  $B_{(s)}$ semi-leptonic decays to the light scalar meson, $B_{(s)}\to S
l\bar{\nu}_l, S l \bar{l}\,\,(l=e,\mu,\tau)$, are investigated in the QCD
light-cone sum rules (LCSR) with chiral current correlator. Having little
knowledge of ingredients of the scalar mesons, we confine ourself to the two
quark picture for them and work with the two possible Scenarios. The resulting
sum rules for the form factors receive no contributions from the twist-3
distribution amplitudes (DA's), in comparison with the calculation of the
conventional LCSR approach where the twist-3 parts play usually an important
role. We specify the range of the squared momentum transfer $q^2$, in which the
operator product expansion (OPE) for the correlators remains valid
approximately. It is found that the form factors satisfy a relation consistent
with the prediction of soft collinear effective theory (SCET). In the effective
range we investigate behaviors of the form factors and differential decay
widthes and compare our calculations with the observations from other
approaches. The present findings can be beneficial to experimentally identify
physical properties of the scalar mesons.
