  We present a calculation of the Mellin moments of the transverse quark spin
densities in the nucleon using lattice QCD. The densities are extracted from
the unpolarized and transversity generalized form factors extrapolated to the
continuum limit using three $N_f=2+1+1$ twisted mass fermion gauge ensembles
simulated with physical quark masses and spanning three lattice spacings. The
first moment of transversely polarized quarks in an unpolarized nucleon shows
an interesting distortion, which can be traced back to the sharp falloff of the
transversity generalized form factor $\bar{B}_{Tn0}(t)$. The isovector tensor
anomalous magnetic moment is determined to be $\kappa_T=1.051(94)$, which
confirms a negative and large Boer-Mulders function, $h_1^{\perp}$, in the
nucleon.
