Investigating the ratio of CKM matrix elements <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mo stretchy="false">|</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>u</mml:mi><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">|</mml:mo><mml:mo>/</mml:mo><mml:mo stretchy="false">|</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">|</mml:mo></mml:math> from semileptonic decay <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>B</mml:mi><mml:mi>s</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mi>K</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:msup><mml:mi>μ</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msub><mml:mi>ν</mml:mi><mml:mi>μ</mml:mi></mml:msub></mml:math> and kaon twist-2 distribution amplitude

Abstract

In this paper, we calculate the ratio of Cabibbo-Kobayashi-Maskawa matrix elements, $|{V}_{ub}|/|{V}_{cb}|$, based on the semileptonic decay ${B}_{s}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}}$. Its key component, the ${B}_{s}\ensuremath{\rightarrow}K$ transition form factor ${f}_{+}^{{B}_{s}\ensuremath{\rightarrow}K}({q}^{2})$, is studied within the QCD light-cone sum rules approach by using a chiral correlator. The derived ${f}_{+}^{{B}_{s}\ensuremath{\rightarrow}K}({q}^{2})$ is dominated by the leading-twist part, and to improve its precision, we construct a new model for the kaon leading-twist distribution amplitude ${\ensuremath{\phi}}_{2;K}(x,\ensuremath{\mu})$, whose parameters are fixed by using the least-squares method with the help of the moments calculated by using the QCD sum rules within the background field theory. The first four moments at the initial scale ${\ensuremath{\mu}}_{0}=1\text{ }\text{ }\mathrm{GeV}$ are $⟨{\ensuremath{\xi}}^{1}{⟩}_{2;K}=\ensuremath{-}0.043{8}_{\ensuremath{-}0.0075}^{+0.0053}$, $⟨{\ensuremath{\xi}}^{2}{⟩}_{2;K}=0.262\ifmmode\pm\else\textpm\fi{}0.010$, $⟨{\ensuremath{\xi}}^{3}{⟩}_{2;K}=\ensuremath{-}0.021{0}_{\ensuremath{-}0.0035}^{+0.0024}$, and $⟨{\ensuremath{\xi}}^{4}{⟩}_{2;K}=0.132\ifmmode\pm\else\textpm\fi{}0.006$, respectively. And the corresponding Gegenbauer moments are ${a}_{1}^{2;K}=\ensuremath{-}0.073{1}_{\ensuremath{-}0.0124}^{+0.0089}$, ${a}_{2}^{2;K}=0.18{2}_{\ensuremath{-}0.030}^{+0.029}$, ${a}_{3}^{2;K}=\ensuremath{-}0.011{4}_{\ensuremath{-}0.0016}^{+0.0008}$, and ${a}_{4}^{2;K}=0.04{1}_{+0.005}^{\ensuremath{-}0.003}$, respectively. At the large recoil region, we obtain ${f}_{+}^{{B}_{s}\ensuremath{\rightarrow}K}(0)=0.27{0}_{\ensuremath{-}0.020}^{+0.025}$. By extrapolating ${f}_{+}^{{B}_{s}\ensuremath{\rightarrow}K}({q}^{2})$ to all the physical allowable region, we obtain a $|{V}_{ub}|$-independent decay width for the semileptonic decay ${B}_{s}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}}$, ${5.626}_{\ensuremath{-}0.864}^{+1.292}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\text{ }\text{ }\mathrm{GeV}$, which then leads to $|{V}_{ub}|/|{V}_{cb}|=0.072\ifmmode\pm\else\textpm\fi{}0.005$.

Topics & Concepts