  We analyze the left-right asymmetry of pion production in semi-inclusive deep
inelastic scattering (SIDIS) process of unpolarized charged lepton on
transversely polarized nucleon target. Unlike available treatments, in which
some specific weighting functions are multiplied to separate theoretically
motivated quantities, we do not introduce any weighting function following the
analyzing method by the E704 experiment. The advantage is that this basic
observable is free of any theoretical bias, although we can perform the
calculation under the current theoretical framework. We present numerical
calculations at both HERMES kinematics for the proton target and JLab
kinematics for the neutron target. We find that with the current theoretical
understanding, Sivers effect plays a key role in our analysis.
