The first measurements of the scattering parameters of Lambda K pairs in
all three charge combinations (Lambda K+, Lambda K-, and Lambda K-S(0))
are presented. The results are achieved through a femtoscopic analysis
of Lambda K correlations in Pb-Pb collisions at root s(NN) = 2.76 TeV
recorded by ALICE at the Large Hadron Collider. The femtoscopic
correlations result from strong final-state interactions and are fit
with a parametrization allowing for both the characterization of the
pair emission source and the measurement of the scattering parameters
for the particle pairs. Extensive studies with the THERMINATOR 2 event
generator provide a good description of the nonfemtoscopic background,
which results mainly from collective effects, with unprecedented
precision. Furthermore, together with HIJING simulations, this model is
used to account for contributions from residual correlations induced by
feed-down from particle decays. The extracted scattering parameters
indicate that the strong force is repulsive in the Lambda K+ interaction
and attractive in the Lambda K- interaction. The data hint that the
Lambda K-S(0) interaction is attractive; however, the uncertainty of the
result does not permit such a decisive conclusion. The results suggest
an effect arising either from different quark-antiquark interactions
between the pairs (s (s) over bar in Lambda K+ and u (u) over bar in
Lambda K-) or from different net strangeness for each system (S = 0 for
Lambda K+, and S = -2 for Lambda K-). Finally, the Lambda K systems
exhibit source radii larger than expected from extrapolation from
identical particle femtoscopic studies. This effect is interpreted as
resulting from the separation in space-time of the single-particle
Lambda and K source distributions
