A matrix formulation for small-x singlet evolution

We propose a matrix evolution equation in (x,k)-space for flavour singlet, unintegrated quark and gluon densities, which generalizes DGLAP and BFKL equations in the relevant limits. The matrix evolution kernel is constructed so as to satisfy renormalization group constraints in both the ordered and antiordered regions of exchanged momenta k, and incorporates the known NLO anomalous dimensions in the MS scheme as well as the NLx BFKL kernel. We provide a hard Pomeron exponent and effective eigenvalue functions that include the nf -dependence, and give also the matrix of resummed DGLAP splitting functions. The results connect smoothly with those of the single-channel approach. The novel Pqa splitting functions show resummation effects delayed down to x = 10 −4, while both Pga entries show a shallow dip around x = 10 −3, similarly to the gg single-channel results. We remark that the matrix formulation poses further constraints on the consistency of a BFKL framework with the MS scheme, which are satisfied at NLO, but marginally violated by small nf/N 2 c -suppressed terms at NNLO. On sabbatical leave of absence from Dipartimento di Fisica, Università di Firenze and INFN, Sezione di Firenze.