NNLO QCD subtraction for top-antitop production in the q q ¯ $$ q\overline{q} $$ channel

Abstract

We present the computation of the double real and real-virtual contributions to top-antitop pair production in the quark-antiquark channel at leading colour. The qq → ttg amplitudes contributing to the real-virtual part are computed with OpenLoops, and their numerical stability in the soft and collinear regions is found to be sufficiently high to perform a realistic NNLO calculation in double precision. The subtraction terms required at real-real and real-virtual levels are constructed within the antenna subtraction formalism extended to deal with the presence of coloured massive final state particles. We show that those subtraction terms approximate the real-real and real-virtual matrix elements in all their singular limits.

NNLO QCD predictions for fully-differential top-quark pair production at the Tevatron

“…This has been possible thanks to the development of subtraction schemes [62][63][64][65][66][67][68][69][70], slicing methods [60,61,71] and the calculation of several two-to-two virtual amplitudes [72][73][74][75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90][91]. As far as top-quark pair production is concerned, besides our own calculation [10,92] only partial results are known at the differential level [93,94]; there is also progress at the level of total crosssection [95] obtained with slicing methods.…”

Towards differential top-anti-top production at NNLO

“…In [6], where we studied the leading colour contributions to top-pair production in the qq channel, it was shown that the subtraction terms constructed at the real-real and real-virtual level approximate the corresponding matrix-elements in all their infrared limits. Furthermore, an explicit and analytic pole cancellation occurs at the real-virtual level between explicit infrared poles of the one-loop matrix-elements and those from integrated double real subtraction terms.…”

“…The integration of the (subtracted) one-loop contributions over the soft and collinear regions of phase space can lead to serious numerical instabilities. This issue has been addressed in [6]. It was shown that using the…”

“…The double real and real-virtual contributions to heavy quark pair production in the qq channel at leading colour presented in [6] For each singular region we used a series of phase-space samples generated with RAMBO [15] by requiring an increasingly small distance, parametrised in terms of appropriate parameters x k , from the relevant singularity. In the next two subsections, we will quantify the level of the real-real and real-virtual cancellations as respectively.…”

“…It has been used for the double real contributions to tt production for the pure fermionic processes [4] and for the gluon initiated process gg → ttqq [5]. More recently, this formalism has been derived to treat infrared divergences in realvirtual contributions for the leading colour contributions to qq → tt [6] and for the purely fermionic contributions (proportional to N l .) in [7].…”