Four-loop large-nf contributions to the non-singlet structure functions F2 and FL

Abstract

Abstract We have calculated the $$ {n}_f^2 $$ n f 2 and $$ {n}_f^3 $$ n f 3 contributions to the flavour non-singlet structure functions F2 and FL in inclusive deep-inelastic scattering at the fourth order in the strong coupling αs. The coefficient functions have been obtained by computing a very large number of Mellin-N moments using the method of differential equations, and then determining the analytic forms in N and Bjorken-x from these. Our new $$ {n}_f^2 $$ n f 2 terms are numerically much larger than the $$ {n}_f^3 $$ n f 3 leading large-nf parts which were already known; they agree with predictions of the threshold and high-energy resummations. Furthermore our calculation confirms the earlier determination of the four-loop $$ {n}_f^2 $$ n f 2 part of the corresponding anomalous dimension. Via the no-π2 theorem for Euclidean physical quantities, we predict the $$ {\zeta}_4{n}_f^3 $$ ζ 4 n f 3 part of the fifth-order anomalous dimension for the evolution of non-singlet quark distributions.