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arXiv 2105.03355hep-phhep-exnucl-th
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用因子分解法研究$D^0 \to K^0_S K^+ K^-$衰变的Dalitz图

Dalitz plot studies of $D^0 \to K^0_S K^+ K^-$ decays in a factorization approach

J. -P. Dedonder, R. Kamiński, L. Leśniak, B. Loiseau

摘要:

在准二体分解框架内分析了$D^0 \to K^0_S K^+ K^-$过程的$\textit{BABAR}$协作数据。在早期的研究中,假设$D^0$跃迁到两个K介子,以及一个K介子和两个K介子之间的跃迁通过占主导地位的中间共振进行,我们近似它们与K介子形状因子成比例。为了获得良好的拟合,必须将从酉相对论耦合通道模型或色散关系方法导出的标量-K介子形状因子乘以唯象能量依赖函数。考虑了$S$ -、$P$ -和$D$ -波中的末态K介子-K介子相互作用。所有的$S$波通道都以统一的方式处理。的$K^+K^-$和$\bar K^0 K^+$ $S$ -波有效质量平方分布,相空间校正,示出,在一个模型独立的方式,是显着不同的。然后,$f_0(980)$共振必须包含在BABAR分析的方差中。最佳拟合有19个自由参数,并表明i)湮灭振幅的主导地位,ii)在近阈值$K^+K^-$不变质量分布的$f_0(980)$介子的一个大的主导地位和iii)一个相当大的分支分数的$K_S^0 \ [ρ(770)^+ + ρ(1450)^+ + ρ(1700)^+] $最终状态。附录提供了一个更新的确定的isoscalar-scalar介子振幅的基础上扩大的数据集。第二个附录提出了两种替代拟合的基础上计算的标量k介子形状因子的Muskhelishvili-Omnès色散关系的方法。这些拟合的$χ^2$非常接近最佳拟合的$χ^2$,但它们显示出$f_0$和$a_0^0$介子的重要贡献,以及$ρ^+$介子的较弱作用。

英文摘要:

The $\textit{BABAR}$ Collaboration data of the $D^0 \to K^0_S K^+ K^-$ process are analyzed within a quasi two-body factorization framework. In earlier studies, assuming $D^0$ transitions to two kaons and the transitions between one kaon and two kaons to proceed through the dominant intermediate resonances, we approximated them as being proportional to the kaon form factors. To obtain good fits, one has to multiply the scalar-kaon form factors, derived from unitary relativistic coupled-channel models or in a dispersion relation approach, by phenomenological energy-dependent functions. The final state kaon-kaon interactions in the $S$-, $P$- and $D$- waves are taken into account. All $S$-wave channels are treated in a unitary way. The $K^+K^-$ and $\bar K^0 K^+$ $S$-wave effective mass squared distributions, corrected for phase space, are shown, in a model-independent manner, to be significantly different. Then the $f_0(980)$ resonance must be included at variance with the BABAR analysis. The best fit has 19 free parameters and indicates i) the dominance of annihilation amplitudes, ii) a large dominance of the $f_0(980)$ meson in the near threshold $K^+K^-$ invariant mass distribution and iii) a sizable branching fraction to the $K_S^0 \ [ρ(770)^+ + ρ(1450)^+ + ρ(1700)^+] $ final states. An appendix provides an update of the determination of the isoscalar-scalar meson-meson amplitudes based on an enlarged set of data. A second appendix proposes two alternative fits based on scalar-kaon form factors calculated from the Muskhelishvili-Omnès dispersion relation approach. These fits have $χ^2$ quite close to that of the best fit but they show important contributions from both the $f_0$ and $a_0^0$ mesons and a weaker role of the $ρ^+$ mesons.

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