Contributions of $$ {K}_0^{\ast } $$(1430) and $$ {K}_0^{\ast } $$(1950) in the three-body decays B → Kπh

<jats:title>A<jats:sc>bstract</jats:sc> </jats:title><jats:p>We study the contributions of the resonant states <jats:inline-formula><jats:alternatives><jats:tex-math>$$ {K}_0^{\ast } $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>K</mml:mi> <mml:mn>0</mml:mn> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math></jats:alternatives></jats:inline-formula>(1430) and <jats:inline-formula><jats:alternatives><jats:tex-math>$$ {K}_0^{\ast } $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>K</mml:mi> <mml:mn>0</mml:mn> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math></jats:alternatives></jats:inline-formula>(1950) in the three-body decays <jats:italic>B → Kπh</jats:italic> (with <jats:italic>h</jats:italic> = <jats:italic>π, K</jats:italic>) in the perturbative QCD approach. The crucial nonperturbative input <jats:italic>F</jats:italic><jats:sub><jats:italic>Kπ</jats:italic></jats:sub>(<jats:italic>s</jats:italic>) in the distribution amplitudes of the <jats:italic>S</jats:italic>-wave <jats:italic>Kπ</jats:italic> system is derived from the matrix element of vacuum to <jats:italic>Kπ</jats:italic> pair. The <jats:italic>C P</jats:italic> averaged branching fraction of the quasi-two-body decay process <jats:italic>B →</jats:italic><jats:inline-formula><jats:alternatives><jats:tex-math>$$ {K}_0^{\ast } $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>K</mml:mi> <mml:mn>0</mml:mn> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math></jats:alternatives></jats:inline-formula>(1950) <jats:italic>h → Kπh</jats:italic> is about one order smaller than that of the corresponding decay <jats:italic>B →</jats:italic><jats:inline-formula><jats:alternatives><jats:tex-math>$$ {K}_0^{\ast } $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>K</mml:mi> <mml:mn>0</mml:mn> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math></jats:alternatives></jats:inline-formula>(1430)<jats:italic>h → Kπh</jats:italic>. In view of the important contribution from the <jats:italic>S</jats:italic>-wave <jats:italic>Kπ</jats:italic> system for the <jats:italic>B → Kπh</jats:italic> decays, it is not appropriate to neglect the <jats:inline-formula><jats:alternatives><jats:tex-math>$$ {K}_0^{\ast } $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>K</mml:mi> <mml:mn>0</mml:mn> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math></jats:alternatives></jats:inline-formula>(1950) in the theoretical or experimental studies for the relevant three-body <jats:italic>B</jats:italic> meson decays. The predictions in this work for the relevant decays are consistent with the existing experimental data.</jats:p>