Search

In 2004 the matrix element method was used in a pioneering work by the Tevatron experiment D0 to determine the top-quark mass from a handful of events. Since then the method has been matured into a powerful analysis tool. While the first applications were restricted to leading-order accuracy, in the meantime also the extension to next-to-leading order (NLO) accuracy has been studied. In this article we explore the potential of the matrix element method at NLO to determine the top-quark mass using events with pair-produced top quarks. We simulate a toy experiment by generating unweighted events with a fixed input mass and apply the matrix element method to construct an estimator for the top-quark mass. Two different setups are investigated: unweighted events obtained from the fixed-order cross section at NLO accuracy as well as events obtained using POWHEG matched to a parton shower. The latter lead to a more realistic simulation and allow to study the impact of higher-order corrections as well as the robustness of the approach. We find that the matrix element method in NLO accuracy leads to a significant reduction of the theoretical uncertainties compared to leading order. In view of the high luminosity phase of the LHC, this observation is especially relevant in analyses which are no longer dominated by statistical uncertainties., Comment: Two references added, particle labels adjusted to improve readability, error bars added in ratio plots, minor changes to the text

This report summarizes the work of the Energy Frontier Topical Group on EW Physics: Heavy flavor and top quark physics (EF03) of the 2021 Community Summer Study (Snowmass). It aims to highlight the physics potential of top-quark studies and heavy-flavor production processes (bottom and charm) at the HL-LHC and possible future hadron and lepton colliders and running scenarios.

Past work has proven the possibility of extracting the top-quark mass, one of the fundamental parameters of the Standard Model, from the comparison of theory predictions and experimental measurements of differential cross-sections for $t\bar{t} j~+~X$ hadroproduction. Various experimental analyses in this respect have already been performed, and new ones are in preparation on the basis of the latest data from $pp$ collisions collected at the Large Hadron Collider. We have produced and made public a comprehensive set of theoretical predictions for the relevant differential distributions, ready to be used for presently ongoing and forthcoming experimental analyses. We investigate the role of different theoretical inputs, in particular the factorization and renormalization scales, PDFs and top-quark mass renormalization schemes, and we quantify the uncertainties related to different choices for these inputs, providing recommendations., Comment: 15 pages, 6 Figures, contribution to Snowmass 2021

We present phenomenological results for $t\bar{t}j + X$ production at the Large Hadron Collider, of interest for designing forthcoming experimental analyses of this process. We focus on those cases where the $t\bar{t}j + X$ process is considered as a signal. We discuss present theoretical uncertainties and the dependence on relevant input parameters entering the computation. For the ${\cal R}$ distribution, which depends on the invariant mass of the $t\bar{t}j$-system, we present reference predictions in the on-shell, $\overline{\mbox{MS}}$ and MSR top-quark mass renormalization schemes, applying the latter scheme to this process for the first time. Our conclusions are particularly interesting for those analyses aiming at extracting the top-quark mass from cross-section measurements., Comment: 64 pages, LaTeX, 38 figures, 14 tables, slightly modified version, as in JHEP

The Matrix Element Method is a promising multi-variate analysis tool which offers an optimal approach to compare theory and experiment according to the Neyman-Pearson lemma. However, until recently its usage has been limited by the fact that only leading-order predictions could be employed. The imperfect approximation of the underlying probability distribution can introduce a significant bias into the analysis which requires a major calibration for the method when applied to parameter determination. Moreover, estimating theoretical uncertainties by scale variation may yield unreliable results. We present the extension of the Matrix Element Method to next-to-leading order in QCD applicable to LHC data defined by common jet algorithms. The accuracy gain is illustrated by simulating a top-quark mass determination from single top-quark events generated with POWHEG+PYTHIA. Additionally, the method's potential for BSM parameter determination is demonstrated by simulating the extraction of a CP-violating Top-Yukawa coupling from events of single top-quarks in association with a Higgs boson., Comment: 9 pages, 4 figures, proccedings to European Physical Society Conference on High Energy Physics - EPS-HEP2019 - 10-17 July, 2019, Ghent, Belgium

