Soft corrections to inclusive DIS at four loops and beyond

Abstract

We study the threshold corrections to the structure functions in deep-inelastic scattering (DIS) at the fifth logarithmic (N${}^4$LL) order of the soft-gluon exponentiation in massless perturbative QCD. Using recent results for the splitting functions and the quark form factor, we derive the fourth-order contribution to the coefficient $f^{\mathrm{q}}$ of the form factor and from it the N${}^4$LL part of the exponentiation coefficient $B^{\mathrm{DIS}}$ in the limit of a large number of colours. An approximation scheme is shown that leads to sufficiently accurate N${}^4$LL results for full QCD. The N${}^4$LL corrections are small and lead to a further stabilization of the perturbative expansion for the soft-gluon exponent.

Comments: 6 pages, LaTeX (PoS style), 4 figures, Contribution to the proceedings of `DIS2019', Torino (Italy), April 2019