ar X iv : h ep - p h / 97 05 45 9 v 1 2 9 M ay 1 99 7 Evolution Kernels for Light - Ray Operators : Twist 2 and Twist 3 Contributions

The general evolution kernels of the twist 2 light–ray operators for unpolarized and polarized deep inelastic scattering are calculated inO(αs). From these evolution kernels a series of special evolution equations can be derived, among them the Altarelli-Parisi equations and the evolution equation for the meson wave function. In the case of twist 3 the results of Balitzki and Braun are confirmed. INTRODUCTION The study of the Compton amplitude for scattering of a virtual photon off a hadron is one of the basic tools in QCD to understand the short–distance behavior of the theory. The Compton amplitude for the general case of non– forward scattering is given by Tμν(p+, p−, Q) = i ∫ dxe〈p2|T (Jμ(x/2)Jν(−x/2))|p1〉, (1) where p+ = p2 + p1, p− = p2 − p1 = q1 − q2 and q = (q1 + q2)/2. The time– ordered product in eq. (1) can be represented in terms of the operator product expansion. Here we use the representation derived in ref. [1,2] T (Jμ(x/2)Jν(−x/2)) ≈ ∫ +∞