In this article we study a Standard Model extension modifying the top-quark Yukawa coupling to the Higgs boson by allowing a mixture of CP-odd and -even couplings. Single top-quark production in association with an additional Higgs boson provides a natural laboratory to search for such extensions. However, because of the small cross section the experimental analysis is challenging. Already the measurement of the cross section for this process is highly non-trivial. Furthermore, using only cross section measurements, a certain parameter region would escape detection. Using an explicit BSM scenario we show that employing the Matrix Element Method a precise measurement becomes feasible. Ignoring signal detection efficiencies an integrated luminosity of about 20 fb^-1 would allow a discovery. Assuming signal detection efficiencies at the level of a few percent a potential signal could be established in the high luminosity phase of the LHC., Comment: 6 pages, 6 figures

In this article we calculate the next-to-leading order (NLO) QCD corrections for single on-shell top-quark production in association with two jets at proton-proton colliders. The tW channel is assumed to be measured independently. The QCD corrections to the inclusive cross section are about 28 (22)\% for top (anti-top) quark production at the 13 TeV LHC. Theoretical errors are dominated by scale uncertainties, which are found to be around 5\% at NLO. Results for various kinematical distributions are also provided using a well-motivated dynamical scale. The QCD corrections are found to have a non-trivial dependence on the phase-space., Comment: 29 pages, 16 figures, 5 Tables

In this article, we present a method to calculate a posteriori event weights at next-to-leading-order (NLO) QCD accuracy for a given jet event defined by the (anti-)$k_t$ algorithm relying on the conventional $2\to 1$ recombination. This is an important extension compared to existing Monte-Carlo tools which generate jet events together with the corresponding weight but do not allow one to calculate the weight for a given event. The method can be used to generate unweighted events distributed according to the fixed-order NLO cross section. In addition, the method allows one to calculate NLO accurate weights for events recorded by experiments. The potential of this ability is illustrated by applying the Matrix Element Method (MEM) to single top-quark events generated with POWHEG in combination with Pythia. For the first time, a systematic study of parton shower effects within the MEM is provided. The method is completely general and can be applied to arbitrary LHC processes., Comment: 25 pages, 5 figures, title changed, article restructured, typos corrected, clarifications added, matches published version

In a recent work the authors have presented a general algorithm to extend the Matrix Element Method (MEM) to the hadronic production of coloured partons taking into account next-to-leading-order (NLO) corrections in quantum chromodynamics (QCD). In this article, the general algorithm is applied to the production of single top quarks at the LHC. In particular, the generation of unweighted events following the NLO predictions is presented. Treating these events as the result of a toy experiment we illustrate the first application of the Matrix Element Method at NLO QCD for hadronic jet production. As a concrete example, we study the determination of the top-quark mass. We show that the inclusion of the NLO corrections can lead to sizeable effects compared to the Matrix Element Method relying on leading-order predictions only and that the incorporation of the NLO corrections is mandatory to obtain reliable estimates of the theoretical uncertainties. In addition, we find that measuring the top-quark mass using the MEM in single top-quark production offers an interesting alternative to mass measurements in top-quark pair production., Comment: references and clarifications added, typos corrected, matches published version

Single top-quark production offers a unique laboratory for precision tests of the Standard Model and searches of possible extensions. Furthermore, assuming the Standard Model, single top-quark production can be used to determine top-quark related couplings. For precise determinations of parameters like the electroweak gauge couplings or the mass of the top quark, efficient, unbiased, and theoretically unambiguous analysis methods are needed. Within this context, the Matrix Element Method (MEM) has been established in hadron collider analyses due to its possibility to top out at utilising the information available in experimental data. However, so far it has mostly been applied in Born approximation only. We discuss the extension to next-to-leading order (NLO) accuracy. As a necessary prerequisite we introduce an efficient method to calculate NLO QCD weights for jet events. As proof of concept and representative example we use the MEM at NLO to reproduce the top-quark mass in a toy experiment where we treat single top-quark events generated at NLO accuracy as pseudo-data. This is the first application of the MEM at NLO accuracy to the hadronic production of jets originating from coloured final state partons. We observe that analysing NLO events with Born likelihoods can introduce a pronounced bias in the extracted mass which would require significant calibration with associated uncertainties. Although we focus on parameter determinations, the methods presented here can also be used to search for new physics using likelihood ratios., Comment: 5 pages with 4 figures; proccedings to XXV International Workshop on Deep-Inelastic Scattering and Related Subjects, 3-7 April 2017, University of Birmingham, UK

