Asymptotic freedom beyond the leading order

We make a quantitative analysis of the full g² interaction corrections to the leading Q² dependence of νW₂ at x ≥ 0.4, as given by an asymptotically free gauge theory. It turns out that due to partial cancellations between various contributions the g² corrections are small. The best fit with the SLAC ep data after including the g² corrections is almost identical to that without these corrections, the only effect being a change in Λ, the one free parameter, which sets the scale of the theory. On the other hand the effect of including target mass corrections is to improve the agreement of the prediction for νW₂^ep with data for large values of x. We study the implications of g² and target mass corrections for R = σ_L/σ_L and conclude, in agreement with other authors, that although both types of corrections are vital they do not account for values of R for x ≥ 0.5 as measured at SLAC.