At the time of writing these proceedings (December 2009), we have just witnessed the successful re-start (after the sudden stop of operations in September 2008) of the world’s most powerful particle accelerator ever built. CERN’s Large Hadron Collider (LHC) has provided first collisions at injection energy (450 GeV per beam) and at the world’s record energy of 1.18 TeV/beam. The centre-of-mass energy was increased to 7 TeV for the runs in 2010 and 2011.

The production of one hard jet in association with missing transverse energy is a major LHC search channel motivated by many scenarios for physics beyond the standard model. In scenarios with a weakly interacting dark matter candidate, like supersymmetry, it arises from the associated production of a quark partner with the dark matter agent. We present the next-to-leading-order cross section calculation as the first application of the fully automized MADGOLEM package. We find moderate corrections to the production rate with a strongly reduced theory uncertainty.

A fully differential calculation of the next-to-leading order QCD corrections to the production of Z-boson pairs in association with a hard jet at the Tevatron and LHC is presented. This process is an important background for Higgs particle and new physics searches at hadron colliders. We find sizable corrections for cross sections and differential distributions, particularly at the LHC. Residual scale uncertainties are typically at the 10% level and can be further reduced by applying a veto against the emission of a second hard jet. Our results confirm that NLO corrections do not simply rescale LO predictions.

In this talk we discuss recent progress concerning precise predictions for hadron colliders. We show results of two applications of tensor reduction using GOLEM methods: the next-to-leading order (NLO) corrections to $pp \to ZZ+$jet as an important background for Higgs particle and new physics searches at hadron colliders, and the NLO corrections to graviton plus jet hadro-production, which is an important channel for graviton searches at the Tevatron and the LHC.

In this talk we review the GOLEM approach to one-loop calculations and present an automated implementation of this technique. This method is based on Feynman diagrams and an advanced reduction of one-loop tensor integrals which avoids numerical instabilities. We have extended our one-loop integral library golem95 with an automated one-loop matrix element generator to compute the virtual corrections of the process $q\bar{q}\to b\bar{b}b\bar{b}$. The implementation of the virtual matrix element has been interfaced with tree-level Monte Carlo programs to provide the full result for the above process.

The production of two b-quark pairs is a prominent background for Higgs and New Physics searches in various extensions of the Standard Model. We present here the next-to-leading order QCD corrections to the quark induced subprocess using the GOLEM approach for the virtual corrections. We show that our result considerably improves the prediction and conclude that the inclusion of next-to-leading order effects is indispensable for reliable studies of four b-quark observables in hadronic collisions.

Many highly developed Monte Carlo tools for the evaluation of cross sections based on tree matrix elements exist and are used by experimental collaborations in high energy physics. As the evaluation of one-loop matrix elements has recently been undergoing enormous progress, the combination of one-loop matrix elements with existing Monte Carlo tools is on the horizon. This would lead to phenomenological predictions at the next-to-leading order level. This note summarises the discussion of the next-to-leading order multi-leg (NLM) working group on this issue which has been taking place during the workshop on Physics at TeV colliders at Les Houches, France, in June 2009. The result is a proposal for a standard interface between Monte Carlo tools and one-loop matrix element programs.

This report summarizes the activities of the SM and NLO Multileg Working Group of the Workshop "Physics at TeV Colliders", Les Houches, France 8-26 June, 2009.

The last 2 years have seen great productivity in the area of multi-parton calculations at leading order (LO), next-to-leading order (NLO) and Next-to-next-to-leading order (NNLO). This document reflects the work done in this sector for a full understanding of both the standard model and beyond the standard model physics at LHC. This document is divided into 6 parts: 1) NLO techniques, standardization, automation, 2) new high order calculations, wish-list, 3) observables, 4) Higgs phenomenology, and 5) MCN/NLO interface

We present a program for the numerical evaluation of form factors entering the calculation of one-loop amplitudes with up to six external legs. The program is written in Fortran95 and performs the reduction to a certain set of basis integrals numerically. using a formalism where inverse Gram determinants can be avoided. It can be used to Calculate one-loop amplitudes with massless internal particles in a fast and numerically stable way.

In this talk I report on recent developments and results relevant for LHC phenomenology at next-to-leading order QCD. Feynman diagrammatic and unitarity based methods have both seen considerable improvements and new ideas recently. Current approaches point towards automated evaluation of one-loop multi-particle amplitudes. Many results for notoriously difficult processes are under construction by several groups and, given the enormous recent progress, it can be concluded that LHC phenomenology at full next-to-leading order level will become the standard approximation soon.

We calculate the order (α2αs3) interference effect between the gluon fusion and weak boson fusion processes allowed at the one-loop level in Higgs boson plus 2 jet production at the LHC. The corresponding one-loop amplitudes, which have not been considered in the literature so far, are evaluated analytically using dimensional regularisation and the necessary master integrals with massive propagators are reported. It is discussed in detail how various mechanisms conspire to make this contribution numerically negligible for experimental studies at the LHC.

This report summarizes the activities of the NLM working group of the Workshop Physics at TeV Colliders, Les Houches, France, 11-29 June, 2007.

In this talk we present recent next-to-leading order results relevant for LHC phenomenology obtained with the GOLEM method. After reviewing the status of this Feynman diagrammatic approach for multi-leg one-loop calculations we discuss three applications: the loop-induced process gg -> Z*Z* and the virtual corrections to the five and six point processes qq -> ZZg and u (u) over bar -> s (s) over barc (c) over bar. We demonstrate that our method leads to representations of such amplitudes which allow for efficient phase space integration. In this context we propose a reweighting technique of the leading order unweighted events by local K-factors.

A calculation of the loop-induced gluon-fusion process gg --> Z(photon)Z(photon) --> l anti-l l' anti-l' is presented, which provides an important background for Higgs boson searches in the H --> ZZ channel at the LHC. We find that the photon contribution is important for Higgs masses below the Z-pair threshold and that the gg-induced process yields a correction of about 15% relative to the NLO QCD prediction for the q anti-q-induced process when only a M(l anti-l), M(l' anti-l') > 5 GeV cut is applied.

A calculation of the loop-induced gluon-fusion process gg → Z∗(γ∗)Z∗(γ∗) → ll̄l′l̄′ is presented, which provides an important background for Higgs boson searches in the H → ZZ channel at the LHC. We find that the photon contribution is important for Higgs masses below the Z-pair threshold and that the gg-induced process yields a correction of about 15% relative to the NLO QCD prediction for the qq̄-induced process when only a Mll̄, Ml′ l̄ > 5 GeV cut is applied.

Report of the Working Group on Higgs Bosons for the Workshop, “Physics at TeV Colliders”, Les Houches, France, 11-29 June, 2007.

We present a calculation of the NLO QCD corrections for the production of three vector bosons at the LHC, namely ZZZ, W(+)W(-)Z, W(+)ZZ, and W+ W-W+ production. The virtual corrections are computed using the recently proposed method of reduction at the integrand level (OPP reduction). Concerning the contributions coming from real emission we used the dipole subtraction to treat the soft and collinear divergences. We find that the QCD corrections for these electroweak processes are in the range between 70 and 100 percent. As such they have to be considered in experimental studies of triple vector boson production at the LHC.