In this article, we present a new implementation of the Laporta algorithm to reduce scalar multi-loop integrals---appearing in quantum field theoretic calculations---to a set of master integrals. We extend existing approaches by using an additional algorithm based on modular arithmetic to remove linearly dependent equations from the system of equations arising from integration-by-parts and Lorentz identities. Furthermore, the algebraic manipulations required in the back substitution are optimized. We describe in detail the implementation as well as the usage of the program. In addition, we show benchmarks for concrete examples and compare the performance to Reduze 2 and FIRE 5. In our benchmarks we find that Kira is highly competitive with these existing tools., Comment: 37 pages, 3 figures

We analyze, within several parameter scenarios of type-II two-Higgs doublet extensions of the standard model, the impact of heavy neutral Higgs-boson resonances on top-quark pair production and their subsequent decay to dileptonic final states at the LHC (13 TeV). In particular, we investigate the effects of heavy Higgs bosons on top-spin observables, that is, the longitudinal top-quark polarization and top-quark spin correlations. We take into account NLO QCD as well as weak interaction corrections and show that top-spin observables, if evaluated in judiciously chosen top-quark pair invariant mass bins, can significantly enhance the sensitivity to heavy Higgs resonances in top-quark pair events., Comment: 36 pages, 9 figures

In this contribution we report on the calculation of the next-to-leading order (NLO) QCD corrections to the hadro-production of heavy neutral Higgs bosons and their decay into top-quark pairs within the type-II two-Higgs-doublet extension of the standard model (SM). We take into account the contributions from resonant Higgs boson production, the non-resonant SM $t\bar{t}$ background as well as the interference of these two contributions. The NLO corrections to the signal and interference contributions are calculated by applying the heavy top-quark mass ($m_t$) limit including an effective rescaling. In our NLO calculation the QCD-Higgs interference is evaluated in the resonance region that provides the dominant part of the heavy Higgs-boson contributions. Evaluating representative $CP$-conserving and $CP$-violating parameter scenarios within the two-Higgs-doublet model (2HDM) we present results for different distributions and, in addition, for observables that depend on the top-quark spin., Comment: 6 pages, 2 figures, contribution to the proceedings of the 38th International Conference on High Energy Physics, 3-10 August 2016, Chicago, USA

We investigate, within the type-II two-Higgs-doublet extension of the standard model (SM), the impact of heavy neutral Higgs boson resonances with unsuppressed Yukawa couplings to top quarks on top-quark pair production at the LHC at next-to-leading order (NLO) in the strong coupling constant. We take into account the resonant Higgs boson contributions, the non-resonant SM $t\bar{t}$ continuum and the interference of these two contributions. The NLO QCD corrections to heavy Higgs production and the interference contributions are calculated in the large top-quark mass ($m_t$) limit, including an effective K-factor rescaling. Our evaluation of the QCD-Higgs interference is focused on the Higgs resonance region. Using representative CP-conserving as well as CP-violating parameter scenarios phenomenological results are presented for different observables., Comment: 10 pages, 4 figures, contribution to the proceedings of the Fourth Annual Large Hadron Collider Physics conference, 13-18 June 2016, Lund, Sweden

The Matrix Element Method (MEM) has proven beneficial to make maximal use of the information available in experimental data. However, so far it has mostly been used in Born approximation only. In this paper we discuss an extension to NLO accuracy. As a prerequisite we present an efficient method to calculate event weights for jet events at NLO accuracy. As illustration and proof of concept we apply the method to the extraction of the top-quark mass in e+e- annihilation. We observe significant differences when moving from LO to NLO which may be relevant for the interpretation of top-quark mass measurements at hadron colliders relying on the MEM., Comment: 6 pages, 3 figures, Presented by T. Martini at the XXXIX International Conference of Theoretical Physics `Matter to the Deepest', Ustro\'n, Poland, September 13th-18th, 2015

