E. W. Nigel Glover

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.

Recursion relations for gauge theory amplitudes with massive particles

We derive general tree-level recursion relations for amplitudes which include massive propagating particles. As an illustration, we apply these recursion relations to scattering amplitudes of gluons coupled to massive scalars. We provide new results for all amplitudes with a pair of scalars and n ≤ 4 gluons. These amplitudes can be used as building blocks in the computation of one-loop 6-gluon amplitudes using unitarity based methods.

Recursion relations for gauge theory amplitudes with massive vector bosons and fermions

We apply the on-shell tree-level recursion relations of Britto, Cachazo, Feng and Witten to a variety of processes involving internal and external massive particles with spin. We show how to construct multi-vector boson currents where one or more off-shell vector bosons couples to a quark pair and number of gluons. We give compact results for single vector boson currents with up to six partons and double vector boson currents with up to four partons for all helicity combinations. We also provide expressions for single vector boson currents with a quark pair and an arbitrary number of gluons for some specific helicity configurations. Finally, we show how to generalise the recursion relations to handle massive particles with spin on internal lines using gg→t as an example.

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.

A calculational formalism for one-loop integrals

We construct a specific formalism for calculating the one-loop virtual corrections for standard model processes with an arbitrary number of external legs. The procedure explicitly separates the infrared and ultraviolet divergences analytically from the finite one-loop contributions, which can then be evaluated numerically using recursion relations. Using the formalism outlined in this paper, we are in position to construct the next-to-leading order corrections to a variety of multi-leg QCD processes such as multi-jet production and vector-boson(s) plus multi-jet production at hadron colliders. The final limiting factor on the number of particles will be the available computer power.

Two-loop corrections to Light-by-Light scattering in Supersymmetric QED

We use an n-dimensional projection method to calculate helicity amplitudes for photon-photon scattering up to the two-loop level, for massless particles inside the loop. We confirm the recent standard model results found by Bern et al using another calculational method. We further apply the method to N = 1 and N = 2 supersymmetric QED. As predicted by the supersymmetric Ward identity, two of the independent amplitudes vanish. The remaining amplitude simplifies as the number of supersymmetries increases. For N = 2 SUSY QED, only contributions of weight 4 remain.

Antenna subtraction for gluon scattering at NNLO

We use the antenna subtraction method to isolate the double real radiation infrared singularities present in gluonic scattering amplitudes at next-to-next-to-leading order. The antenna subtraction framework has been successfully applied to the calculation of NNLO corrections to the 3-jet cross section and related event shape distributions in electron-positron annihilation. Here we consider processes with two coloured particles in the initial state, and in particular two-jet production at hadron colliders such as the Large Hadron Collider (LHC). We construct a subtraction term that describes the single and double unresolved contributions from the six-gluon tree-level process using antenna functions with initial state partons and show numerically that the subtraction term correctly approximates the matrix elements in the various single and double unresolved configurations.

One-loop phi-MHV amplitudes using the unitarity bootstrap

We consider a Higgs boson coupled to gluons via the five-dimensional effective operator HtrGμνGμν produced by considering the heavy top quark limit of the one-loop coupling of Higgs and gluons in the standard model. We treat H as the real part of a complex field that couples to the selfdual gluon field strengths and compute the one-loop corrections to amplitudes involving , two colour adjacent negative helicity gluons and an arbitrary number of positive helicity gluons - the so-called -MHV amplitudes. We use four-dimensional unitarity to construct the cut-containing contributions and the recently developed recursion relations to obtain the rational contribution for an arbitrary number of external gluons. We solve the recursion relations and give explicit results for up to four external gluons. These amplitudes are relevant for Higgs plus jet production via gluon fusion in the limit where the top quark mass is large compared to all other scales in the problem.

Multi-gluon collinear limits from MHV diagrams

We consider the multi-collinear limit of multi-gluon QCD amplitudes at tree level. We use the MHV rules for constructing colour ordered tree amplitudes and the general collinear factorization formula to derive timelike splitting functions that are valid for specific numbers of negative helicity gluons and an arbitrary number of positive helicity gluons (or vice versa). As an example we present new results describing the collinear limits of up to six gluons.

The high energy limit of QCD at two loops

By taking the high-energy limit of the two-loop amplitudes for parton-parton scattering, we have tested the validity of the loop expansion of the high-energy amplitude, arising from a reggeized gluon passed in the crossed channel. As expected, we have found that it holds at LL and NLL accuracy, and hence we have independently re-evaluated the two-loop Regge trajectory, finding full agreement with the previous results by Fadin and collaborators. We have found, though, that the universality implied by the exchange of a single reggeized gluon in the crossed channel is violated at the next-to-next-to-leading logarithmic level.