Theoretical study of the process <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:msubsup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:msubsup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math> and the isovector partner of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>f</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>
Xin Jiang Zhu, De-Min Li, En Wang, Li‐Sheng Geng, Ju-Jun Xie
Abstract
We present a theoretical study of ${a}_{0}(1710)$, the isovector partner of ${f}_{0}(1710)$, in the process ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{K}_{S}^{0}{K}_{S}^{0}$. The weak interaction part proceeds through the charm quark decay process: $c(\overline{s})\ensuremath{\rightarrow}(s+\overline{d}+u)(\overline{s})$, while the hadronization part takes place in two mechanisms, differing in how the quarks from the weak decay combine into $\ensuremath{\pi}{K}^{*}$ with a quark-antiquark pair $q\overline{q}$ with the vacuum quantum numbers. In addition to the contribution from the tree diagram of the ${K}^{*+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{K}_{S}^{0}$, we have also considered the ${K}^{*}{\overline{K}}^{*}$ final-state interactions within the chiral unitary approach to generate the intermediate state ${a}_{0}(1710)$, then it decays into the final states ${K}_{S}^{0}{K}_{S}^{0}$. We find that the recent experimental measurements on the ${K}_{S}^{0}{K}_{S}^{0}$ and ${\ensuremath{\pi}}^{+}{K}_{S}^{0}$ invariant mass distributions can be well reproduced, and the proposed mechanism can provide valuable information on the nature of scalar ${f}_{0}(1710)$ and its isovector partner ${a}_{0}(1710)$.