In this article we illustrate how event weights for jet events can be calculated efficiently at next-to-leading order (NLO) accuracy in QCD. This is a crucial prerequisite for the application of the Matrix Element Method in NLO. We modify the recombination procedure used in jet algorithms, to allow a factorisation of the phase space for the real corrections into resolved and unresolved regions. Using an appropriate infrared regulator the latter can be integrated numerically. As illustration, we reproduce differential distributions at NLO for two sample processes. As further application and proof of concept, we apply the Matrix Element Method in NLO accuracy to the mass determination of top quarks produced in e+e- annihilation. This analysis is relevant for a future Linear Collider. We observe a significant shift in the extracted mass depending on whether the Matrix Element Method is used in leading or next-to-leading order., Comment: 35 pages, 12 figures, references & acknowledgments added, typos corrected, matches published version

The top quark is the heaviest of all known elementary particles. It was discovered in 1995 by the CDF and D0 experiments at the Tevatron. With the start of the LHC in 2009, an unprecedented wealth of measurements of the top quark's production mechanisms and properties have been performed by the ATLAS and CMS collaborations, most of these resulting in smaller uncertainties than those achieved previously. At the same time, huge progress was made on the theoretical side yielding significantly improved predictions up to next-to-next-to-leading order in perturbative QCD. Due to the vast amount of events containing top quarks, a variety of new measurements became feasible and opened a new window to precisions tests of the Standard Model and to contributions of new physics. In this review, originally written for a recent book on the results of LHC Run 1, top-quark measurements obtained so far from the LHC Run 1 are summarised and put in context with the current understanding of the Standard Model., Comment: 35 pages, 25 figures. To appear in "The Large Hadron Collider -- Harvest of Run 1", Thomas Sch\"orner-Sadenius (ed.), Springer, 2015 (532 pages, 253 figures; ISBN 978-3-319-15000-0; eBook ISBN 978-3-319-15001-7, for more details, see http://www.springer.com/de/book/9783319150000)

In these proceedings we report our progress in the development of the publicly available C++ library NJet for accurate calculations of high-multiplicity one-loop amplitudes. As a phenomenological application we present the first complete next-to-leading order (NLO) calculation of five jet cross section at hadron colliders., Comment: 8 pages, 5 figures, Contribution to the proceedings of "ACAT 2013" conference, Beijing, China, May 2013

We present theoretical predictions for five jet production in proton-proton collisions at next-to-leading order accuracy in QCD. Inclusive as well as differential observables are studied for collision energies of 7 and 8 TeV. In general the next-to-leading order corrections stabilize the theoretical predictions with respect to scale variations. In case of the inclusive jet cross sections, we compare with experimental data where possible and find reasonable agreement. We observe that the four-to-three and five-to-four jet ratios show better perturbative convergence than the known three-to-two ratio and are promising candidates for future alpha_s measurements. Furthermore, we present a detailed analysis of uncertainties related to parton distribution functions. The full colour virtual matrix elements used in the computation were obtained with the NJet package, a publicly available library for the evaluation of one-loop amplitudes in massless QCD., Comment: 14 pages, 24 figures, 5 tables

A new method to measure the top-quark mass in high energetic hadron collisions is presented. We use theoretical predictions calculated at next-to-leading order accuracy in quantum chromodynamics to study the (normalized) differential distribution of the \ttbaronejet cross section with respect to its invariant mass $\sqrt{\sttj}$. The sensitivity of the method to the top-quark mass together with the impact of various theoretical and experimental uncertainties has been investigated and quantified. The new method allows for a complementary measurement of the top-quark mass parameter and has a high potential to become competitive in precision with respect to established approaches. Furthermore we emphasize that in the proposed method the mass parameter is uniquely defined through one-loop renormalization.

We study three and four jet production in hadronic collisions at next-to-leading order accuracy in massless QCD. We cross check results previously obtained by the BlackHat collaboration for the LHC with a centre-of-mass energy of sqrt(s)=7 TeV and present new results for the LHC operating at 8 TeV. We find large negative NLO corrections reducing the leading-order cross sections by about 40-50%. Furthermore we observe an important reduction of the scale uncertainty. In addition to the cross sections we also present results for differential distributions. The dynamical renormalization/factorization scale used in the calculation leads to a remarkably stable K-factor. The results presented here were obtained with the NJet package, a publicly available library for the evaluation of one-loop amplitudes in massless QCD., Comment: 10+9 pages, 20 figures, 15 tables. v2: reference added. additional table of comparisons with known results at 7 TeV. published version

