  We report on the first global QCD analysis of the quark transversity
distributions in the nucleon from semi-inclusive deep-inelastic scattering
(SIDIS), using a new Monte Carlo method based on nested sampling and
constraints on the isovector tensor charge $g_T$ from lattice QCD. A
simultaneous fit to the available SIDIS Collins asymmetry data is compatible
with $g_T$ values extracted from a comprehensive reanalysis of existing lattice
simulations, in contrast to previous analyses which found significantly smaller
$g_T$ values. The contributions to the nucleon tensor charge from $u$ and $d$
quarks are found to be $\delta u = 0.3(2)$ and $\delta d = -0.7(2)$ at a scale
$Q^2 = 2$ GeV$^2$.

High Energy Physics - Phenomenology;High Energy Physics - Experiment;High Energy Physics - Lattice;Nuclear Theory