Quasi-two-body decays $B_{(s)}\to D(\rho (1450),\rho (1700))\to D\pi \pi$ in the perturbative QCD factorization approach

Abstract

By employing a framework for the quasi-two-body decays in the perturbative QCD (PQCD) factorization approach, we calculate the branching ratios of the decays $B_{(s)}\to D(\rho (1450),\rho (1700))\to D\pi \pi$ with $D=(D_{(s)},{\bar{D}}_{(s)})$. The pion vector form factor $F_{\pi }$, acquired from a {\it BABAR} Collaboration analysis of $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}(\gamma )$ data, is involved in the two-pion distribution amplitudes ${\Phi }_{\pi \pi }^{I=1}$. The PQCD predictions for the branching ratios of the considered quasi-two-body decays are in the range of $10^{-10}\sim 10^{-4}$. The PQCD predictions for $\mathcal{B}(B^0\to {\bar{D}}^0({\rho }^0(1450),{\rho }^0(1700))\to {\bar{D}}^0{\pi }^{+}{\pi }^{-})$ agree well with the measured values as reported by LHCb if one takes still large theoretical errors into account. Unlike the traditional way of the PQCD approach, one can extract the decay rates for the two-body decays $B_{(s)}\to D(\rho (1450),\rho (1700))$ from the results of the corresponding quasi-two-body decays. The PQCD predictions for $\mathcal{B}(B_{(s)}\to D\rho (1450))$ and $\mathcal{B}(B_{(s)}\to D\rho (770))$ are similar in magnitude: an interesting relation to be tested by future experimental measurements.

8 pages, 1 figure and 3 tables. Some modifications, matching the published version

References in corpus (15)

• Amplitude analysis of $B^{-}\to D^{+}{\pi }^{-}{\pi }^{-}$ decays
• Charmless Three-body Decays of B Mesons
• The $B(B_s)\to D_{(s)}P$, $D_{(s)}V$, $D_{(s)}^{\ast }P$ and $D_{(s)}^{\ast }V$ decays in the perturbative QCD approach
• Direct CP Violation in Charmless Three-body Decays of $B$ Mesons
• Quasi-two-body decays $B\to K\rho \to K\pi \pi$ in perturbative QCD approach
• $S$-wave resonance contributions to the $B_{(s)}^0\to J/\psi {\pi }^{+}{\pi }^{-}$ and $B_s\to {\pi }^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-}$ decays
• CP violation in $B^{\pm }\to {\pi }^{\pm }{\pi }^{+}{\pi }^{-}$ in the region with low invariant mass of one ${\pi }^{+}{\pi }^{-}$ pair
• Interference between f0(980) and rho(770) resonances in B --> pion-pion-kaon decays
• Study of $\overline{B^0}\to D^0{\pi }^{+}{\pi }^{-}$ decays
• Amplitude Analysis of B0-->K+ pi- pi0 and Evidence of Direct CP Violation in B--> K* pi decays
• The S-wave resonance contributions in the $B_s^0$ decays into $\psi (2S,3S)$ plus pion pair
• Charmless B -> PPP Decays: the Fully-Symmetric Final State
• Quasi-two-body decays $B_{(s)}\to P{D}_0^{\ast }(2400)\to PD\pi$ in the perturbative QCD approach
• Update analysis of two-body charmed $B$ meson decays
• SU(3) and Isospin Breaking Effects on B to PPP Amplitudes

Cited by in corpus (4)

• Quasi-two-body decays $B_{(s)}\to P{D}_0^{\ast }(2400)\to PD\pi$ in the perturbative QCD approach
• Quasi-two-body decays $B\to D{K}^{\ast }(892)\to DK\pi$ in the perturbative QCD approach
• Quasi-two-body decays $B_c\to D_{(s)}[\rho (770),\rho (1450),\rho (1700)\to ]\pi \pi$ in the perturbative QCD factorization approach
• Three body radiative decay $B_s\to \varphi {\bar{K}}^0\gamma$ in the PQCD approach