AI 中文总结
本工作基于BESIII数据，在手征幺正方法中研究$D_s^+ \to π^+ π^0 π^0 η$的两种衰变机制，解释相关共振的产生及不变质量谱特征，发现加入额外共振仅小幅改善拟合。
AI 中文摘要
本工作基于BESIII数据，从理论上研究$D_s^+ \to π^+ π^0 π^0 η$的衰变机制，考虑两种机制：一是两个动力学产生的共振的产生，即$D_s^+ \to a_0(980)^+ f_0(500,980)$；二是含一个动力学产生的共振的过程，即$D_s^+ \to a_1(1260)^+\boldsymbol{\text{η}}$。第一种机制中，包含$\boldsymbol{π^+η}$与$\boldsymbol{K^+\bar{K}^0}$的相互作用以产生$a_0(980)^+$，同时采用涉及$\boldsymbol{π^+π^-}$、$\boldsymbol{π^0π^0}$、$\boldsymbol{K^+K^-}$、$\boldsymbol{K^0\bar{K}^0}$、$\boldsymbol{ηη}$及$\boldsymbol{π^0η}$的耦合道相互作用以产生$f_0(500)$与$f_0(980)$。第二种机制中，包含$\boldsymbol{πρ}$与$\boldsymbol{\bar{K}^*{K} - K^*\bar{K}}$道以产生$a_1(1260)$。基于这些相互作用，在手征幺正方法中计算振幅，并用于计算$D_s^+ \to π^+ π^0 π^0 η$的不变质量谱。结果表明，$\boldsymbol{π^+η}$不变质量谱中1000 MeV附近的峰可被很好地解释为来自尖点效应的$a_0(980)^+$；与$f_0(500)$一同产生的$f_0(980)$是$\boldsymbol{π^0π^0}$谱中1000 MeV附近小结构的成因；$a_1(1260)^+$及其衰变至$\boldsymbol{ρ^+π^0}$、随后$\boldsymbol{ρ^+}$衰变，可很好地描述$\boldsymbol{π^+π^0π^0}$与$\boldsymbol{π^+π^0}$的质量谱；在$\boldsymbol{π^+η}$谱中加入额外的800 MeV附近的共振，仅使拟合得到边缘改善。
英文摘要
In this work, we theoretically investigate the decay mechanism of $D_s^+ \to π^+ π^0 π^0 η$ based on BESIII data, considering two mechanisms: the production of two dynamically generated resonances, $D_s^+ \to a_0(980)^+ f_0(500,980)$, and a process with one dynamically generated resonance, $D_s^+ \to a_1(1260)^+η$. In the first mechanism, the interactions $π^+η$ and $K^+\bar{K}^0$ are included to generate the $a_0(980)^+$, while coupled-channel interactions involving $π^+π^-$, $π^0π^0$, $K^+K^-$, $K^0\bar{K}^0$, $ηη$, and $π^0η$ are adopted to generate the $f_0(500)$ as well as the $f_0(980)$. For the second mechanism, the $πρ$ and $\bar{K}^*{K} - K^*\bar{K}$ channels are included to generate the $a_1(1260)$. With these interactions, the amplitudes are calculated in the chiral unitary approach and used to compute the invariant mass spectra of $D_s^+ \to π^+ π^0 π^0 η$. The results suggest that the peak near 1000~\text{MeV} in the $π^+η$ invariant mass spectrum can be well interpreted as the $a_0(980)^+$ arising from a cusp effect. The $f_0(980)$, generated together with the $f_0(500)$, is responsible for the small structure near 1000 MeV in the $π^0π^0$ spectrum. The $a_1(1260)^+$ and its decay to $ρ^+π^0$ followed by the subsequent $ρ^+$ decay provide a good description of the $π^+π^0π^0$ and $π^+π^0$ mass spectra. The inclusion of an additional resonance near 800 MeV in the $π^+η$ spectrum leads to only a marginal improvement of the fit.
Comments10 pages, 6 figures
