Branching Ratio and Polarization of B \to a_1(1260)(b_1(1235))ρ(ω, ϕ) Decays in the PQCD Approach
Abstract
Within the framework of perturbative QCD approach, we study the charmless two-body decays into final states involving one axial-vector (A),
a
1
(1260)
or
b
1
(1235)
, and one vector (V), namely
ρ(ω,ϕ)
. Using the decays constants and the light-cone distribution amplitudes for these mesons derived from the QCD sum rule method, we find the following results: (a) Except the decays
B
¯
0
→
a
0
1
ρ
0
(ω)
, other tree-dominated decays
B→
a
1
ρ(ω)
have larger branching ratios, at the order of
10
−5
. (b)Except the decays
B
¯
→
b
+
1
ρ
−
and
B
−
→
b
0
1
ρ
−
, other
B→
b
1
ρ(ω)
decays have smaller branching ratios, at the order of
10
−6
. (c) The decays
B→
a
1
(
b
1
)ϕ
are highly suppressed and have very small branching ratios, at the order of
10
−9
. (d) For the decays
B
¯
0
→
a
0
1
ρ
0
and
B
−
→
b
−
1
ρ
0
, their two transverse polarizations are larger than their longitudinal polarizations, which are about 43.3% and 44.9%, respectively. (d) The two transverse polarizations have near values in the decays
B→
a
1
ρ(ω)
, while have large differences in some of
B→
b
1
ρ(ω)
decays. (e) For the decays
B
−
→
a
0
1
ρ
−
,
b
0
1
ρ
−
and
B
¯
0
→
b
0
1
ρ
0
,
b
0
1
ω
, where the transverse polarization fractions range from 4.7 to 7.5%, we calculate their direct CP-violating asymmetries with neglecting the transverse polarizations and find that those for two charged decays have smaller values, which are about 11.8% and -3.7%, respectively.