Time-reversal odd fragmentation and distribution functions in pp and ep single spin asymmetries

We present some estimates of T-odd fragmentation and distribution functions, ${H}_{1}^{\ensuremath{\perp}}$ and ${f}_{1T}^{\ensuremath{\perp}},$ evaluated on the basis of a fit on experimental data in ${p}^{\ensuremath{\uparrow}}p.$ Assuming the T-odd fragmentation function to be responsible for the single spin asymmetry in pion production in ${p}^{\ensuremath{\uparrow}}p,$ we find the ratio ${H}_{1}^{\ensuremath{\perp}}{/D}_{1}$ to be in good agreement with the experimental results from DELPHI data on $\stackrel{\ensuremath{\rightarrow}}{Z}2$-jet decay. We use our estimates to make predictions for ${\mathrm{ep}}^{\ensuremath{\uparrow}}.$