We introduce a new technique to generate scattering amplitudes at one loop. Traditional tree algorithms, which handle diagrams with fixed momenta, are promoted to generators of loop-momentum polynomials that we call open loops. Combining open loops with tensor-integral and Ossola-Papadopoulos-Pittau reduction results in a fully flexible, very fast, and numerically stable one-loop generator. As demonstrated with nontrivial applications, the open-loop approach will permit us to obtain precise predictions for a very wide range of collider processes.

We discuss the evaluation of the collinear single-logarithmic contributions to virtual electroweak corrections at high energies. More precisely, we proof the factorization of the mass singularities originating from loop diagrams involving collinear virtual gauge bosons coupled to external legs. We discuss, in particular, processes involving external longitudinal gauge bosons, which are treated using the Goldstone-boson equivalence theorem. The proof of factorization is performed within the 't Hooft-Feynman gauge at one-loop order and applies to arbitrary electroweak processes that are not mass-suppressed at high energies. As basic ingredient we use Ward identities for Green functions with arbitrary external particles involving a gauge boson collinear to one of these. The Ward identities are derived from the BRS invariance of the spontaneously broken electroweak gauge theory.

We report on the first calculation of next-to-next-to-leading order (NNLO) QCD corrections to the inclusive production of ZZ pairs at hadron colliders. Numerical results are presented for pp collisions with centre-of-mass energy ($\sqrt{s}$) ranging from 7 to 14 TeV. The NNLO corrections increase the NLO result by an amount varying from $11\%$ to $17\%$ as $\sqrt{s}$ goes from 7 to 14 TeV. The loop-induced gluon fusion contribution provides about $60\%$ of the total NNLO effect. When going from NLO to NNLO the scale uncertainties do not decrease and remain at the $\pm 3\%$ level.Comment: Reference added, version published on Physics Letters

Charged gauge boson pair production at the Large Hadron Collider allows detailed probes of the fundamental structure of electroweak interactions. We present precise theoretical predictions for on-shell W+ W- production that include, for the first time, QCD effects up to next to next to leading order in perturbation theory. As compared to next to leading order, the inclusive W+ W- cross section is enhanced by 9% at 7 TeV and 12% at 14 TeV. The residual perturbative uncertainty is at the 3% level. The severe contamination of the W+ W- cross section due to top-quark resonances is discussed in detail. Comparing different definitions of top-free W+ W- production in the four and five flavor number schemes, we demonstrate that top-quark resonances can be separated from the inclusive W+ W- cross section without a significant loss of theoretical precision.

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