Double real radiation corrections to $t\bar{t}$ production at the LHC: the all-fermion processes

TL;DR

The paper develops and validates an NNLO antenna subtraction framework for hadronic tt̄ production with all-fermion final states, extending the method to include massive final-state quarks. It constructs subtraction terms for double real radiation using final-final, initial-final, and initial-initial antenna configurations, including new massive four-parton antennae and their limits, and demonstrates their accuracy through point-by-point numerical tests in unresolved regions. The work covers both identical and non-identical flavour fermionic channels, addressing angular (azimuthal) correlations and soft/collinear limits, and provides explicit formulas for relevant subtraction terms. This constitutes a crucial step toward a complete NNLO prediction for tt̄ production at the LHC, paving the way for incorporating gluon-initiated channels and mixed real-virtual contributions. The methodology combines rigorous phase-space factorisations with antenna-based singularity subtraction, yielding a tractable path to precision top-quark phenomenology at high-energy colliders.

Abstract

We present the double real radiation corrections to the hadronic $t \bar{t}$ production stemming from partonic processes with fermions only. For this purpose, we extend the NNLO antenna subtraction formalism developed originally for the computation of jet observables in $e^+e^-$ annihilation to include the evaluation of hadronic observables involving a massive pair of particles. In all partonic processes, we checked the validity of our subtraction terms given for leading and subleading colour contributions numerically by showing that the ratio between real radiation matrix elements and subtraction terms approaches unity in all single and double unresolved configurations.

Figures (9)

• Figure 1: \ref{['fig.pic1']} Ilustration of a double soft event. \ref{['fig.ds']} Distribution of R for 10000 double soft phase space points.
• Figure 2: \ref{['fig.pic2']} Topology of the triple collinear limit \ref{['fig.tc3561']} Distribution of R for 10000 double triple collinear space points.
• Figure 3: \ref{['fig.pic3']} Kinematics of the final-final single collinear limit. \ref{['fig.coll561']} Distribution of R for 10000 single collinear phase space points.
• Figure 4: Distribution of R for 10000 single collinear phase space points after azimuthal terms have been eliminated by combining phase points related by a $\pi/2$ rotation about the collinear axis.
• Figure 5: Distribution of R for 10000 triple collinear phase space points.