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Soft corrections to inclusive deep-inelastic scattering at four loops and beyond

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arxiv 1912.12920 v2 pith:O5ZND2CB submitted 2019-12-30 hep-ph

Soft corrections to inclusive deep-inelastic scattering at four loops and beyond

Goutam Das (Siegen U. , TP1) , Sven-Olaf Moch (Hamburg U. , Inst. Theor. Phys. II) , Andreas Vogt (Liverpool U. , Dept. Math) This is my paper
classification hep-ph
keywords fourloopsalphacorrectionsformcompletedeep-inelasticderive
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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 $SU(n_c)$ gauge group the results are exact in the large-$n_c$ approximation and for QCD with $n_c=3$ we present precise approximations. We extend the threshold resummation exponent $G^N$ in Mellin-$N$ space to the fifth logarithmic (N$^4$LL) order collecting the terms $\alpha_{\rm s}^{\,3} (\alpha_{\rm s} \ln N)^n$ to all orders in the strong coupling constant $\alpha_{\rm s}$. We study the numerical effect of the N$^4$LL 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 $\varepsilon$ at four loops.

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