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We report on our on-going study of the $B_s \to K\ell\nu$ decay in $N_f=2+1$lattice QCD. We employ fully relativistic setup in which the M\"obiusdomain-wall action is used for all quark flavors. The lattice cutoff is $a^{-1}\sim 2.5$ GeV, where we take bottom quark masses up to $m_Q\!<\!0.7a^{-1}$ inorder to control discretization errors. We present preliminary results for therelevant form factors extracted from correlator ratios by inspecting theirground state saturation.

$B_s \to K\ell\nu$ form factors from lattice QCD with domain-wall heavy quarks