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

TL;DR

This paper employs the perturbative QCD factorization approach to calculate branching ratios of specific quasi-two-body B meson decays involving rho resonances, providing predictions consistent with experimental data and offering insights into two-body decay rates.

Contribution

The study introduces a framework for calculating quasi-two-body B meson decay branching ratios using PQCD, incorporating experimental pion form factors and enabling extraction of two-body decay rates from quasi-two-body results.

Findings

Predicted branching ratios range from 10^{-10} to 10^{-4}.

Predictions for certain decay modes agree with LHCb measurements.

Identified a relation between decay rates of different rho resonances.

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 $\Phi^{I=1}_{\pi\pi}$. 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 ${\cal B}(B^0\to \bar{D}^0 (\rho^0(1450),\rho^0(1700)) \to \bar{D}^0 \pi^+\pi^-)$ 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 ${\cal B}(B_{(s)} \to D \rho(1450))$ and ${\cal B}(B_{(s)} \to D \rho(770))$ are similar in magnitude: an interesting relation to be tested by future experimental measurements.