We present a C++ library for the numerical evaluation of one-loop virtual corrections to multi-jet production in massless QCD. The pure gluon primitive amplitudes are evaluated using NGluon. A generalized unitarity reduction algorithm is used to construct arbitrary multiplicity fermion-gluon primitive amplitudes. From these basic building blocks the one-loop contribution to the squared matrix element, summed over colour and helicities, is calculated. No approximation in colour is performed. While the primitive amplitudes are given for arbitrary multiplicities we provide the squared matrix elements only for up to 7 external partons allowing the evaluation of the five jet cross section at next-to-leading order accuracy. The library has been recently successfully applied to four jet production at next-to-leading order in QCD., Comment: 31 pages, 6 figures, 6 tables

Recent advances in our understanding of tree-level QCD amplitudes in the massless limit exploiting an effective (maximal) supersymmetry have led to the complete analytic construction of tree-amplitudes with up to four external quark-anti-quark pairs. In this work we compare the numerical efficiency of evaluating these closed analytic formulae to a numerically efficient implementation of the Berends-Giele recursion. We compare calculation times for tree-amplitudes with parton numbers ranging from 4 to 25 with no, one, two and three external quark lines. We find that the exact results are generally faster in the case of MHV and NMHV amplitudes. Starting with the NNMHV amplitudes the Berends-Giele recursion becomes more efficient. In addition to the runtime we also compared the numerical accuracy. The analytic formulae are on average more accurate than the off-shell recursion relations though both are well suited for complicated phenomenological applications. In both cases we observe a reduction in the average accuracy when phase space configurations close to singular regions are evaluated. We believe that the above findings provide valuable information to select the right method for phenomenological applications., Comment: 22 pages, 9 figures, Mathematica package GGT.m and example notebook is included in submission

We present heavy-flavor production in association with one jet in hadronic collisions matched to parton shower Monte Carlo predictions at next-to-leading order QCD with account of top-quark decays and spin correlations. We use the POWHEGBOX for the interface to the parton shower programs PYTHIA or HERWIG. Phenomenological studies for the LHC and the Tevatron are presented with particular emphasis on the inclusion of spin-correlation effects in top decay and the impact of the parton shower on the top-quark charge asymmetries. As a novel application of the present calculation the measurement of the top-quark mass is discussed., Comment: 4 pages latex, 6 figures, Procs. of XX International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS 2012)

We present a numerical implementation for virtual corrections to multi-jet production at Next-to-Leading order. Using the algorithm of generalised unitarity we compute primitive amplitudes from tree-level input. These basic ingredients are then used to compute full colour and helicity summed corrections., Comment: 8 pages, 5 figures, 2 tables. Talk given at RADCOR 2011, Mamallapuram, India, 26 - 30 September, 2011

We present the publicly available program NGluon allowing the numerical evaluation of primitive amplitudes at one-loop order in massless QCD. The program allows the computation of one-loop amplitudes for an arbitrary number of gluons. The focus of the present article is the extension to one-loop amplitudes including an arbitrary number of massless quark pairs. We discuss in detail the algorithmic differences to the pure gluonic case and present cross checks to validate our implementation. The numerical accuracy is investigated in detail., Comment: Talk given at ACAT 2011 conference in London, 5-9 September

We present a calculation of heavy-flavor production in hadronic collisions in association with one jet matched to parton shower Monte Carlo programs at next-to-leading order in perturbative QCD. Top-quark decays are included and spin correlations in the decay products are taken into account. The calculation builds on existing results for the radiative corrections to heavy-quark plus one jet production and uses the POWHEG BOX for the interface to the parton shower programs PYTHIA or HERWIG. A broad phenomenological study for the Large Hadron Collider and the Tevatron is presented. In particular we study---as one important sample application---the impact of the parton shower on the top-quark charge asymmetry., Comment: 38 pages, 14 figures, 6 tables. Few references and comments added. Version accepted for publication

