Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasi-two-body decays $B_c \to D_{(s)} [\rho(770),\rho(1450),\rho(1700)
  \to ] \pi \pi$ in the perturbative QCD factorization approach   In this paper, we studied the quasi-two-body $B_c \to D_{(s)} [
\rho(770),\rho(1450),\rho(1700) \to ] \pi \pi$ decays by employing the
perturbative QCD (PQCD) factorization approach. The two-pion distribution
amplitudes $\Phi_{\pi\pi}$ are applied to include the final-state interactions
between the pion pair, while the time-like form factors $F_{\pi}(w^2)$
associated with the $P$-wave resonant states $\rho(770)$, $\rho(1450)$ and
$\rho(1700)$ are extracted from the experimental data of the $e^+e^-$
annihilation. We found that: (a) the PQCD predictions for the branching ratios
of the quasi-two-body $B_c \to D_{(s)} [\rho(770), \rho(1450), \rho(1700) \to ]
\pi \pi$ decays are in the order of $10^{-9}$ to $ 10^{-5}$ and the direct $CP$
violations around $(10-40)\%$ in magnitude; (b) the two sets of the large
hierarchy $R_{1a,1b,1c}$ and $R_{2a,2b,2c}$ for the ratios of the branching
ratios of the considered decays are defined and can be understood in the PQCD
factorization approach, while the self-consistency between the quasi-two-body
and two-body framework for $B_{c} \to D_{(s)} [\rho(770) \to ] \pi \pi$ and
$B_{c} \to D_{(s)} \rho(770)$ decays are confirmed by our numerical results;
(c) taking currently known ${\cal B}(\rho(1450)\to\pi\pi)$ and ${\cal
B}(\rho(1700) \to \pi\pi)$ as input, we extracted the theoretical predictions
for ${\cal B}(B_{c} \to D \rho(1450)) $ and ${\cal B}(B_{c} \to D \rho(1700))$
from the PQCD predictions for the decay rates of the quasi-two-body decays
$B_{c} \to D [\rho(1450), \rho(1700) \to ] \pi \pi$. All the PQCD predictions
will be tested in the future experiments.

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The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
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The categories of this paper are: chem-ph
1
The categories of this paper are: cs