Loop integration results using numerical extrapolation for a non-scalar integral

Loop integration results have been obtained using numerical integration and extrapolation. An extrapolation to the limit is performed with respect to a parameter in the integrand which tends to zero. Results are given for a non-scalar four-point diagram. Extensions to accommodate loop integration by existing integration packages are also discussed. These include: using previously generated partitions of the domain and roundoff error guards.Comment: 4 pages, 3 figures, revised, contribution to ACAT03 (Dec. 2003

Computational Particle Physics for Event Generators and Data Analysis

High-energy physics data analysis relies heavily on the comparison between experimental and simulated data as stressed lately by the Higgs search at LHC and the recent identification of a Higgs-like new boson. The first link in the full simulation chain is the event generation both for background and for expected signals. Nowadays event generators are based on the automatic computation of matrix element or amplitude for each process of interest. Moreover, recent analysis techniques based on the matrix element likelihood method assign probabilities for every event to belong to any of a given set of possible processes. This method originally used for the top mass measurement, although computing intensive, has shown its power at LHC to extract the new boson signal from the background. Serving both needs, the automatic calculation of matrix element is therefore more than ever of prime importance for particle physics. Initiated in the eighties, the techniques have matured for the lowest order calculations (tree-level), but become complex and CPU time consuming when higher order calculations involving loop diagrams are necessary like for QCD processes at LHC. New calculation techniques for next-to-leading order (NLO) have surfaced making possible the generation of processes with many final state particles (up to 6). If NLO calculations are in many cases under control, although not yet fully automatic, even higher precision calculations involving processes at 2-loops or more remain a big challenge. After a short introduction to particle physics and to the related theoretical framework, we will review some of the computing techniques that have been developed to make these calculations automatic. The main available packages and some of the most important applications for simulation and data analysis, in particular at LHC will also be summarized.Comment: 19 pages, 11 figures, Proceedings of CCP (Conference on Computational Physics) Oct. 2012, Osaka (Japan) in IOP Journal of Physics: Conference Serie

GRACE at ONE-LOOP: Automatic calculation of 1-loop diagrams in the electroweak theory with gauge parameter independence checks

We describe the main building blocks of a generic automated package for the calculation of Feynman diagrams. These blocks include the generation and creation of a model file, the graph generation, the symbolic calculation at an intermediate level of the Dirac and tensor algebra, implementation of the loop integrals, the generation of the matrix elements or helicity amplitudes, methods for the phase space integrations and eventually the event generation. The report focuses on the fully automated systems for the calculation of physical processes based on the experience in developing GRACE-loop. As such, a detailed description of the renormalisation procedure in the Standard Model is given emphasizing the central role played by the non-linear gauge fixing conditions for the construction of such automated codes. The need for such gauges is better appreciated when it comes to devising efficient and powerful algorithms for the reduction of the tensorial structures of the loop integrals. A new technique for these reduction algorithms is described. Explicit formulae for all two-point functions in a generalised non-linear gauge are given, together with the complete set of counterterms. We also show how infrared divergences are dealt with in the system. We give a comprehensive presentation of some systematic test-runs which have been performed at the one-loop level for a wide variety of two-to-two processes to show the validity of the gauge check. These cover fermion-fermion scattering, gauge boson scattering into fermions, gauge bosons and Higgs bosons scattering processes. Comparisons with existing results on some one-loop computation in the Standard Model show excellent agreement. We also briefly recount some recent development concerning the calculation of mutli-leg one-loop corrections.Comment: 131 pages. Manuscript expanded quite substantially with the inclusion of an overview of automatic systems for the calculation of Feynman diagrams both at tree-level and one-loop. Other additions include issues of regularisation, width effects and renormalisation with unstable particles and reduction of 5- and 6-point functions. This is a preprint version, final version to appear as a Phys. Re

The Generalised Instrument

Thesis (M.E.Sc.) -- University of Adelaide, 199

Minimisations sous contraintes et flots du périmètre et de l'énergie de Willmore

We study the minimisation with constraints of the perimeter and of the Willmore energie and the flow of the Willmore energie, defined by minimising movements. The geometric optimisation problems and flows we handle rely on a lower semicontinuous property that we enforce by taking the lower semicontinuous envelop of the energies including the constraints.In the first part of the thesis, we consider three optimisation problems. The first one deals with the perimeter and connectedness constraints in the plan. The second one is a reconstruction problem of a volumetric domain from planar slices. This reconstruction is based on the minimisation of the perimeter or of the Willmore energy with inclusion-exclusion constraints. A phase field numerical approach and experiments are implemented. The third problem is the study of closed curves confined in an open bounded subset of the plane that minimise the bending energy (or Willmore energy). The second part of the thesis studies the Willmore flow defined by minimising movements. The flow of a regular surface is complex to analyse and may develop singularities in finite time. We use the lower semicontinuous envelop of the Willmore energy and the minimising movement to define a long time flow for surfaces with less regularity. This flow is studied within two contexts: for the sum of the Willmore energy and the perimeter in the plane and for the Willmore energy of radial functions with a non-increasing profile in any dimension.Nous étudions la minimisation du périmètre et de l'énergie de Willmore en présence de contraintes ainsi que le flot, défini par les mouvements minimisants, de l'énergie de Willmore. Les problèmes d'optimisation géométriques et les flots que nous considérons reposent sur une propriété de semi-continuité inférieure que nous pouvons assurer en prenant l'enveloppe semi-continue inférieurement des énergies incluant les contraintes.Dans la première partie de la thèse, nous étudions trois problèmes d'optimisation. Le premier concerne le périmètre avec une contrainte de connexité. Le second est un problème de reconstruction de domaine à partir de sections planaires. Cette reconstruction est basée sur la minimisation du périmètre ou de l'énergie de Willmore avec des contraintes d'inclusion-exclusion. Nous développons un modèle de champ de phase pour implémenter numériquement la reconstruction en 2D et 3D à partir de contraintes d'inclusion-exclusion variées. Le troisième problème est l'étude des propriétés des courbes fermées, confinées dans un ouvert borné du plan, minimisant l'énergie élastique (Willmore).La deuxième partie étudie le flot de l'énergie de Willmore par les mouvements minimisants. Le flot pour une surface régulière est difficile à analyser, entre autre car il peut développer des singularités en temps fini. L'enveloppe semi-continue inférieurement et les mouvements minimisants permettent de définir un flot en temps long pour des surfaces moins régulières. Ce flot est étudié dans deux situations~: pour la somme de l'énergie de Willmore et du périmètre dans le plan et pour l'énergie de Willmore des fonctions radiales à profil décroissant en toute dimension