Automatic Loop Calculations with FeynArts, FormCalc, and LoopTools

This article describes three Mathematica packages for the automatic calculation of one-loop Feynman diagrams: the diagrams are generated with FeynArts, algebraically simplified with FormCalc, and finally evaluated numerically using the LoopTools package. The calculations are performed analytically as far as possible, with results given in a form well suited for numerical evaluation. The latter is straightforward with the utility programs provided by FormCalc (e.g. for translation into Fortran code) and the implementations of the one-loop integrals in LoopTools. The programs are also equipped for calculations in supersymmetric models.Comment: 6 pages, uses axodraw and npb.sty. Talk given at Loops and Legs 2000, Bastei, Germany, April 9-1

On e+e- --> W+W- --> 4f(+gamma) at LEP2

The results on e+e- --> W+W- --> 4f(+gamma) obtained by different groups are compared with each other. Differences in the results for the total cross section of up to about 0.6% are traced back to different ways of implementing the double-pole approximation.Comment: 11 pages, late

Radiative corrections to e+e- --> WW --> 4f with RACOONWW

RACOONWW is the first Monte Carlo generator for e+e- --> WW --> 4f(+gamma) that includes the electroweak O(alpha) radiative corrections in the double-pole approximation completely. Some numerical results for LEP2 energies are discussed, and the predictions for the total W-pair cross section are confronted with LEP2 data.Comment: 7 pages, latex, 5 postscript files, to appear in the Proceedings of the 5th Zeuthen Workshop on Elementary Particle Theory ``Loops and Legs in Quantum Field Theory'', Bastei/Koenigstein, Germany, April 9-14, 200

Four-fermion production at gamma gamma colliders: 2. Radiative corrections in double-pole approximation

The O(alpha) electroweak radiative corrections to gamma gamma --> WW --> 4f within the electroweak Standard Model are calculated in double-pole approximation (DPA). Virtual corrections are treated in DPA, leading to a classification into factorizable and non-factorizable contributions, and real-photonic corrections are based on complete lowest-order matrix elements for gamma gamma --> 4f + gamma. Soft and collinear singularities appearing in the virtual and real corrections are combined alternatively in two different ways, namely by using the dipole subtraction method or by applying phase-space slicing. The radiative corrections are implemented in a Monte Carlo generator called COFFERgammagamma, which optionally includes anomalous triple and quartic gauge-boson couplings in addition and performs a convolution over realistic spectra of the photon beams. A detailed survey of numerical results comprises O(alpha) corrections to integrated cross sections as well as to angular, energy, and invariant-mass distributions. Particular attention is paid to the issue of collinear-safety in the observables.Comment: 42 pages, latex, 34 postscript figure

Generating Feynman Diagrams and Amplitudes with FeynArts 3

This paper describes the Mathematica package FeynArts used for the generation and visualization of Feynman diagrams and amplitudes. The main features of version 3 are: generation of diagrams at three levels, user-definable model files, support for supersymmetric models, and publication-quality Feynman diagrams in PostScript or LaTeX.Comment: 10 pages, minor changes in the text and markup, version to appear in Comp. Phys. Com

Electroweak Corrections to e+e- --> 4 fermions

The calculation of the full electroweak O(alpha) corrections to the charged-current four-fermion production processes e+e- --> nu_tau tau+ mu- anti-nu_mu, u anti-d mu- anti-nu_mu, and u anti-d s anti-c is briefly reviewed. The calculation is performed using the complex-mass scheme for the gauge-boson resonances. The evaluation of the occurring one-loop tensor integrals, which include 5- and 6-point functions, requires new techniques. The effects of the complete O(alpha) corrections to the total cross section and to the production-angle distribution are discussed and compared to predictions based on the double-pole approximation, revealing that the latter approximation is not sufficient to fully exploit the potential of a future linear collider in an analysis of W-boson pairs at high energies.Comment: 5 pages, LaTeX, 6 postscript figures, to appear in the proceedings of the "7th International Symposium on Radiative Corrections (RADCOR05)", Shonan Village, 200

Reduction of one-loop tensor 5-point integrals

A new method for the reduction of one-loop tensor 5-point integrals to related 4-point integrals is proposed. In contrast to the usual Passarino-Veltman reduction and other methods used in the literature, this reduction avoids the occurrence of inverse Gram determinants, which potentially cause severe numerical instabilities in practical calculations. Explicit results for the 5-point tensor coefficients are presented up to rank 4. The expressions for the reduction of the relevant 1-, 2-, 3-, and 4-point tensor coefficients to scalar integrals are also included; apart from these standard integrals no other integrals are needed.Comment: 24 pages, latex, some references adde

RacoonWW1.3: A Monte Carlo program for four-fermion production at e^+ e^- colliders

We present the Monte Carlo generator RacoonWW that computes cross sections to all processes e^+ e^- -> 4f and e^+ e^- -> 4f + gamma and calculates the complete O(alpha) electroweak radiative corrections to e^+ e^- -> W W -> 4f in the electroweak Standard Model in double-pole approximation. The calculation of the tree-level processes e^+ e^- -> 4f and e^+ e^- -> 4f + gamma is based on the full matrix elements for massless (polarized) fermions. When calculating radiative corrections to e^+ e^- -> W W -> 4f the complete virtual doubly-resonant electroweak corrections are included, i.e. the factorizable and non-factorizable virtual corrections in double-pole approximation, and the real corrections are based on the full matrix elements for e^+ e^- -> 4f + gamma. The matching of soft and collinear singularities between virtual and real corrections is done alternatively in two different ways, namely by using a subtraction method or by applying phase-space slicing. Higher-order initial-state photon radiation and naive QCD corrections are taken into account. RacoonWW also provides anomalous triple gauge-boson couplings for all processes e^+ e^- -> 4f and anomalous quartic gauge-boson couplings for all processes e^+ e^- -> 4f + gamma.Comment: 62 pages, LaTeX, elsart styl

One-loop leading logarithms in electroweak radiative corrections: II. Factorization of collinear singularities

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.Comment: 28 pages, late