  We report a state-of-the-art lattice calculation of the isovector quark
transversity distribution of the proton at the physical pion mass. Within the
framework of large-momentum effective theory (LaMET), we compute the
transversity quasi-distributions using clover valence fermions on 2+1+1-flavor
(up/down, strange, charm) HISQ-lattice configurations with boosted proton
momenta as large as 3.0~GeV. The relevant lattice matrix elements are
nonperturbatively renormalized in regularization-independent
momentum-subtraction (RI/MOM) scheme and systematically matched to the physical
transversity distribution. With high statistics, large proton momenta and
meticulous control of excited-state contamination, we provide the best
theoretical prediction for the large-$x$ isovector quark transversity
distribution, with better precision than the most recent global analyses of
experimental data. Our result also shows that the sea quark asymmetry in the
proton transversity distribution is consistent with zero, which has been
assumed in all current global analyses.
