AbstractIn 2017, LHCb collaboration reported their first observation of the rare decays $$B_s \rightarrow \phi (f_0(980)$$
B
s
→
ϕ
(
f
0
(
980
)
$$/f_2(1270) \rightarrow ) \pi ^+\pi ^-$$
/
f
2
(
1270
)
→
)
π
+
π
-
and the evidence of $$B^0 \rightarrow \phi (f_0(980)/f_2(1270)\rightarrow )\pi ^+\pi ^-$$
B
0
→
ϕ
(
f
0
(
980
)
/
f
2
(
1270
)
→
)
π
+
π
-
. Motivated by this, we study these quasi-two-body decays in the perturbative QCD approach. The branching fractions, CP asymmetries and the polarization fractions are calculated. We find that within the appropriate two-meson wave functions, the calculated branching fractions are in agreement with the measurements of LHCb. Based on the narrow-width approximation, We also calculate the branching fractions of the quasi-two-body $$B_{d,s}\rightarrow \phi (f_0(980)/f_2(1270)\rightarrow ) \pi ^0\pi ^0$$
B
d
,
s
→
ϕ
(
f
0
(
980
)
/
f
2
(
1270
)
→
)
π
0
π
0
and $$B_{d,s}\rightarrow \phi (f_2(1270)\rightarrow ) K^+K^-$$
B
d
,
s
→
ϕ
(
f
2
(
1270
)
→
)
K
+
K
-
, and hope the predictions to be tested in the ongoing LHCb and Belle II experiments. Moreover, the processes $$B_{d,s}\rightarrow \phi f_2(1270)$$
B
d
,
s
→
ϕ
f
2
(
1270
)
are also analyzed under the approximation. We note that the CP asymmetries of these decays are very small, because these decays are either penguin dominant or pure penguin processes.