Will the subprocesses <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>ρ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>770</mml:mn><mml:mo>,</mml:mo><mml:mn>1450</mml:mn><mml:msup><mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math> contribute large branching fractions for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mo>±</mml:mo></mml:mrow></mml:msup><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:msup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math> decays?

Abstract

We analyze the quasi-two-body decays ${B}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}\ensuremath{\rho}(770,1450{)}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{K}^{+}{K}^{\ensuremath{-}}$ in the perturbative QCD approach. The results in this work do not support that large branching fractions contributed by the resonances $\ensuremath{\rho}(770,1450{)}^{0}$ in the ${B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}{K}^{+}{K}^{\ensuremath{-}}$ decays. The virtual contribution for ${K}^{+}{K}^{\ensuremath{-}}$ from the tail of the resonance $\ensuremath{\rho}(770{)}^{0}$ which has been ignored in the experimental studies is about 1.5 times of the $\ensuremath{\rho}(1450{)}^{0}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}$ contribution, with the predicted branching fractions ${\mathcal{B}}_{v}=(1.31\ifmmode\pm\else\textpm\fi{}0.27)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ and $\mathcal{B}=(8.96\ifmmode\pm\else\textpm\fi{}2.61)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$, respectively, for these two subprocesses in the ${B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}{K}^{+}{K}^{\ensuremath{-}}$ decays. The absence of $\ensuremath{\rho}(770{)}^{0}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}$ for the decay amplitude of a three-body hadronic $B$ decay involving charged kaon pair could probably result in a larger proportion for the contribution from the resonance $\ensuremath{\rho}(1450{)}^{0}$ in experimental analysis.

Topics & Concepts