Branching Fractions and CP Violations in Decays of Charged and Neutral Beauty Mesons to Pion and Kaon Mesons

Abstract

The most precise measurement of the $CP$ asymmetry in the decay ${{B}^{ + }} \to {{K}^{ + }}{{\pi }^{0}}$ was recently reported by LHCb collaboration with the value of $0.025 \pm 0.015 \pm 0.006 \pm 0.003$. This experimental result exceeds the precision on the current world average. In this study, the $CP$ violation in the decay ${{B}^{ + }} \to {{K}^{ + }}{{\pi }^{0}}$ has been calculated under the factorization approach. This decay mode includes all current-current and penguin diagrams that their amplitudes are considered separately. In each of the tree and penguin amplitudes, the strong and weak phases have been introduced with the $\delta$ and $\phi$ parameters, respectively. We have obtanied ${{\delta }_{1}} = 0,$ ${{\delta }_{2}} = 77^\circ$ for the decay of ${{B}^{ + }} \to {{K}^{ + }}{{\pi }^{0}}$ and ${{\delta }_{1}} = 0,$ ${{\delta }_{2}} = 13^\circ$ for the decay of ${{B}^{0}} \to {{K}^{ + }}{{\pi }^{ - }}$ decay ${{\varphi }_{1}} = 68.5^\circ ,$ ${{\varphi }_{2}} = 0$ for both decays. The $CP$ asymmetry is calculated to be $0.045_{{ - 0.002}}^{{ + 0.005}}$. A nonzero difference between direct $CP$ asymmetries of the decays ${{B}^{ + }} \to {{K}^{ + }}{{\pi }^{0}}$ and ${{B}^{0}} \to {{K}^{ + }}{{\pi }^{ - }}$ has also been evaluated. This difference is achieved to be $0.130_{{ - 0.005}}^{{ + 0.010}}$, in which is compatible with the experimental value approved by the LHCb collaboration, $0.108 \pm 0.017$. Finally, from the sum of the amplitudes, we have calculated the total amplitude and obtained comparable results with experimental values for the branching ratios of ${{B}^{ + }} \to {{K}^{ + }}{{\pi }^{0}}$ and ${{B}^{0}} \to {{K}^{ + }}{{\pi }^{ - }}$ decays.