We present a computer library for the numerical evaluation of colour-ordered n-gluon amplitudes at one-loop order in pure Yang-Mills theory. The library uses the recently developed technique of generalised unitarity. Running in double precision the library yields reliable results for up to 14 gluons with only a small fraction of events requiring a re-evaluation using extended floating point arithmetic. We believe that the library presented here provides an important contribution to future LHC phenomenology. The program may also prove useful in cross checking results obtained by other methods. In addition, the code provides a sample implementation which may serve as a starting point for further developments., Comment: 35 pages, 7 figures. v2 minor corrections and additional discussion on asymptotic scaling. published version

In this contribution we discuss conceptual issues of current mass measurements performed at the Tevatron. In addition we propose an alternative method which is theoretically much cleaner and to a large extend free from the problems encountered in current measurements. In detail we discuss the direct determination of the top-quark's running mass from the cross section measurements performed at the Tevatron., Comment: 8 pages, 4 figures. To appear in the proceedings of the 45th Rencontres de Moriond

We report on the calculation of the next-to-leading order QCD corrections to the production of W-boson pairs in association with a hard jet at the Tevatron and the LHC, which is an important source of background for Higgs and new-physics searches. Leptonic decays of the W bosons are included by applying an improved version of the narrow-width approximation that treats the W bosons as on-shell particles, but keeps the information on the W spin. A selection of differential NLO QCD cross sections is provided both for the LHC and the Tevatron. The QCD corrections stabilize the LO prediction for the cross section with respect to scale variations. The differential LO cross sections are generally not simply rescaled by the corrections. Their shapes are particularly distorted if an additional energy scale is involved., Comment: 6pp. To appear in the proceedings of 9th International Symposium on Radiative Corrections (RADCOR 2009): Applications of Quantum Field Theory to Phenomenology, Ascona, Switzerland, 25-30 Oct 2009

We report on a calculation of the next-to-leading order QCD corrections to the production of W-boson pairs in association with a hard jet at hadron colliders, which is an important source of background for Higgs and new-physics searches at the LHC. If a veto against the emission of a second hard jet is applied, the corrections stabilize the leading-order prediction for the cross section considerably., Comment: 6 pages, latex, 5 figures, 7 eps-files, to appear in the proceedings of 9th Workshop on Elementary Particle Theory: Loops and Legs in Quantum Field Theory, Sondershausen, Germany, 20-25 Apr 2008

We discuss the production of top--anti-top quark pairs in association with a hard jet at the Tevatron and at the LHC and we report on the calculation of the next-to-leading order QCD corrections to this process. Numerical results for the top--anti-top+jet cross section and the forward--backward charge asymmetry are presented. The corrections stabilize the leading-order prediction for the cross section. In contrast, the charge asymmetry receives large corrections. The dependence of the cross section as well as the asymmetry on the minimum transverse momenta used to define the additional jet is studied in detail for the Tevatron., Comment: To appear in the proceedings of 8th International Symposium on Radiative Corrections (RADCOR 2007): Application of Quantum Field Theory to Phenomenology, Florence, Italy, 1-6 Oct 2007

We present an update of the theoretical predictions for the cross section of top-quark pair production at Tevatron and LHC. In particular we employ improvements due to soft gluon resummation at next-to-next-to-leading logarithmic accuracy. We expand the resummed results and derive analytical finite-order cross sections through next-to-next-to-leading order which are exact in all logarithmically enhanced terms near threshold. These results are the best present estimates for the top-quark pair production cross section. We investigate the scale dependence as well as the sensitivity on the parton luminosities., Comment: v2 published in PRD; references added, eqs.(19),(21) corrected and cross section numbers updated

We report on the calculation of the next-to-leading order QCD corrections to the production of W-boson pairs in association with a hard jet at hadron colliders, which is an important source of background for Higgs and new-physics searches. If a veto against the emission of a second hard jet is applied, the corrections stabilize the leading-order prediction for the cross section considerably., Comment: 6 pages, latex, 4 ps figures, to appear in the proceedings of the "8th International Symposium on Radiative Corrections (RADCOR07)", Florence, Italy, October 1-5, 2007

The comparison of numerical data with published plots is a frequently occurring task. In this article I present a short computer program written in Java(TM) helping in those cases where someone wants to get the numbers out of a plot but is not able to read the plot with a decent accuracy and cannot contact the author of the plot directly for whatever reason. The accuracy reached by this method depends on many factors. For the examples illustrated in this paper a precision at the level of a few per mille could be reached. The tool might help in improving the quality of future publications., Comment: The program can be obtained from http://puwer.web.cern.ch/puwer/EasyNData/

The measurement of top quark spin correlation is an important tool for precise studies of top quark interactions. In this letter I construct a quantization axis maximizing the spin correlation at the LHC within the Standard Model. Using this axis a spin correlation of 48% or even more, on applying additional cuts, can be reached. This represents a significant improvement compared to the helicity bases studied thus far.

