Power-suppressed contributions to deep-inelastic processes

We present results of a direct calculation of leading power-law corrections to the proton and pion structure functions at large $x$ to order $\frac{1}{Q^4}$ for $\nu W_2^{\mathrm{proton}}$ and $\frac{1}{Q^2}$ for $W_L^{\mathrm{proton}}$ and to order $\frac{1}{Q^2}$ for $\nu W_2^{\mathrm{pion}}$ and $W_L^{\mathrm{pion}}$. For $\nu W_2$ we find large $\sim {\mathrm{}(1-x)\mathrm{}}^4$ corrections to the leading $\sim {\mathrm{}(1-x)\mathrm{}}^3$ behavior as $x\to 1$ and substantial $\frac{{\mathrm{}(1-x)\mathrm{}}^2}{Q^2}$ corrections, a phenomenologically desirable form. We find a very large value for the coefficient of $\frac{1}{Q^2}$ in ${\left(\frac{{\sigma }_L}{{\sigma }_T}\right)}^{\mathrm{proton}}$. The $\frac{1}{Q^2}$ correction to $\nu W_2^{\mathrm{pion}}$ is of the form proposed by Berger and Brodsky but much smaller than their estimate after complete normalization constraints are imposed. In addition, this correction is not purely longitudinal until ($1-x$) is very near zero.