This article displays a proof of concept of the mixed analytical/numerical method, presented in previous publications, to compute two-loop functions with up to five massive propagators in a scalar theory having three- and four-leg vertices as the Higgs sector of the Standard Model. Several amplitudes are considered with two, three, and four external legs. Some of them diverge in the ultraviolet region and we demonstrate that the method works in that case. It is shown that all these classes of amplitudes can be generated by four master topologies. The results of a numerical evaluation for some kinematics are presented; they are compared to public software and agree well within the error bars quoted by the different programs.

A framework to represent and compute two-loop N-point Feynman diagrams as double-integrals is discussed. The integrands are "generalised one-loop type" multi-point functions multiplied by simple weighting factors. The final integrations over these two variables are to be performed numerically, whereas the ingredients involved in the integrands, in particular the "generalised one-loop type" functions, are computed analytically. The idea is illustrated on a few examples of scalar three- and four-point functions.

We report on an ongoing work initiated by Prof. Shimizu, proposing a method to numerically compute two-loop scalar integrals as sums of two-dimensional integrals of generalised one-loop N-point functions analytically computed and integrated over some simple weight functions. The analytic computation of the generalised one-loop N-point functions in a systematic way motivates a novel approach sketched in this talk.

This article is the third and last of a series presenting an alternative method for computing the one-loop scalar integrals. It extends the results of the first two articles to the infrared divergent case. This novel method enjoys a couple of interesting features as compared with the methods found in the literature. It directly proceeds in terms of the quantities driving algebraic reduction methods. It yields a simple decision tree based on the vanishing of internal masses and one-pinched kinematic matrices, which avoids a profusion of cases. Lastly, it extends to kinematics more general than the physical, e.g. collider processes, relevant at one loop. This last feature may be useful when considering the application of this method beyond one loop using generalized one-loop integrals as building blocks.

This article is the first of a series of three presenting an alternative method of computing the one-loop scalar integrals. This novel method enjoys a couple of interesting features as compared with the method closely following 't Hooft and Veltman adopted previously. It directly proceeds in terms of the quantities driving algebraic reduction methods. It applies to the three-point functions and, in a similarway, to the four-point functions. It also extends to complex masses without much complication. Lastly, it extends to kinematics more general than that of the physical, e.g., collider processes relevant at one loop. This last feature may be useful when considering the application of this method beyond one loop using generalized one-loop integrals as building blocks.

We present a part of an ongoing work initiated by Prof. Shimizu on a method to compute numerically two loop scalar integrals as a sum of two dimensional integrals of generalized scalar one loop four point functions. This implies to have a formula for the one loop scalar four point functions which is valid outside the physical domain, this is the object of the present work.

We revisit the implementation of the metric-independent Fock–Schwinger gauge in the Abelian Chern–Simons field theory defined in ℝ 3 by means of a homotopy condition. This leads to the Lagrangian [Formula: see text] in terms of curvatures F and of the Poincaré homotopy operator h. The corresponding field theory provides the same link invariants as the Abelian Chern–Simons theory. Incidentally the part of the gauge field propagator which yields the link invariants of the Chern–Simons theory in the Fock–Schwinger gauge is recovered without any computation.

We implement the metric-independent Fock–Schwinger gauge in the quantum Chern–Simons (CS) field theory defined in a three-manifold M which is homeomorphic with ℝ3. The expressions of various components of the propagator are determined. Although the gauge field propagator differs from the Gauss linking density, we prove that its integral along two oriented knots is equal to the linking number.

The role played by Deligne-Beilinson cohomology in establishing the relation between Chern-Simons theory and link invariants in dimensions higher than three is investigated. Deligne-Beilinson cohomology classes provide a natural abelian Chern-Simons action, non trivial only in dimensions 4l + 3, whose parameter k is quantized. The generalized Wilson (2l + 1)-loops are observables of the theory and their charges are quantized. The Chern-Simons action is then used to compute invariants for links of (2l + 1)-loops, first on closed (4l + 3)-manifolds through a novel geometric computation, then on \documentclass[12pt]{minimal}\begin{document}$\mathbb {R}^{4l+3}$\end{document}R4l+3 through an unconventional field theoretic computation.

In this article we provide representations for the one-loop three point functions in 4 and 6 dimensions in the general case with complex masses. The latter are part of the GOLEM library used for the computation of one-loop multileg amplitudes. These representations are one-dimensional integrals designed to be free of instabilites induced by inverse powers of Gram determinants, therefore suitable for stable numerical implementations.

We discuss the isolation of prompt photons in hadronic collisions by means of narrow isolation cones and the QCD computation of the corresponding cross sections. We reconsider the occurence of large perturbative terms with logarithmic dependence on the cone size and their impact on the fragmentation scale dependence. We cure the apparent perturbative violation of unitarity for small cone sizes, which had been noticed earlier in next-to-leading-order (NLO) calculations, by resumming the leading logarithmic dependence on the cone size. We discuss possible implications regarding the implementation of some hollow cone variants of the cone criterion, which simulate the experimental difficulty to impose isolation inside the region filled by the electromagnetic shower that develops in the calorimeter.

