Four-loop large-n_f contributions to the non-singlet structure functions F_2 and F_L

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 F _2 and F _ L in inclusive deep-inelastic scattering at the fourth order in the strong coupling α _s. 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- n _ f 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- π ^2 theorem for Euclidean physical quantities, we predict the ζ 4 n f 3 $$ {\zeta}_4{n}_f^3 $$ part of the fifth-order anomalous dimension for the evolution of non-singlet quark distributions.