, Lanzhou University（兰州大学理论物理中心）；College of Physics and Engineering, Qufu Normal University（曲阜师范大学物理工程学院）
γ* N → Δ（1232）跃迁是研究强子形变、微扰QCD在中等动量转移下的适用性以及非微扰现象对强子观测量影响的一个窗口。我们解释说，阿什公约的磁跃迁形状因子必须下降快于中子的磁形状因子和非零值的相关四极比揭示了夸克轨道角动量的核子和Δ（1232）的影响，并表明，这些四极比确实接近其预测的渐近极限，虽然缓慢。