The 2011 Les Houches workshop was the first to confront LHC data. In the two years since the previous workshop there have been significant advances in both soft and hard QCD, particularly in the areas of multi-leg NLO calculations, the inclusion of those NLO calculations into parton shower Monte Carlos, and the tuning of the non-perturbative parameters of those Monte Carlos. These proceedings describe the theoretical advances that have taken place, the impact of the early LHC data, and the areas for future development.

This Report summarises the results of the second year's activities of the LHC Higgs Cross Section Working Group. The main goal of the working group was to present the state of the art of Higgs Physics at the LHC, integrating all new results that have appeared in the last few years. The first working group report Handbook of LHC Higgs Cross Sections: 1. Inclusive Observables (CERN-2011-002) focuses on predictions (central values and errors) for total Higgs production cross sections and Higgs branching ratios in the Standard Model and its minimal supersymmetric extension, covering also related issues such as Monte Carlo generators, parton distribution functions, and pseudo-observables. This second Report represents the next natural step towards realistic predictions upon providing results on cross sections with benchmark cuts, differential distributions, details of specific decay channels, and further recent developments.

In this talk we present techniques for calculating one-loop amplitudes for multi-leg processes using Feynman diagrammatic methods in a semi-algebraic context.Our approach combines the advantages of the different methods allowing for a fast evaluation of the amplitude while monitoring the numerical stability of the calculation.In phase space regions close to singular kinematics we use a method avoiding spurious Gram determinants in the calculation.As an applica-

We present a program for the numerical evaluation of scalar integrals and tensor form factors entering the calculation of one-loop amplitudes which supports the use of complex masses in the loop integrals. The program is built on an earlier version of the golem95 library, which performs the reduction to a certain set of basis integrals using a formalism where inverse Gram determinants can be avoided. It can be used to calculate one-loop amplitudes with arbitrary masses in an algebraic approach as well as in the context of unitarity-inspired numerical reconstruction of the integrand.Program summaryProgram title: golem95-1.2.0Catalogue identifier: AEEO_v2_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEEO_v2_0.htmlProgram obtainable from: CPC Program Library, Queen's University. Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 182 492No. of bytes in distributed program, including test data, etc.: 950 549Distribution format: tar.gzProgramming language: Fortran95Computer: Any computer with a Fortran95 compilerOperating system: Linux, UnixRAM: RAM used per integral/form factor is insignificantClassification: 4.4, 11.1External routines: Some finite scalar integrals are called from OneLOop[1,2], the option to call them from LoopTools [3,4] is also implemented.Catalogue identifier of previous version: AEEO_v1_0Journal reference of previous version: Comput. Phys. Comm. 180 (2009) 2317Does the new version supersede the previous version?: YesNature of problem: Evaluation of one-loop multi-leg integrals occurring in the calculation of next-to-leading order corrections to scattering amplitudes in elementary particle physics. In the presence of massive particles in the loop, propagators going on-shell can cause singularities which should be regulated to allow for a successful evaluation.Solution method: Complex masses can be used in the loop integrals to stand for a width of an unstable particle, regulating the singularities by moving the poles away from the real axis.Reasons for new version: The previous version was restricted to massless particles in the loop.Summary of revisions: Real and complex masses are supported, a general mu parameter for the renormalization scale is introduced, improvements in the caching system and the user interface.Running time: Depends on the nature of the problem. A single call to a rank 6 six-point form factor at a randomly chosen kinematic point, using complex masses, takes 0.06 seconds on an Intel Core 2 Q9450 2.66 GHz processor.

In this talk we present techniques for calculating one-loop amplitudes for multi-leg processes using Feynman diagrammatic methods in a semi-algebraic context. Our approach combines the advantages of the different methods allowing for a fast evaluation of the amplitude while monitoring the numerical stability of the calculation. In phase space regions close to singular kinematics we use a method avoiding spurious Gram determinants in the calculation. As an applica-

We report on the current status of the Golem project which aims at the construction of a general one-loop evaluator for matrix elements. We construct the one-loop matrix elements from Feynman diagrams in a highly automated way and provide a library for the reduction and numerically stable evaluation of the tensor integrals involved in this approach. Furthermore, we present applications to physics processes relevant for the LHC.

G. Cullen,a N. Greiner,b A. Guffanti,c J.P. Guillet,d G. Heinrich,e S. Karg, f N. Kauer,g T. Kleinschmidt,e M. Koch-Janusz,h G. Luisoni,e P. Mastrolia,i, j,k G. Ossola,l E. Pilon,d T. Reiter∗,h M. Rodgers,e F. Tramontano,k I. Wigmore,a a School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3JZ, UK, b Department of Physics, University of Illinois at Urbana-Champaign, Urbana IL, 61801, USA, c Physikalisches Institut, Albert-Ludwigs-Universität, 79104 Freiburg, Germany, d LAPTH, 74941 Annecy le Vieux Cedex, France, e IPPP, University of Durham, Durham DH1 3LE, UK, f Institut für Theoretische Teilchenphysik und Kosmologie, RWTH Aachen University,

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