Quasitwobody decays B_{c} → D_{(s)}[ρ(770),ρ(1450),ρ(1700)→]ππ in the perturbative QCD factorization approach
Abstract
In this paper, we studied the quasitwobody B_{c} →D_{(s)} [ ρ (770) , ρ (1450) , ρ (1700) → ] ππ decays by employing the perturbative QCD (PQCD) factorization approach. The twopion distribution amplitudes Φ_{ππ} are applied to include the finalstate interactions between the pion pair, while the timelike form factors F_{π} (w^{2}) associated with the Pwave resonant states ρ (770), ρ (1450) and ρ (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 quasitwobody B_{c} →D_{(s)} [ ρ (770) , ρ (1450) , ρ (1700) → ] ππ 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 1 a , 1 b , 1 c} and _{R 2 a , 2 b , 2 c} for the ratios of the branching ratios of the considered decays are defined and can be understood in the PQCD factorization approach, while the selfconsistency between the quasitwobody and twobody framework for B_{c} →D_{(s)} [ ρ (770) → ] ππ and B_{c} →D_{(s)} ρ (770) decays are confirmed by our numerical results; (c) taking currently known B (ρ (1450) → ππ) and B (ρ (1700) → ππ) as input, we extracted the theoretical predictions for B (B_{c} → Dρ (1450)) and B (B_{c} → Dρ (1700)) from the PQCD predictions for the decay rates of the quasitwobody decays B_{c} → D [ ρ (1450) , ρ (1700) → ] ππ. All the PQCD predictions will be tested in the future experiments.
 Publication:

Nuclear Physics B
 Pub Date:
 January 2018
 DOI:
 10.1016/j.nuclphysb.2017.12.004
 Bibcode:
 2018NuPhB.926..584M