Top-quark pair production at high invariant mass: an NNLO soft plus virtual approximation
Andrea Ferroglia, Ben D. Pecjak, Li Lin Yang
TL;DR
This work delivers a soft plus virtual NNLO QCD approximation for the top-quark pair invariant-mass distribution, valid up to corrections of order $m_t^2/M^2$, representing the most complete fixed-order differential result to date. It constructs the NNLO contribution by leveraging double-soft and small-mass factorization to combine hard, soft, fragmentation, and heavy-flavor matching components, together with IR-subtracted massless two-loop virtual corrections to obtain the finite NNLO hard function. Numerically, the new non-logarithmic (delta-function) terms modestly enhance the distribution compared to prior approximations, with larger relative impact at lower $M$, while at high $M$ NNLL soft-gluon resummation becomes essential due to poor fixed-order convergence. The results inform boosted-top phenomenology and highlight the ongoing need to blend fixed-order calculations with resummation (and eventually electroweak corrections) to accurately describe highly boosted top quarks at the LHC and future colliders.
Abstract
We obtain a soft plus virtual approximation to the NNLO QCD contributions to the top-pair invariant mass distribution at hadron colliders. It is valid up to corrections of order m_t^2/M^2, with M the pair invariant mass. This is currently the most complete QCD calculation for a differential cross section in top-quark pair production, and is useful for describing the high invariant mass region characteristic of boosted top quarks. We use our results to construct an improved NNLO approximation for the pair invariant mass distribution and compare it with previous, less complete approximations based on logarithmic terms from NNLL soft-gluon resummation alone. We find that the new NNLO approximation produces moderate enhancements of the differential cross section compared to previous ones, the effect being slightly more important at low values of invariant mass than at high ones. On the other hand, at high values of invariant mass the new NNLO corrections are dominated by even higher-order effects included in NNLL soft-gluon resummation, reaffirming the need for resummation in describing the highly boosted regime.