Aude Gehrmann-De Ridder

Antenna subtraction at NNLO

The computation of exclusive QCD jet observables at higher orders requires a method for the subtraction of infrared singular configurations arising from multiple radiation of real partons. We present a subtraction scheme relevant for NNLO perturbative calculations in e+e−→ jets. The building blocks of the scheme are antenna functions derived from the matrix elements for tree-level 1→3 and 1→4 and one-loop 1→3 processes. By construction, these building blocks have the correct infrared behaviour when one or two particles are unresolved. At the same time, their integral over the antenna phase space is straightforward. As an example of how to use the scheme we compute the NNLO contributions to the subleading colour QED-like contribution to e+e−→3 jets. To illustrate the application of NNLO antenna subtraction for different colour structures, we construct the integrated forms of the subtraction terms needed for the five-parton and four-parton contributions to e+e−→3 jets at NNLO in all colour factors, and show that their infrared poles cancel analytically with the infrared poles of the two-loop virtual correction to this observable.

Infrared structure ofe+e−→ 3 jets at NNLO

We describe the calculation of the next-to-next-to-leading order (NNLO) QCD corrections to three-jet production and related event shape observables in electron-positron annihilation. Infrared singularities due to double real radiation at tree level and single real radiation at one loop are subtracted from the full QCD matrix elements using antenna functions, which are then integrated analytically and added to the two loop contribu- tion. Using this antenna subtraction method, we obtain numerically finite contributions from five-parton and four-parton processes, and observe an explicit analytic cancellation of infrared poles in the four-parton and three-parton contributions. All contributions are implemented in a flexible parton-level event generator programme, allowing the numeri- cal computation of any infrared-safe observable related to three-jet final states to NNLO accuracy.

Antenna subtraction at NNLO with hadronic initial states: initial-final configurations

We extend the antenna subtraction method to include initial states containing one hadron at NNLO. We present results for all the necessary subtraction terms, antenna functions, for the master integrals required to integrate them over the relevant phase space and finally for the integrated antennae themselves. Where applicable, our results are cross-checked against the known NNLO coefficient functions for deep inelastic scattering processes.

NNLO QCD corrections to jet production at hadron colliders from gluon scattering

A bstractWe present the next-to-next-to-leading order (NNLO) QCD corrections to dijet production in the purely gluonic channel retaining the full dependence on the number of colours. The sub-leading colour contribution in this channel first appears at NNLO and increases the NNLO correction by around 10% and exhibits a pT dependence, rising from 8% at low pT to 15% at high pT. The present calculation demonstrates the utility of the antenna subtraction method for computing the full colour NNLO corrections to dijet production at the Large Hadron Collider.

Antenna subtraction at NNLO with hadronic initial states: double real radiation for initial-initial configurations with two quark flavours

The antenna subtraction formalism allows to calculate QCD corrections to jet observables. Within this formalism, the subtraction terms are constructed using antenna functions describing all unresolved radiation between a pair of hard radiator partons. In this paper, we focus on the subtraction terms for double real radiation contributions to jet observables in hadron-hadron collisions evaluated at NNLO. An essential ingredient to these subtraction terms are the four-parton antenna functions with both radiators in the initial state. We outline the construction of the double real subtraction terms, classify all relevant antenna functions and describe their integration over the relevant antenna phase space. For the initial-initial antenna functions with two quark flavours, we derive the phase space master integrals and obtain the integrated antennae.

Double virtual corrections for gluon scattering at NNLO

A bstractWe use the antenna subtraction method to isolate the double virtual infrared singularities present in gluonic scattering amplitudes at next-to-next-to-leading order. In previous papers, we derived the subtraction terms that rendered (a) the double real radiation tree-level process finite in the single and double unresolved regions of phase space and (b) the mixed single real radiation one-loop process both finite and well behaved in the unresolved regions of phase space. Here, we show how to construct the double virtual subtraction term using antenna functions with both initial- and final-state partons which remove the explicit infrared poles present in the two-loop amplitude. As an explicit example, we write down the subtraction term for the four-gluon two-loop process. The infrared poles are explicitly and locally cancelled in all regions of phase space leaving a finite remainder that can be safely evaluated numerically in four-dimensions.

Antenna subtraction with massive fermions at NNLO: double real initial-final configurations

A bstractWe derive the integrated forms of specific initial-final tree-level four-parton antenna functions involving a massless initial-state parton and a massive final-state fermion as hard radiators. These antennae are needed in the subtraction terms required to evaluate the double real corrections to

Double real radiation corrections to

t\overline{t}

t\overline t

hadronic production at the NNLO level stemming from the partonic processes

production at the LHC: the all-fermion processes

q\overline{q}\to t\overline{t}{q^{\prime }}{{\overline{q}}^{\prime }}