Constraints from conformal covariance on the mixing of operators of lowest twist

Abstract

In massless QCD the operators which diagonalize the anomalous dimension matrix to first order in α s form representations of the conformal group. This is proved by using anomalous Ward identities. Only a subgroup, the so-called collinear conformal group SU(1, 1) ≅ SO(2, 1), acts on the restricted class of operators of lowest twist. Towers of local operators bilinear and trilinear in the quark fields are constructed. They are considered as polynomials in the derivatives acting on the basic quark fields: bilinear operators are given by Jacobi polynomials, trilinear operators by Appell's polynomials. By using the explicit form of the anomalous dimension matrix we verify that the constructed bilinear collinear conformal operators are in fact eigenvectors. As the conformal trilinear operator basis is degenerate, the eigenvectors of the mixing matrix of trilinear operators are not determined by conformal covariance alone. However, by taking a conformal basis the number of independent operators is reduced considerably.