  We apply recent developments in large momentum effective theory (LaMET) to
formulate a non-perturbative calculation of the single-transverse spin
asymmetry in terms of the quasi transverse-momentum-dependent quark
distribution functions from the so-called Sivers mechanism. When the spin
asymmetry is defined as the ratio of the quark Sivers function over the spin
averaged distribution, it can be directly calculated in terms of the relevant
quasi distributions with the soft functions and perturbative matching kernels
cancelling out. Apart from the general formula presented, we have verified the
result in the small transverse distance limit at one-loop order, which reduces
to a collinear expansion at twist-three level.
