Measurement of CKM angle $\boldsymbol {\phi_3}$ from $\boldsymbol {B^\pm \to D(K_S^{0}h^-h^+)h^\pm}$ decays at Belle and Belle~II

Sumitted to PubDB: 2022-04-06

Category: Phd Thesis, Visibility: Public

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Authors James Libby, Niharika Rout
Date Jan. 1, 2016
Belle II Number BELLE2-PTHESIS-2022-002
Abstract The thesis reports the measurement of the CKM unitarity triangle angle $ \phi_{3} $ using a model-independent Dalitz plot analysis of $ B^{\pm} \to D(K_{S}^{0}h^{+}h^{-})K^{\pm} $ ($h = \pi$ or $K$) decays, where $D$ can either be a $D^0$ or a $\bar{D^0}$, which currently provides the best sensitivity. The $D$ phase space is divided into bins based on the phase-difference of $D^0$ and $\bar{D^0}$ at each point of the phase space. The decay rates of $B^\pm$ in the $i^{\rm th}$ bin are given as \begin{equation*} \Gamma_{i}^{\pm} \propto F_{i} + r_{B}^{2}\overline{F}_{i} + 2\sqrt{F_{i}\overline{F}_{i}}(c_{i}x_{\pm} + s_{i}y_{\pm}), \end{equation*} where $(x_{\pm}, y_{\pm}) = r_{B}(\cos(\pm \phi_{3} + \delta_{B}),~\sin(\pm \phi_{3}+ \delta_{B}))$. Here, $ F_{i} $ and $\overline{F}_{i}$ are the fraction of events in the $ i^{\rm th} $ bin of a flavour tagged $ D^0 $ and $\bar{D^0}$ decays and are obtained from $ B^{\pm} \to D(K_{S}^{0}h^{+}h^{-})h^{\pm} $ sample. The values of the amplitude-averaged strong-phase difference parameters, $ c_{i} $ and $ s_{i} $, are taken from combined measurement of BESIII and CLEO-c data. This is the first measurement that simultaneously uses Belle and Belle~II data, combining samples corresponding to integrated luminosities of 711~fb$^{-1}$ and 128~fb$^{-1}$, respectively. All data were accumulated from energy-asymmetric $e^+e^-$ collisions at a centre-of-mass energy corresponding to the mass of the $\Upsilon(4S)$ resonance. The $\phi_3$ value is measured to be $\left(78.4 \pm 11.4 \pm 0.5 \pm 1.0 \right)^{\circ}$, where the first uncertainty is statistical, the second the experimental systematic and the third is from the uncertainties on the strong-phase difference parameters. The thesis also reports the measurement of the beam energy in the centre-of-mass frame for the Belle~II detector using fully reconstructed neutral and charged $B$ decays from various final states. An accurate determination of the beam energy is crucial for many physics analyses and detector calibrations. The reported shift is of the order of 0.5~MeV from the nominal beam energy value.
Conference Chennai

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