We recalculate the next-to-leading order Altarelli-Parisi kernel using a method which relates it to the splitting amplitudes describing the collinear factorization properties of scattering amplitudes. The method breaks up the calculation of the kernel into individual pieces which have an independent physical interpretation., Comment: References added

We present the calculation of the nf-contributions to the two-loop amplitude for e+ e- --> q qbar g and give results for the full one-loop amplitude to order eps^2 in the dimensional regularization parameter. Our results agree with those recently obtained by Garland et al.. The calculation makes extensive use of an efficient method based on nested sums to calculate two-loop integrals with arbitrary powers of the propagators. The use of nested sums leads in a natural way to multiple polylogarithms with simple arguments, which allow a straightforward analytic continuation., Comment: 31 pages, a file "coefficients.h" with the results in FORM format is included

High precision analyses of experimental data for e+ e- annihillation, such as determination of jet rates or event shape observables, call for complete next-to-next-to-leading order (NNLO) perturbative QCD predictions. In this talk, we discuss the various ingredients entering the calculation of the NNLO corrections in e+ e- annihillation., Comment: 6 pages, talk given at the Europhysics Conference on HEP, Budapest, July 2001

Expansion of higher transcendental functions in a small parameter are needed in many areas of science. For certain classes of functions this can be achieved by algebraic means. These algebraic tools are based on nested sums and can be formulated as algorithms suitable for an implementation on a computer. Examples, such as expansions of generalized hypergeometric functions or Appell functions are discussed. As a further application, we give the general solution of a two-loop integral, the so-called C-topology, in terms of multiple nested sums. In addition, we discuss some important properties of nested sums, in particular we show that they satisfy a Hopf algebra., Comment: 28 pages, minor changes

We recompute the functions describing the collinear factorization of one-loop amplitudes using the unitarity-based method. We present the results in a form suitable for use as an ingredient in two-loop calculations. We also present a function summarizing the behavior at one loop in both the soft and collinear limits., Comment: two references added, minor changes in the text

We present in detail a calculation of the next-to-leading order QCD corrections to the process $e^+e^-\to 3$ jets with massive quarks. To isolate the soft and collinear divergencies of the four parton matrix elements, we modify the phase space slicing method to account for masses. Our computation allows for the prediction of oriented three jet events involving heavy quarks, both on and off the Z resonance, and of any event shape variable which is dominated by three jet configurations. We show next-to-leading order results for the three jet fraction, the differential two jet rate, and for the thrust distribution at various c.m. energies., Comment: 51 pages, LaTeX, 16 postscript figures

We calculate the cross section for $e^+ e^-$ annihilation into three jets for massive quarks at next-to-leading order in perturbative QCD, both on and off the $Z$ resonance. Our computation allows the implementation of any jet clustering algorithm. We give results for the three-jet cross section involving $b$ quarks for the JADE and Durham algorithm at c.m. energies $\sqrt s = m_Z$. We also discuss a three-jet observable that is sensitive to the mass of the $b$ quark., Comment: 11 pages, using revtex; 6 postscript figures included. Figures have been changed

We investigate the prospects to observe effects of transverse polarization of top quarks in $pp,p\bar{p}\to t\bar{t}X$. QCD absorptive parts generate a polarization of top quarks and antiquarks transverse to the production plane in the partonic processes $q\bar{q}\to t\bar{t}$ and $gg\to t\bar{t}$, which reaches values of a few percent. These perturbative QCD effects are decreased at the hadronic level. A measurement through momentum correlations among the $t$ and $\bar{t}$ decay products will be difficult both at an upgraded Tevatron and at the LHC., Comment: 14 pages, LaTeX; 8 uuencoded, tar-compressed figures added separately