  We calculate the nucleon isovector scalar charge in lattice QCD using overlap
fermions on five ensembles of gauge configurations generated by the RBC/UKQCD
collaboration using the domain-wall quark action with $2+1$ dynamical flavors.
The five ensembles cover five pion masses, $m_\pi \approx$ 139, 171, 302, 337
and 371 MeV, and four lattice spacings, $a \approx $ 0.06, 0.08, 0.11 and 0.14
fm. Three to six valence quark masses are computed on each ensemble to
investigate the pion mass dependence. The extrapolation to the physical pion
mass, continuum and infinite volume limits is obtained by a global fit of all
data to a formula originated from partially quenched chiral perturbation
theory. The excited-states contamination is carefully analyzed with 3--5
sink-source separations and multi-state fits. Our final result, in the
$\overline{\text{MS}}$ scheme at 2 GeV, is $g_{S}^{u-d}= 0.94
(10)_{stat}(8)_{sys}$, where the first error is the statistical error and the
second is the systematic error.
