Quasi-two-body decays in perturbative QCD*

Abstract

In this work, we investigate the quasi-two-body decays $B_c\to D^*h\to D\pi h$ with $h = (K^0,\pi^0,\eta,\eta^{\prime})$ using the perturbative QCD(PQCD)
approach. The description of final state interactions between the $D\pi$ pair is achieved through the two-meson distribution amplitudes (DAs),
which are normalized to the time-like form factor. The PQCD predictions on the branching ratios of the quasi-two-body decays $B_c\to D^*h\to D\pi h$
show an obvious hierarchy: $Br(B_{c}^+ \to D^{*+} K^{0}\to D^0\pi^+K^{0})=({5.05}_{-0.91}^{+0.88})\times{10}^{-6},
Br(B_{c}^+ \to D^{*+} \pi^{0}\to D^0\pi^+\pi^{0})=({1.05}_{-0.18}^{+0.26})\times{10}^{-7}, Br(B_{c}^+ \to D^{*+} \eta\to D^0\pi^+\eta)
=({6.81}_{-1.08}^{+1.33})\times{10}^{-8}$ and $Br(B_{c}^+ \to D^{*+} \eta^\prime\to D^0\pi^+\eta^\prime)=({4.26}_{-0.68}^{+0.83})\times{10}^{-8}$.
 From the invariant mass $m_{D\pi}$-dependences of the decay spectrums, one can find that the branching fractions are concentrated in a narrow region
 around the $D^{*}$ pole mass.
So one can obtain the branching ratios for the corresponding two-body decays $B_c\to D^{*+}h$ under the narrow width approximation. We find that the branching ratios of
the decays $B_c\to D^{*+}K^0$
and $B_c\to D^{*+}\pi^0$ are consistent well with the previous PQCD calculations, while there exists $3\sim4$ times differences for the decays
$B_c\to D^{*+}\eta^{(\prime)}$.
These predictions will be tested by the future experiments. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.