Abstract
We study the threshold corrections for inclusive deep-inelastic scattering (DIS) and their all-order resummation. Using recent results for the QCD form factor, related anomalous dimensions and Mellin moments of DIS structure functions at four loops we derive the complete soft and collinear contributions to the DIS Wilson coefficients at four loops. For a general SU(nc) gauge group the results are exact in the large-nc approximation and for QCD with nc = 3 we present precise approximations. We extend the threshold resummation exponent GN in Mellin-N space to the fifth logarithmic (N4LL) order collecting the terms {alpha}_{mathrm{s}}^3 (αs ln N)n to all orders in the strong coupling constant αs. We study the numerical effect of the N4LL corrections using both the fully exponentiated form and the expansion of the coefficient function in towers of logarithms. As a byproduct, we derive a numerical result for the complete pole structure of the QCD form factor in the parameter of dimensional regularization ε at four loops.
Highlights
Functions [1, 2] this resummation has been performed to next-to-next-to-next-to-leading logarithmic (N3LL) accuracy in Mellin-N space [8], where the resummation takes the form of an exponentiation which organizes the respective logarithms αsn lnl N, with l = 2n, . . . , 1
We study the threshold corrections for inclusive deep-inelastic scattering (DIS) and their all-order resummation
The relevant quantity BDIS controlling the resummation of the quark jet function has been extracted at four-loop order
Summary
Any process-dependent contributions from large-angle soft gluons emissions are contained in the function ∆iDnItS which, evaluates to unity, i.e., ∆iDnItS = 1, since the corresponding evolution kernels vanish at all order in αs for inclusive DIS [42, 43]. Note that for resummation to N4LL accuracy the function g5DIS(λ) needs the five-loop coefficient β4 of the QCD beta function in eq (2.6) which is available due to [46,47,48,49], as well as the cusp anomalous dimension up to five loops, i.e., the coefficient A5 which has recently been estimated [50] (see below). One needs the evolution kernel BDIS(αs) of the jet function in eq (2.4) to four-loop order, i.e., the term B4DIS, which will be addressed below. We will collect and discuss all necessary resummation coefficients
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