Differences between charged-current coefficient functions

Abstract

Second-and third-order results are presented for the structure functions of charged-current deepinelastic scattering in the framework of massless perturbative QCD. We write down the two-loop differences between the corresponding crossing-even and -odd coefficient functions, including those for the longitudinal structure function not covered in the literature so far. At three loops we compute the lowest five moments of these differences for all three structure functions and provide approximate expressions in Bjorken-x space. Also calculated is the related third-order coefficient-function correction to the Gottfried sum rule. We confirm the conjectured suppression of these quantities if the number of colours is large. Finally we derive the second-and third-order QCD contributions to the Paschos-Wolfenstein ratio used for the determination of the weak mixing angle from neutrino-nucleon deep-inelastic scattering. These contributions are found to be small.

Charged current deep-inelastic scattering at three loops

“…[1,2,8,9] at hand we have all ingredients for a future computation of the "all-n" results in Mellin-n space, or equivalently the complete expression in Bjorken-x space after an inverse Mellin transform. However, applying the present results we can already comment on a number of phenomenological issues, which we do in a companion paper [21].…”

“…[21]. Future research will be devoted to the calculation of some higher Mellin moments, potentially n = 11, .…”

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

“…(2.7) in Ref. [45]. Also that equation for δc (2) 3 ≡ c (2) 3,+ − c (2) 3,− contains terms up to ln 3 x, hence c (2) 3,− and c (2) 3,+ already differ in the leading logarithm.…”

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

“…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].…”