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

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.

Renormalization of twist-two operators and four-loop splitting functions in QCD

“…The splitting functions at three-loop accuracy in QCD were computed almost 20 years ago [4,5], and allowed the complete determination of NNLO PDFs. At four-loop order, only partial results are available [6][7][8][9][10][11][12][13][14][15][16][17]. Those results were already used to obtain approximate N 3 LO PDFs [18,19].…”