Role of scalar mesons <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>a</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>980</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>a</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>1710</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>D</mml:mi><mml:mi>s</mml:mi><mml:mo>+</mml:mo></mml:msubsup><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:msup><mml:mi>K</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msubsup><mml:mi>K</mml:mi><mml:mi>S</mml:mi><mml:mn>0</mml:mn></mml:msubsup></mml:math> decay
Xin Jiang Zhu, Haonan Wang, De-Min Li, En Wang, Li‐Sheng Geng, Ju-Jun Xie
Abstract
Recently, the BESIII Collaboration has measured the ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{K}^{+}{K}_{S}^{0}$ decay and reported the observation of scalar meson ${a}_{0}(1710{)}^{+}$ in the ${K}^{+}{K}_{S}^{0}$ invariant mass spectrum. Based on the previous study about such a state in the ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{K}_{S}^{0}{K}_{S}^{0}$ decay, we perform a theoretical study of ${a}_{0}(1710{)}^{+}$ in the process ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{a}_{0}(1710{)}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{K}^{+}{K}_{S}^{0}$. In addition to the ${a}_{0}(1710)$ state, the contributions of ${K}^{*}$ and ${a}_{0}(980)$ are also taken into account. Firstly, we consider the contributions from the tree diagrams of ${K}^{*+}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{0}$ and ${\overline{K}}^{*0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\overline{K}}^{0}$. Secondly, we describe the final state interaction of $K\overline{K}$ in the chiral unitary approach to study the contribution of ${a}_{0}(980)$, while the ${a}_{0}(1710)$ state is dynamically generated from the ${K}^{*}{\overline{K}}^{*}$ interaction, and then decays into ${K}^{+}{\overline{K}}^{0}$. Since the final ${K}^{+}{K}_{S}^{0}$ state is in pure isospin $I=1$, the ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{K}^{+}{K}_{S}^{0}$ decay is an ideal process to study the ${a}_{0}(1710{)}^{+}$ and ${a}_{0}(980{)}^{+}$ resonances. It is found that the recent BESIII experimental measurements on the ${K}^{+}{K}_{S}^{0}$, ${\ensuremath{\pi}}^{0}{K}^{+}$, and ${\ensuremath{\pi}}^{0}{K}_{S}^{0}$ invariant mass distributions can be well reproduced, which supports the molecular ${K}^{*}{\overline{K}}^{*}$ nature of the scalar ${a}_{0}(1710)$ resonance.