Two-loop QCD corrections to $Wb\bar{b}$ production at hadron colliders

TL;DR

The paper achieves an analytic two-loop QCD calculation for $u\bar{d}\to W^+b\bar{b}$ in the leading-color, massless-$b$ limit by performing IBP reduction over finite fields to a master-integral basis and constructing a dedicated basis of Chen iterated integrals for the finite remainder. This enables analytic pole subtraction and a compact representation of the finite part, with a reduced function basis (the $\{g_i^{(w)}\}$) that significantly lowers the numerical complexity. The authors verify consistency with Ward identities and cross-check against independent helicity computations, and provide numerical benchmarks. The approach opens the door to precise NNLO predictions for planar $2\to3$ processes like $pp\to W/Z+2j$ and informs future work on non-planar topologies and broader applications in Higgs-related backgrounds.

Abstract

We present an analytic computation of the two-loop QCD corrections to $u\bar{d}\to W^+b\bar{b}$ for an on-shell $W$-boson using the leading colour and massless bottom quark approximations. We perform an integration-by-parts reduction of the unpolarised squared matrix element using finite field reconstruction techniques and identify an independent basis of special functions that allows an analytic subtraction of the infrared and ultraviolet poles. This basis is valid for all planar topologies for five-particle scattering with an off-shell leg.

Figures (4)

• Figure 1: Leading order Feynman diagrams contributing to $u\bar{d}\to W^+b\bar{b}$ .
• Figure 2: Sample Feynman diagrams in the leading colour two-loop $u\bar{d}\to W^+b\bar{b}$ amplitude.
• Figure 3: Topologies with maximum number of propagators.
• Figure 4: The finite remainder $F^{(L)} = F_\mathrm{even}^{(L)} + \mathrm{tr}_5 F_\mathrm{odd}^{(L)}$ for $u\bar{d}\to W^+b\bar{b}$ at one and two loops as a function of the variable $x_2$ defined in Eq. \ref{['eq:parametrisation']}.