Charged current deep-inelastic scattering at three loops

Abstract

We derive for deep-inelastic neutrino(ν)-proton(P) scattering in the combination νP −νP the perturbative QCD corrections to three loops for the charged current structure functions F 2 , F L and F 3 . In leading twist approximation we calculate the first five odd-integer Mellin moments in the case of F 2 and F L and the first five even-integer moments in the case of F 3 . As a new result we obtain the coefficient functions to O(α 3 s ) while the corresponding anomalous dimensions agree with known results in the literature.

Third-order QCD corrections to the charged-current structure function

“…For the corresponding W + −W − coefficient function c (3) 3,+ only the six lowest even-integer moments have been computed so far [52,53]. As observed below Eq.…”

On higher-order flavour-singlet splitting and coefficient functions at large x

“…The vanishing of the leading ln 6 (1−x) contributions is due to a cancellation of contributions. Below we will address the question whether this cancellation is accidental or a structural feature.…”

“…The above (spin-averaged) splitting functions are presently known to n = 2 [1,2], i.e., the nextto-next-to-leading order (NNLO ≡ N 2 LO). The coefficient functions for the most important structure functions (including F 3 for charge-averaged W -exchange) have also been fully computed to order α 3 s [3][4][5], while the less important chargeasymmetry W -cases are available only through a couple of low-integer Mellin-N moments [6,7]. The frontier in the present massless case are now the α 4 s corrections, for which first results have been obtained at the lowest value of N [8,9].…”

CC DIS at $\alpha_s^3$ in Mellin-$N$ and Bjorken-$x$ spaces

“…. , 10 for F ν p−ν p 3 [6]. Meanwhile calculation of new results for 11'th moment for the first and 12'th moment for the latter case has been finished.…”

“…Meanwhile calculation of new results for 11'th moment for the first and 12'th moment for the latter case has been finished. We use scale choice µ r = µ f = Q and standard QCD colour factors C A = 3 and C F = 4/3 throughout this paper and denote the Mellin-N moments of corresponding coefficient functions as C ns a,N , a = 2, 3, L. Following the formalism outlined in [6] [7,8] (the α 3 s coefficient functions for this process are those of photon-exchange DIS, but without the contributions of the f l 11 flavour classes) and F νP+νP 3 [9] facilitate analytic continuations to these values of N. This continuation has been performed using the x-space expressions and the Mellin transformation package provided with version 3 of FORM [10]. Thus we are in a position to derive the respective moments of the hitherto unknown third-order contributions to the even-odd differences which are defined as…”