Four-loop non-singlet QCD splitting functions are verified for consistency and used to finalize analytical forms for the gluon virtual anomalous dimension and N^4LL threshold resummation coefficients, revealing a new small-x logarithmic structure.
Higher-Order Corrections in Threshold Resummation
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abstract
We extend the threshold resummation exponents G^N in Mellin-N space to the fourth logarithmic (N^3LL) order collecting the terms alpha_s^2 (alpha_s ln N)^n to all orders in the strong coupling constant as. Comparing the results to our previous three-loop calculations for deep-inelastic scattering (DIS), we derive the universal coefficients B_q and B_g governing the final-state jet functions to order alpha_s^3, extending the previous quark and gluon results by one and two orders. A curious relation is found at second order between these quantities, the splitting functions and the large-angle soft emissions in Drell-Yan type processes. We study the numerical effect of the N^3LL corrections using both the fully exponentiated form and the expansion of the coefficient function in towers of logarithms.
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Derives resummed coefficient functions for SIDIS in double-soft and single-soft threshold limits, with explicit NNLL coefficients extracted in the nonsinglet channel by matching to fixed-order results.
A general all-order expression for threshold resummation of rapidity distributions at fixed partonic rapidity is derived for colorless final states, with NNLL coefficients determined from NNLO Drell-Yan results and shown to match a translated SCET result.
NLO+NLL QCD corrections to gluon-fusion ZH production increase the cross-section by ~20% and reduce scale uncertainties from 20% to 12% at LHC energies, combined with Drell-Yan N3LL results.
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Properties and implications of the four-loop non-singlet splitting functions in QCD
Four-loop non-singlet QCD splitting functions are verified for consistency and used to finalize analytical forms for the gluon virtual anomalous dimension and N^4LL threshold resummation coefficients, revealing a new small-x logarithmic structure.
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Threshold resummation of Semi-Inclusive Deep-Inelastic Scattering
Derives resummed coefficient functions for SIDIS in double-soft and single-soft threshold limits, with explicit NNLL coefficients extracted in the nonsinglet channel by matching to fixed-order results.
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Threshold resummation of rapidity distributions at fixed partonic rapidity
A general all-order expression for threshold resummation of rapidity distributions at fixed partonic rapidity is derived for colorless final states, with NNLL coefficients determined from NNLO Drell-Yan results and shown to match a translated SCET result.
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Associated $ZH$ production in gluon fusion process at NLO+NLL
NLO+NLL QCD corrections to gluon-fusion ZH production increase the cross-section by ~20% and reduce scale uncertainties from 20% to 12% at LHC energies, combined with Drell-Yan N3LL results.