Search

KLOE and Babar have an observed discrepancy of 2% to 5% in the invariant pion pair production cross section. These measurements are based on approximate NLO $ ��^+ ��^- ��$ cross section predictions of the Monte Carlo event generator PHOKHARA7.0. In this article, the complete NLO radiative corrections to $ ��^+ ��^- ��$ production are calculated and implemented in the Monte Carlo event generator PHOKHARA9.0. Numerical reliability is guaranteed by two independent approaches to the real and the virtual corrections. The novel features include the contribution of pentagon diagrams in the virtual corrections, which form a gauge-invariant set when combined with their box diagram partners. They may contribute to certain distributions at the percent level. Also the real emission was complemented with two-photon final state emission contributions not included in the generator PHOKHARA7.0. We demonstrate that the numerical influence reaches, for realistic charge-averaged experimental setups, not more than 0.1% at KLOE and 0.3% at BaBar energies. As a result, we exclude the approximations in earlier versions of PHOKHARA as origin of the observed experimental discrepancy., 28 pages, 8 figures

Die Berechnung von Tensorintegralen ist eines der komplizierteren Probleme bei der Berechnung von Einschleifen-Feynmandiagrammen. In dieser Arbeit wird die Computerprogrammbibliothek PJFry entwickelt, mit der Tensorintegrale mit bis zu fünf äusseren Beinen und unter Zugrundelegung beliebiger Kinematik numerisch ausgewertet werden können. Im Programm PJFry sind Algorithmen implementiert, mit denen bei der Reduktion von Pentagon-Tensoren inverse Potenzen der Gramdeterminanten vermieden werden können. Gramdeterminanten der Boxdiagramme werden unter Verwendung von Rekursionsrelationen mit variabler Raum-Zeit-Dimension in einem Satz neuer Basisintegrale isoliert. Die neuen Basisintegrale werden ebenfalls durch Rekursionsrelationen mit variabler Raum-Zeit-Dimension oder durch Entwicklung in kleinen Gramdeterminanten ausgewertet. Die Konvergenz letzterer wird durch Padé-Extrapolation erheblich beschleunigt. Ein Cache-System erlaubt die mehrfache Verwendung von numerischen Bausteinen und erhöht zusätzlich die Effizienz des Programmpakets. Ausser ausführlichen Tests von Struktur und Genauigkeit der Algorithmen wird eine nichtriviale Beispielanwendung ausgearbeitet und mit dem Programm NGluon verglichen: die Berechnung von fünf-Gluon-Helizitätsamplituden. Schließlich werden die virtuellen Einschleifenkorrekturen zur Myonpaarproduktion mit Emission energiereicher ("harter") Photonen berechnet. Die Methode wird erläutert, wie auch Renormierung und Behandlung der Polstruktur in dimensionaler Regularisierung. Numerische Vorhersagen für differentielle Wirkungsquerschnitte werden berechnet, unter Zugrundelegung der kinematischen Situationen, wie sie bei den Detektoren KLOE (DAFNE, Frascati) und BaBar (SLAC) typisch sind. In this thesis we discuss the problem of evaluation of tensor integrals appearing in a typical one-loop Feynman diagram calculation. We present a computer library for the numerical evaluation of tensor integrals with up to 5 legs and arbitrary kinematics. The code implements algorithms based on the formalism which avoids the appearance of inverse Gram determinants in the reduction of pentagon diagrams. The Gram determinants of box integrals are isolated in the set of new basis integrals by using dimensional recurrence relations. These integrals are then evaluated by dimensional recurrence or expansion in small Gram determinant, which is improved by Padé extrapolation. A cache system allows reuse of identical building blocks and increases the efficiency. After describing the cross checks and accuracy tests, we show a sample application to the evaluation of five gluon helicity amplitudes, which is compared with the output of the program NGluon. In the last part the program is applied to the calculation of the one-loop virtual corrections to the muon pair production with hard photon emission. The computation method is explained, followed by a discussion of renormalization and pole structure. Finally, we present numerical results for differential cross sections with kinematics of the KLOE and BaBar detectors.

We report on some recent developments in algebraic tensor reduction of one-loop Feynman integrals. For 5-point functions, an efficient tensor reduction was worked out recently and is now available as numerical C++ package, PJFry, covering tensor ranks until five. It is free of inverse 5-point Gram determinants, and inverse small 4-point Gram determinants are treated by expansions in higher-dimensional 3-point functions. By exploiting sums over signed minors, weighted with scalar products of chords (or, equivalently, external momenta), extremely efficient expressions for tensor integrals contracted with external momenta were derived. The evaluation of 7-point functions is discussed. In the present approach one needs for the reductions a $(d+2)$-dimensional scalar 5-point function in addition to the usual scalar basis of 1- to 4-point functions in the generic dimension $d=4-2 \epsilon$. When exploiting the four-dimensionality of the kinematics, this basis is sufficient. We indicate how the $(d+2)$-dimensional 5-point function can be evaluated., Comment: 8 pages, 1 figure. Contribution to Proceedings of "10th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology)" - Radcor2011, September 26-30, 2011, Mamallapuram, India

8 pp. (2011)., The C++ package PJFry 1.0.0 [1, 2] – a one loop tensor integral library – is introduced. We use an algebraic approach to tensor reduction. As a result, the tensor integrals are presented in terms of scalar one- to four-point func- tions, which have to be provided by an external library, e.g. QCDLoop/FF or OneLOop or LoopTools/FF. The reduction is implemented until five-point functions of rank five. A numerical example is shown, including a special treatment for small or vanishing inverse four-point Gram determinants. Future modules of PJFry might cover the treatment of n-point functions with n ≥ 6; the corresponding formulae are worked out. Further, an extremely efficient approach to tensor reduction relies on evaluations of complete contractions of the tensor integrals with external momenta. For this, we worked out an algo- rithm for the analytical evaluation of sums over products of signed minors with scalar products of chords, i.e. differences of external momenta. As a result, the usual multiple sums over tensor coefficients are replaced for the numerical evaluation by compact combinations of the basic scalar functions.

We report on the three Mathematica packages hexagon, CSectors, AMBRE. They are useful for the evaluation of one- and two-loop Feynman integrals with a dependence on several kinematical scales. These integrals are typically needed for LHC and ILC applications, but also for higher order corrections at meson factories. hexagon is a new package for the tensor reduction of one-loop 5-point and 6-point functions with rank R=3 and R=4, respectively; AMBRE is a tool for derivations of Mellin-Barnes representations; CSectors is an interface for the package sector_decomposition and allows a convenient, direct evaluation of tensor Feynman integrals., 9 pages, 1 figure, subm. to PoS(ACAT08)124

We present an update of the Binoth Les Houches Accord (BLHA) to standardise the interface between Monte Carlo programs and codes providing one-loop matrix elements. (C) 2013 Elsevier B.V. All rights reserved.

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., Comment: 220 pages

We present an update of the Binoth Les Houches Accord (BLHA) to standardise the interface between Monte Carlo programs and codes providing one-loop matrix elements., Comment: 24 pages, 1 pdf figure