A partial wave analysis of antiproton–proton annihilation data in flight at 900 \(\mathrm {MeV/}c\) into \({\pi ^0\pi ^0\eta }\), \({\pi ^0\eta \eta }\) and \({K^+K^-\pi ^0}\) is presented. The data were taken at LEAR by the Crystal Barrel experiment in 1996. The three channels have been coupled together with \(\pi \pi \)-scattering isospin I = 0 S- and D-wave as well as I = 1 P-wave data utilizing the K-matrix approach. Analyticity is treated using Chew–Mandelstam functions. In the fit all ingredients of the K-matrix, including resonance masses and widths, were treated as free parameters. In spite of the large number of parameters, the fit results are in the ballpark of the values published by the Particle Data Group. In the channel \({\pi ^0\pi ^0\eta }\) a significant contribution of the spin exotic \(I^G=1^-\) \(J^{PC}=1^{-+}\) \(\pi _1\)-wave with a coupling to \(\pi ^0 \eta \) is observed. Furthermore the contributions of \(\phi (1020) \pi ^0\) and \(K^*(892)^\pm K^\mp \) in the channel \({K^+K^-\pi ^0}\) have been studied in detail. The differential production cross section for the two reactions and the spin-density-matrix elements for the \(\phi (1020)\) and \(K^*(892)^\pm \) have been extracted. No spin-alignment is observed for both vector mesons. The spin density matrix elements have been also determined for the spin exotic wave.

中文翻译：

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$$ {\ bar {p} p} \，\ rightarrow \，\ pi ^ 0 \ pi ^ 0 \ eta $$p¯p→π0π0η，$$ {\ pi ^ 0 \ eta \ eta}的耦合通道分析$$π0ηη和$$ {K ^ + K ^-\ pi ^ 0} $$ K +K-π0在900 MeV / c处以及$$ {\ pi \ pi} $$ππ-散射数据

反质子-质子an灭数据在900 \（\ mathrm {MeV /} c \）到\（{\ pi ^ 0 \ pi ^ 0 \ eta} \），\（{\ pi ^ 0 \ eta \ eta} \）和\（{K ^ + K ^-\ pi ^ 0} \）。数据是通过1996年的Crystal Barrel实验在LEAR上获得的。这三个通道已与\（\ pi \ pi \）耦合在一起利用K矩阵方法，对同位旋I散射I = 0的S和D波以及I = 1的P波数据。使用Chew–Mandelstam函数处理分析性。在拟合中，将K矩阵的所有成分（包括共振质量和宽度）都视为自由参数。尽管有大量参数，但拟合结果仍处于“粒子数据组”（Particle Data Group）发布的值的基础上。在通道\（{\ pi ^ 0 \ pi ^ 0 \ eta} \）中，自旋奇异\（I ^ G = 1 ^-\） \（J ^ {PC} = 1 ^ {-+ } \） \（\ pi _1 \）-与\（\ pi ^ 0 \ eta \）耦合的波。此外，通道中的\（\ phi（1020）\ pi ^ 0 \）和\（K ^ *（892）^ \ pm K ^ \ mp \）的贡献\（{K ^ + K ^-\ pi ^ 0} \）已被详细研究。提取了两个反应的差分生产截面以及\（\ phi（1020）\）和\（K ^ *（892）^ \ pm \）的自旋密度矩阵元素。两个向量介子均未观察到自旋对准。还已经为自旋奇异波确定了自旋密度矩阵元素。