AbstractPion–kaon ($$\pi K$$
π
K
) pairs occur frequently as final states in heavy-particle decays. A consistent treatment of $$\pi K$$
π
K
scattering and production amplitudes over a wide energy range is therefore mandatory for multiple applications: in Standard Model tests; to describe crossed channels in the quest for exotic hadronic states; and for an improved spectroscopy of excited kaon resonances. In the elastic region, the phase shifts of $$\pi K$$
π
K
scattering in a given partial wave are related to the phases of the respective $$\pi K$$
π
K
form factors by Watson’s theorem. Going beyond that, we here construct a representation of the scalar $$\pi K$$
π
K
form factor that includes inelastic effects via resonance exchange, while fulfilling all constraints from $$\pi K$$
π
K
scattering and maintaining the correct analytic structure. As a first application, we consider the decay $${\tau \rightarrow K_S\pi \nu _\tau }$$
τ
→
K
S
π
ν
τ
, in particular, we study to which extent the S-wave $$K_0^*(1430)$$
K
0
∗
(
1430
)
and the P-wave $$K^*(1410)$$
K
∗
(
1410
)
resonances can be differentiated and provide an improved estimate of the CP asymmetry produced by a tensor operator. Finally, we extract the pole parameters of the $$K_0^*(1430)$$
K
0
∗
(
1430
)
and $$K_0^*(1950)$$
K
0
∗
(
1950
)
resonances via Padé approximants, $$\sqrt{s_{K_0^*(1430)}}=[1408(48)-i\, 180(48)]\,\text {MeV}$$
s
K
0
∗
(
1430
)
=
[
1408
(
48
)
-
i
180
(
48
)
]
MeV
and $$\sqrt{s_{K_0^*(1950)}}=[1863(12)-i\,136(20)]\,\text {MeV}$$
s
K
0
∗
(
1950
)
=
[
1863
(
12
)
-
i
136
(
20
)
]
MeV
, as well as the pole residues. A generalization of the method also allows us to formally define a branching fraction for $${\tau \rightarrow K_0^*(1430)\nu _\tau }$$
τ
→
K
0
∗
(
1430
)
ν
τ
in terms of the corresponding residue, leading to the upper limit $${\text {BR}(\tau \rightarrow K_0^*(1430)\nu _\tau )<1.6 \times 10^{-4}}$$
BR
(
τ
→
K
0
∗
(
1430
)
ν
τ
)
<
1.6
×
10
-
4
.
EXPERIENCE OF INSPECTION OF DAMAGES OF METAL BEARING STRUCTURES
