Towards NNLO QCD predictions for off-shell top-quark pair production and decays

A bstract We consider QCD radiative corrections to $$ {W}^{+}{W}^{-}b\overline{b} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>W</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>W</mml:mi> <mml:mo>−</mml:mo> </mml:msup> <mml:mi>b</mml:mi> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> production with leptonic decays and massive bottom quarks at the LHC. We perform an exact next-to-leading order (NLO) calculation within the q T -subtraction formalism and validate it against an independent computation in the dipole subtraction scheme. Non-resonant and off-shell effects related to the top quarks and the leptonic decays of the W ± bosons are consistently included. We also consider the approximation in which the real-emission contribution is computed exactly while the virtual is evaluated in the double-pole approximation (DPA), which formally requires the inclusion of both factorisable and non-factorisable corrections. We evaluate such contributions and show that the DPA performs remarkably well at both the inclusive and differential levels. We then extend our calculation to the next-to-next-to-leading order (NNLO). All tree-level and one-loop amplitudes are evaluated exactly, while the missing two-loop virtual contribution is estimated using the DPA. The factorisable two-loop corrections are explicitly computed by relying on available results for the polarised two-loop on-shell top-quark pair production amplitudes and the corresponding top-quark decays. The non-factorisable contributions are inferred by exploiting the cancellation of logarithmic singularities in the Γ t → 0 limit through an on-shell matching procedure. The NNLO corrections for the inclusive cross section are found to increase the NLO prediction by approximately 11%, with a numerical uncertainty that is conservatively estimated to be below the 2% level — significantly smaller than the 5% residual perturbative uncertainties.