Next-to-Next-to-Leading Electroweak Logarithms for W-Pair Production at LHC

TL;DR

This work tackles high-energy electroweak radiative corrections to W-pair production at the LHC using the NNLL evolution-equation framework.It derives explicit one- and two-loop corrections to the differential partonic cross section and provides hadronic distributions after PDF convolution.Results show substantial negative one-loop Sudakov terms (up to ~40%) and positive two-loop terms (up to ~10–20%), with cancellations depending on W polarization.The study highlights that achieving sub-percent accuracy requires completing the two-loop linear logarithm terms, motivating further calculations of mass-dependent anomalous dimensions.

Abstract

We derive the high energy asymptotic of one- and two-loop corrections in the next-to-next-to-leading logarithmic approximation to the differential cross section of $W$-pair production at the LHC. For large invariant mass of the W-pair the (negative) one-loop terms can reach more than 40%, which are partially compensated by the (positive) two-loop terms of up to 10%.

Figures (9)

• Figure 1: Tree level diagrams contributing to the partonic process
• Figure 2: Goldstone equivalence theorem at Born level
• Figure 3: Fermion/scalar scattering in an external singlet vector field and scattering of a gauge boson in an external scalar field. The momentum of external field satisfies $p^2=s=-Q^2$.
• Figure 4: One and two-loop corrections to the partonic cross section for left-handed $u$-quarks in the initial state, transverse (left panel) and longitudinal (right panel) $W$-bosons at $\sqrt{\hat{s}}= 1$ TeV.
• Figure 5: One and two-loop corrections to the partonic cross section for left-handed $d$-quarks in the initial state, transverse (left panel) and longitudinal (right panel) $W$-bosons at $\sqrt{\hat{s}}= 1$ TeV.