交叉对称约束下弹性散射数据酉多道再分析的$ρ(1250)$的强有力证据
Strong evidence of $ρ(1250)$ from a unitary multichannel reanalysis of elastic scattering data with crossing-symmetry constraints
摘要：
分析弹性$P$波$ππ$相移和非弹性高达2 GeV，旨在确定相应的$J^{PC}=1^{--}$激发$ρ$共振和专注于$ρ(1250)$与$ρ(1450)$的争议。该方法采用了一种改进的参数化方面的一个明显的单一的和分析的三通道$S$ -矩阵与其复杂的能量极点位置。所包括的通道是$ππ$、$\rho2π$和$ρρ$，后两个通道在模拟几种实验观察到的具有附近阈值的衰减模式的意义上是有效的。在另一种拟合中，$\rho2π$模式被$ωπ$取代，后者也是实验相关通道。相对于先前的工作的改进相当于通过一次减去色散关系称为GKPY方程的最大交叉对称性的强制执行。一个单独的分析涉及π介子电磁形状因子，这再次证明了在处理非常广泛和高度非弹性共振时保证幺正性和解析性的巨大重要性。在$ρ(1250)$与$ρ(1450)$的情况下，不这样做的结果表明，引起约170兆电子伏的预测质量的错误。从这些分析中可以清楚地看出，在2 GeV以下有5种$ρ$矢量态，即$ρ(770)$、$ρ(1250)$、$ρ(1450)$、$ρ(1600)$和$ρ(1800)$，其中$ρ(1250)$无疑是最重要的激发态$ρ$共振。的稳定性，以及实施的统一性，解析性和近似交叉对称性的分析提供了非常有力的支持，这些任务。介子光谱可能产生的深远影响进行了讨论。
英文摘要：
An analysis is presented of elastic $P$-wave $ππ$ phase shifts and inelasticities up to 2 GeV, aimed at identifying the corresponding $J^{PC}=1^{--}$ excited $ρ$ resonances and focusing on the $ρ(1250)$ vs. $ρ(1450)$ controversy. The approach employs an improved parametrization in terms of a manifestly unitary and analytic three-channel $S$-matrix with its complex-energy pole positions. The included channels are $ππ$, $\rho2π$, and $ρρ$, the latter two being effective in the sense that they mimic several experimentally observed decay modes with nearby thresholds. In an alternative fit, the $\rho2π$ mode is replaced by $ωπ$, which is also an experimentally relevant channel. The improvement with respect to prior work amounts to the enforcement of maximum crossing symmetry through once-subtracted dispersion relations called GKPY equations. A separate analysis concerns the pion electromagnetic form factor, which again demonstrates the enormous importance of guaranteeing unitarity and analyticity when dealing with very broad and highly inelastic resonances. In the case of $ρ(1250)$ vs. $ρ(1450)$, the failure to do so is shown to give rise to an error in the predicted mass of about 170 MeV. A clear picture emerges from these analyses, identifying five vector $ρ$ states below 2 GeV, viz. $ρ(770)$, $ρ(1250)$, $ρ(1450)$, $ρ(1600)$, and $ρ(1800)$, with $ρ(1250)$ being indisputably the most important excited $ρ$ resonance. The stability of the fits as well as the imposition of unitarity, analyticity, and approximate crossing symmetry in the analyses lend very strong support to these assignments. The possibly far-reaching consequences for meson spectroscopy are discussed.
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