Fermionic Electroweak Two-Loop Corrections to Drell-Yan and Related Processes

TL;DR

This work computes the complete fermionic electroweak $NNLO$ corrections to Drell-Yan and related fermion-pair production using a semi-numerical approach based on dispersion relations for fermion sub-loops and Feynman parameterization for triangle sub-loops. UV divergences are removed analytically through subtraction terms, while IR divergences are handled by universal QED factorization and IR matching, with on-shell renormalization in multiple EW schemes. The numerical results for $e^+e^-\to \mu^+\mu^-$, $u\bar u$, and $d\bar d$ final states show NNLO corrections at the level of about $1\%$ relative to NLO, with quantified uncertainties from light-quark masses and missing higher orders. These fermionic $NNLO$ corrections provide a crucial ingredient for precision Drell-Yan predictions and must be combined with QCD corrections and MC radiation simulations to fully exploit collider data at HL-LHC and future colliders.

Abstract

We perform a complete calculation of the next-to-next-to-leading order (NNLO) electroweak fermionic corrections to fermion-pair production processes, where "fermionic" refers to contributions with closed fermion loops. We did this via a semi-numerical technique that used dispersion relations for the fermion sub-loop in two-loop box and vertex diagrams and dispersion relations and Feynman parameters for vertex diagrams with fermionic triangle sub-loops. UV and IR divergences are treated with suitable subtraction terms. We present numerical results for the cross-sections of $e^+e^-\to μ^+μ^-/u\bar{u}/d\bar{d}$ and differential distributions at representative center-of-mass energies. The NNLO corrections are found to modify the NLO cross-section on the order of 1%.

Figures (5)

• Figure 1: Example diagrams for second-order electroweak corrections to fermion scattering. The cross in diagram (d) indicates a counterterm.
• Figure 2: Example diagrams of sub-loops with longitudinal contributions
• Figure 3: Electroweak corrections to the differential unpolarized cross-section at $\sqrt{s}=240$ GeV at NLO and NNLO. The width of the red curves reflect the light quark mass uncertainty.
• Figure 4: Electroweak corrections to the total unpolarized cross-section at NLO and NNLO. The width of the red curves reflect the light quark mass uncertainty.
• Figure 5: Similar to Fig. \ref{['fig:totxsec']}, but for the $A_4$ parameter.