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

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

News from FormCalc and LoopTools

The FormCalc package automates the computation of FeynArts amplitudes up to one loop including the generation of a Fortran code for the numerical evaluation of the squared matrix element. Major new or enhanced features in Version 5 are: iterative build-up of essentially arbitrary phase-spaces including cuts, convolution with density functions, and uniform treatment of kinematical variables. The LoopTools library supplies the one-loop integrals necessary for evaluating the squared matrix element. Its most significant extensions in Version 2.2 are the five-point family of integrals, and complex and alternate versions.Comment: 5 pages, to appear in the proceedings of the 7th International Symposium on Radiative Corrections (RADCOR05), Shonan Village, Japan, 200

Electroweak corrections to hadronic event shapes

We report on a recent calculation of the electroweak O(\alpha^3\alpha_s) corrections to 3-jet production and related event-shape observables at e+e- colliders. The calculation properly accounts for the experimental photon isolation criteria and for the corrections to the total hadronic cross section. Corrections to the normalised event-shape distributions, which are exemplarily discussed here for the thrust distribution at LEP and linear-collider energies, turn out to be at the few-per-cent level and show remnants of the radiative return to the Z pole even after inclusion of appropriate cuts.Comment: 6 pages, latex, 4 eps figures, contribution to the proceedings of the 9th International Symposium on Radiative Corrections (RADCOR 2009), October 25-30 2009, Ascona, Switzerlan

Electroweak corrections to hadronic event shapes and jet production in e+e- annihilation

We present a complete calculation of the electroweak O(alpha^3 alpha_s) corrections to three-jet production and related event-shape observables at electron--positron colliders. The Z-boson resonance is described within the complex-mass scheme, rendering the calculation valid both in the resonance and off-shell regions. Higher-order initial-state radiation is included in the leading-logarithmic approximation. We properly account for the corrections to the total hadronic cross section and for the experimental photon isolation criteria. To this end we implement contributions of the quark-to-photon fragmentation function both in the slicing and subtraction formalism. The effects of the electroweak corrections on various event-shape distributions and on the three-jet rate are studied. They are typically at the few-per-cent level, and remnants of the radiative return are found even after inclusion of appropriate cuts.Comment: 47 pages, 20 figure

Running couplings for the simultaneous decoupling of heavy quarks

Scale-invariant running couplings are constructed for several quarks being decoupled together, without reference to intermediate thresholds. Large-momentum scales can also be included. The result is a multi-scale generalization of the renormalization group applicable to any order. Inconsistencies in the usual decoupling procedure with a single running coupling can then be avoided, e.g. when cancelling anomalous corrections from t,b quarks to the axial charge of the proton.Comment: 12 pages, 1 figure, version to appear in PLB. Pages 8-11 and Fig. 1 are new, with consequent changes to the abstract, page 2, and the references. We show that our multi-scale renormalization group is needed to achieve anomaly cancellation in t,b decoupling from the weak neutral current, and extend it to include large moment

Towards W b bbar + j at NLO with an automatized approach to one-loop computations

We present results for the O(alpha_s) virtual corrections to q g -> W b bbar q' obtained with a new automatized approach to the evaluation of one-loop amplitudes in terms of Feynman diagrams. Together with the O(alpha_s) corrections to q q' -> W b bbar g, which can be obtained from our results by crossing symmetry, this represents the bulk of the next-to-leading order virtual QCD corrections to W b bbar + j and W b + j hadronic production, calculated in a fixed-flavor scheme with four light flavors. Furthermore, these corrections represent a well defined and independent subset of the 1-loop amplitudes needed for the NNLO calculation of W b bbar. Our approach was tested against several existing results for NLO amplitudes including selected O(alpha_s) one-loop corrections to W + 3 j hadronic production. We discuss the efficiency of our method both with respect to evaluation time and numerical stability.Comment: 14 pages, 3 figure

Do precision electroweak constraints guarantee e+e−e^+e^- collider discovery of at least one Higgs boson of a two-Higgs-doublet model?

We consider a CP-conserving two-Higgs-doublet type II model with a light scalar or pseudoscalar neutral Higgs boson (\h=\hl or \h=\ha) that has no $ZZ/WW$ coupling and, thus, cannot be detected in \epem\to Z\h (Higgs-strahlung) or \nu\anti\nu \h (via $WW$ fusion). Despite sum rules which ensure that the light \h must have significant t\anti t or b\anti b coupling, for a wedge of moderate \tanb, that becomes increasingly large as \mh increases, the \h can also escape discovery in both b\anti b \h and t\anti t \h production at a \rts=500-800\gev \epem collider (for expected luminosities). If the other Higgs bosons happen to be too heavy to be produced, then no Higgs boson would be detected. We demonstrate that, despite such high masses for the other Higgs bosons, only the low-\tanb portion of the no-discovery wedges in [\mh,\tanb] parameter space can be excluded due to failure to fit precision electroweak observables. In the \tanb\gsim 1 regions of the no-discovery wedges, we find that the 2HDM fit to precision electroweak observables has small $\Delta\chi^2$ relative to the best minimal one-doublet SM fit.Comment: 14 pages, 4 figures. 1st two figures have been reformatted to improve readabilit

Decoupling heavy particles simultaneously

The renormalization group is extended to cases where several heavy particles are decoupled at the same time. This involves large logarithms which are scale-invariant and so cannot be eliminated by a change of renormalization scheme. A set of scale-invariant running couplings, one for each heavy particle, is constructed without reference to intermediate thresholds. The entire heavy-quark correction to the axial charge of the weak neutral current is derived to next-to-leading order, and checked in leading order by evaluating diagrams explicitly. The mechanism for cancelling contributions from the top and bottom quarks in the equal-mass limit is surprisingly non-trivial.Comment: 6 pages, 4 figures. Talk presented at the "QCD Down Under" Workshop, Barossa Valley and Adelaide, Australia, 10-19 March 2004, with ref 8 now linked to hep-ph/050727

A novel approach to light-front perturbation theory

We suggest a possible algorithm to calculate one-loop n-point functions within a variant of light-front perturbation theory. The key ingredients are the covariant Passarino-Veltman scheme and a surprising integration formula that localises Feynman integrals at vanishing longitudinal momentum. The resulting expressions are generalisations of Weinberg's infinite-momentum results and are manifestly Lorentz invariant. For n = 2 and 3 we explicitly show how to relate those to light-front integrals with standard energy denominators. All expressions are rendered finite by means of transverse dimensional regularisation.Comment: 10 pages, 5 figure