An analysis of the time-dependent CP asymmetryin decays in the standard model

A. Ali; E. Lunghi; A. Ya. Parkhomenko

doi:10.1140/epjc/s2004-01883-4

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2024 Impact factor 4.8

Particles and Fields

Eur. Phys. J. C (2004) 36: 183-200
https://doi.org/10.1140/epjc/s2004-01883-4

theoretical physics

An analysis of the time-dependent CP asymmetryin $B \to \pi \pi$ decays in the standard model

A. Ali¹^*, E. Lunghi² and A. Ya. Parkhomenko³

¹ Theory Group, Deutsches Elektronen-Synchrotron DESY, 22603, Hamburg, Germany
² Institut für Theoretische Physik, Universität Bern, 3012, Bern, Switzerland
³ Institut für Theoretische Physik, Universität Zürich, 8057, Zürich, Switzerland

^* e-mail: ahmed.ali@desy.de

Abstract

Measurements of the time-dependent CP-asymmetry in the decay $B^0_d (t)\to \pi^ + \pi^-$ and its charge conjugate by the BELLE and BABAR collaborations currently yield $C_{\pi \pi}^{ + -} = -0.46 \pm 0.13$ and $S_{\pi \pi}^{ + -} = -0.74 \pm 0.16$ , characterizing the direct and mixing-induced CP-asymmetries, respectively. We study the implication of these measurements on the CKM phenomenology taking into account the available information in the quark mixing sector. Our analysis leads to the results that the ratio |P_c/T _c| involving the QCD-penguin and tree amplitudes and the related strong phase difference $\delta_c = \delta_c^P - \delta_c^T$ in the $B^0_d/\bar{B}_d^0 \to \pi^ + \pi^-$ decays are quite substantial. Using the isospin symmetry to constrain |P_c/T _c| and $\cos (2\theta)$ , where $2 \theta$ parameterizes the penguin-induced contribution, we present a fit of the current data including the measurements of $S_{\pi \pi}^{ + -}$ and $C_{\pi \pi}^{ + -}$ . Our best-fits yield $\alpha = 92^\circ$ , $\beta = 24^\circ$ , $\gamma = 64^\circ$ , $\vert P_c/T_{\mathrm c}\vert = 0.77$ , and $\delta_c = -43^\circ$ . At 68% C.L., the ranges are $81^\circ \leq \alpha \leq 103^\circ$ , $21.9^\circ \leq \beta \leq 25.5^\circ$ , $54^\circ \leq \gamma \leq 75^\circ$ , $0.43 \leq \vert P_c/T_{\mathrm c}\vert \leq 1.35$ and $-64^\circ \leq \delta_c \leq -29^\circ$ . Currently en vogue dynamical approaches to estimate the hadronic matrix elements in $B \to \pi \pi$ decays do not provide a good fit of the current data.