W Pair Production at the LHC - I. Virtual O(alpha_s^2) Corrections in the High Energy Limit

TL;DR

This work addresses NNLO QCD virtual corrections to $q\bar q\rightarrow W^+W^-$ in the high-energy limit, computing the two-loop interference with the Born amplitude and the one-loop squared contribution. The authors reduce the massive two-loop problem to 71 master integrals, employing Mellin-Barnes representations and asymptotic expansions in $m^2/s$ to obtain analytic finite remainders, while verifying the infrared structure via Catani's formalism. A new coupling $c_4$ emerges from $s$-channel $Z$ exchange, and the finite parts are organized by color with explicit expressions in terms of $m_s$, $x$, logarithms $L_m,L_s,L_x,L_y$ and polylogarithms. The results provide a crucial step toward a full NNLO prediction for WW production, laying the groundwork for including real-virtual and double-real contributions and future mass expansions. These high-precision virtual corrections are essential for accurate WW backgrounds in Higgs analyses and tests of the Standard Model at the LHC.

Abstract

We present the result for the two-loop and the one-loop squared virtual QCD corrections to the W boson pair production in the quark-anti-quark-annihilation channel in the limit where all kinematical invariants are large compared to the mass of the W boson. The infrared pole structure is in agreement with the prediction of Catani's general formalism for the singularities of two loop amplitudes.