Perturbative QCD for B_s \to a_1(1260)(b_1(1235))P(V) Decays
Abstract
Within the framework of perturbative QCD approach, we study the charmless two-body decays
B
s
→
a
1
(1260)(
b
1
(1235))P(V)
(
P,V
represent the light pseudo-scalar and vector mesons, respectively.). 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) The decays
B
¯
0
s
→
a
−
1
K
+
(
K
∗+
)
have the contributions from the factorization emission diagrams with a large Wilson coefficient
C
2
+
C
1
/3
(order of 1), so they have the largest branching ratios and arrive at
10
−5
order. While for the decays
B
¯
0
s
→
a
0
1
K
0
(
K
∗0
)
, the Wilson coefficient is
C
1
+
C
2
/3
in tree level and color suppressed, so their branching ratios are small and fall in the order of
10
−7
∼
10
−8
. For the decays
B
¯
0
s
→
b
1
K(
K
∗
)
, all of their branching ratios are of order few times
10
−6
. (b) For the pure annihilation type decays
B
¯
0
s
→
a
1
(
b
1
)ρ
except the decays
B
¯
0
s
→
a
1
π
having large branching ratios of order few times
10
−6
, the most other decays have the branching ratios of
10
−7
order. The branching ratios of the decays
B
¯
0
s
→
a
0
1
(
b
0
1
)ω
are the smallest and fall in the order of
10
−8
∼
10
−9
. (c)The branching ratios and the direct CP-asymmetries of decays
B
¯
0
s
→
a
0
1
(
b
0
1
)
η
(′)
are very sensitive to take different Gegenbauer moments for
η
(′)
. (d) Except for the decays
B
¯
0
s
→
a
0
1
K
∗0
,
a
0
1
ω,
b
0
1
ω
, the longitudinal polarization fractions of other
B
¯
0
s
→
a
1
(
b
1
)V
decays are very large and more than 90%. (e) Compared with decays
B
¯
0
s
→
a
1
(
b
1
)P
, most of
B
¯
0
s
→
a
1
(
b
1
)V
decays have smaller direct CP asymmetries.