Predictions for double spin asymmetry A_{LT} in Semi Inclusive DIS

In the leading order of QCD parton model of Semi Inclusive Deep Inelastic Scattering (SIDIS) the double spin asymmetry $A_{LT}$ arises due to the longitudinal polarization of quarks in the transversely polarized nucleon. The corresponding $k_T^2$ weighted distribution function $g_{1T}^{(1)}$ can be related to ordinary helicity distribution $g_1(x)$ measured in DIS. Using recent parameterizations for (un)polarized distribution and fragmentation functions we calculated $A_{LT}$ asymmetry on transversely polarized proton and deuteron targets for different types hadron production. The predictions are given for COMPASS, HERMES and JLab energies. The role of Lorentz invariance relations and positivity constraints are discussed.