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Double real radiation corrections to $t\bar{t}$ production at the LHC: the $gg\rightarrow t\bar{t}q\bar{q}$ channel

We present the double real radiation contributions to the $t \bar t$ hadronic production cross section stemming from the partonic process $gg\rightarrow t\bar{t}q\bar{q}$. We explicitly construct the antenna subtraction terms for this gluon-gluon initiated process starting from the double soft behaviour of the double real radiation matrix elements using soft currents. Those subtraction terms, given in leading and subleading colour contributions, require the use of new genuine NNLO four-parton antenna functions involving massive fermions. Those are also presented together with their infrared limits in this paper. We checked the validity of our subtraction terms numerically by showing that the ratio between the real radiation matrix elements and the subtraction terms approaches unity in all single and double unresolved regions of phase space.