AbstractWe study the contributions for the $$K^+K^-$$
K
+
K
-
and $$K^0\bar{K}^0$$
K
0
K
¯
0
originating from the intermediate states $$\phi (1020)$$
ϕ
(
1020
)
and $$\phi (1680)$$
ϕ
(
1680
)
in the charmless three-body decays $$B\rightarrow K\bar{K} h$$
B
→
K
K
¯
h
, with $$h=(\pi , K)$$
h
=
(
π
,
K
)
, in the perturbative QCD approach. The subprocesses $$\phi (1020,1680)\rightarrow K\bar{K}$$
ϕ
(
1020
,
1680
)
→
K
K
¯
are introduced into the distribution amplitudes of $$K\bar{K}$$
K
K
¯
system via the kaon electromagnetic form factors with the coefficients taken from the fitted results. The predictions of the branching fractions for the decays $$B\rightarrow \phi (1680)h$$
B
→
ϕ
(
1680
)
h
with the intermediate state $$\phi (1680)$$
ϕ
(
1680
)
decays into $$K^+K^-$$
K
+
K
-
or $$K^0\bar{K}^0$$
K
0
K
¯
0
are about $$6{-}8\%$$
6
-
8
%
of the corresponding results for the quasi-two-body decays $$B\rightarrow \phi (1020)h \rightarrow K^+ K^- h$$
B
→
ϕ
(
1020
)
h
→
K
+
K
-
h
in this work.
Electromagnetic transition form factors of baryons in a relativistic Faddeev approach
