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.
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