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The transverse momentum dependent helicity distributions of valence quarksare calculated in the light-cone diquark model by adopting two differentapproaches. We use the model results to analyze the $P_{h\perp}$-dependentdouble spin asymmetries for $\pi^+$, $\pi^-$ and $\pi^0$ productions insemi-inclusive deep inelastic scattering, and find that the asymmetries agreewith the CLAS data in one of the approaches. By taking the Fourier transform ofthe transverse momentum dependent helicity distributions, we obtain thehelicity distributions of valence quarks in the transverse coordinate space,and then apply them further to predict the Bessel-weighted double spinasymmetries of $\pi^+$, $\pi^-$ and $\pi^0$ productions in semi-inclusive deepinelastic scattering at CLAS, COMPASS and HERMES for the first time. The shapeof the Bessel-weighted double spin asymmetry thereby provides a direct probe onthe transverse structure of longitudinally polarized quarks.

Quark helicity distributions in transverse momentum space and transverse coordinate space