Higher-Twist Contribution to Pion Structure Function: 4-Fermi Operators

We present quenched lattice QCD results for the contribution of higher-twist operators to the lowest non-trivial moment of the pion structure function. To be specific, we consider the combination $F_2^{\pi^+} + F_2^{\pi^-} - 2 F_2^{\pi^0}$whichhas$I = 2$ and receives contributions from 4-Fermi operators only. We introduce the basis of lattice operators. The renormalization of the operators is done perturbatively in the $\overline{\mathrm{M}\mathrm{S}}$ scheme using the 't Hooft-Veltman prescription for ${\gamma }_5$, taking particular care of mixing effects. The contribution is found to be of $O(f_{\pi }^2\mathrm{/}{Q}^2)$, relative to the leading contribution to the moment of $F_2^{{\pi }^{+}}$.