Measurement of CKM Angle $$\phi _{3}$$ Using $$B^{\pm } \rightarrow D (K_\mathrm{S}^{0}\pi ^{+}\pi ^{-}\pi ^{0})K^{\pm }$$ Decays at Belle

Abstract

The CKM angle \(\phi _3\) can be determined in a theoretically clean way as it is accessible via the tree-level decays, \(B^{\pm }\rightarrow DK^{\pm }\). The current uncertainty on \(\phi _3\) is significantly larger than that of the standard model (SM) prediction. A more precise measurement of \(\phi _3\) is crucial for testing the SM description of CP violation and probing for new physics effects. The statistical uncertainty can be reduced if information from additional D meson final states is included, which in practice means new three and four-body decay modes. Here, we measure \(\phi _3\) with \(B^{\pm }\rightarrow D(K_\mathrm{S}^0\pi ^+\pi ^-\pi ^0)K^{\pm }\) decays using a data sample corresponding to an integrated luminosity of 711 fb\(^{-1}\) collected with the Belle detector at KEKB asymmetric \(e^+e^-\) collider. This four-body D final state has a large branching fraction of 5.2% and the phase space is rich with different resonance substructures. We adopt a model-independent method to estimate \(\phi _3\) by studying various regions of the phase space. The D decay strong-phase information is obtained from the quantum-correlated D meson pairs produced at CLEO-c.