  We report a state-of-the-art lattice QCD calculation of the isovector quark
transversity distribution of the proton in the continuum and physical mass
limit using large-momentum effective theory. The calculation is done at four
lattice spacings $a=\{0.098,0.085,0.064,0.049\}$~fm and various pion masses
ranging between $220$ and $350$ MeV, with proton momenta up to $2.8$ GeV. The
result is non-perturbatively renormalized in the hybrid scheme with self
renormalization which treats the infrared physics at large correlation distance
properly, and extrapolated to the continuum, physical mass and infinite
momentum limit. We also compare with recent global analyses for the nucleon
isovector quark transversity distribution.
