We present a first study of gluonic twist-four corrections to the deep inelastic structure function $F_2$ at small x and small $Q^2.$ The calculations are based upon the double logarithmic approximation of the coupled twist-four evolution equations of the gluonic twist-four operators that are expected to be dominant at small x. We first review the analytical results which are presently available and define the framework of our calculation. In the second part we discuss the connection with DIS diffractive dissociation which can be used to estimate the size of some of the twist-four corrections. In the final part we show, for three different choices of the input distributions, the relative magnitude of the leading-twist and the twist-four contributions.

• Received 13 July 1999

DOI:https://doi.org/10.1103/PhysRevD.61.034009