Search

We present a new calculation of next-to-leading-order corrections of the strong and electroweak interactions to like-sign W-boson scattering at the Large Hadron Collider, implemented in the Monte Carlo integrator Bonsay. The calculation includes leptonic decays of the $\mathrm{W}$ bosons. It comprises the whole tower of next-to-leading-order contributions to the cross section, which scale like $\alpha_\mathrm{s}^3\alpha^4$, $\alpha_\mathrm{s}^2\alpha^5$, $\alpha_\mathrm{s}\alpha^6$, and $\alpha^7$ in the strong and electroweak couplings $\alpha_\mathrm{s}$ and $\alpha$. We present a detailed survey of numerical results confirming the occurrence of large pure electroweak corrections of the order of $\sim-12\%$ for integrated cross sections and even larger corrections in high-energy tails of distributions. The electroweak corrections account for the major part of the complete next-to-leading-order correction, which amounts to $15{-}20\%$ in size, depending on the details of the event selection chosen for analysing vector-boson-scattering. Moreover, we compare the full next-to-leading-order corrections to approximate results based on the neglect of contributions that are not enhanced by the vector-boson scattering kinematics (VBS approximation) and on resonance expansions for the $\mathrm{W}$-boson decays (double-pole approximation); the quality of this approximation is good within $\sim 1.5\%$ for integrated cross sections and the dominating parts of the differential distributions. Finally, for the leading-order predictions, we construct different versions of effective vector-boson approximations, which are based on cross-section contributions that are enhanced by collinear emission of $\mathrm{W}$ bosons off the initial-state (anti)quarks; in line with previous findings in the literature, it turns out that the approximative quality is rather limited for applications at the LHC., Comment: 57 pages, 70 figures; version published in JHEP

Last year we released version 2.0 of the Feynman integral reduction program Kira. In this contribution we first report on changes and new features since then and, secondly, on new features for upcoming releases.

We present the new version 2.0 of the Feynman integral reduction program Kira and describe the new features. The primary new feature is the reconstruction of the final coefficients in integration-by-parts reductions by means of finite field methods with the help of FireFly. This procedure can be parallelized on computer clusters with MPI. Furthermore, the support for user-provided systems of equations has been significantly improved. This mode provides the flexibility to integrate Kira into projects that employ specialized reduction formulas, direct reduction of amplitudes, or to problems involving linear system of equations not limited to relations among standard Feynman integrals. We show examples from state-of-the-art Feynman integral reduction problems and provide benchmarks of the new features, demonstrating significantly reduced main memory usage and improved performance w.r.t. previous versions of Kira., Comment: 32 pages, v2: minor changes and clarifications, matches published version except for another fixed typo in Eq. (7)

We present the new version of OpenLoops, an automated generator of tree and one-loop scattering amplitudes based on the open-loop recursion. One main novelty of OpenLoops 2 is the extension of the original algorithm from NLO QCD to the full Standard Model, including electroweak (EW) corrections from gauge, Higgs and Yukawa interactions. In this context, among several new features, we discuss the systematic bookkeeping of QCD-EW interferences, a flexible implementation of the complex-mass scheme for processes with on-shell and off-shell unstable particles, a special treatment of on-shell and off-shell external photons, and efficient scale variations. The other main novelty is the implementation of the recently proposed on-the-fly reduction algorithm, which supersedes the usage of external reduction libraries for the calculation of tree-loop interferences. This new algorithm is equipped with an automated system that avoids Gram-determinant instabilities through analytic methods in combination with a new hybrid-precision approach based on a highly targeted usage of quadruple precision with minimal CPU overhead. The resulting significant speed and stability improvements are especially relevant for challenging NLO multi-leg calculations and for NNLO applications., Comment: 80 pages, 6 figures, 11 Tables; V2: matches version published in EPJC

The Future Circular Collider (FCC) at CERN, a proposed 100-km circular facility with several colliders in succession, culminates with a 100 TeV proton-proton collider. It offers a vast new domain of exploration in particle physics, with orders of magnitude advances in terms of Precision, Sensitivity and Energy. The implementation plan foresees, as a first step, an Electroweak Factory electron-positron collider. This high luminosity facility, operating between 90 and 365 GeV centre-of-mass energy, will study the heavy particles of the Standard Model, Z, W, Higgs, and top with unprecedented accuracy. The Electroweak Factory $e^+e^-$ collider constitutes a real challenge to the theory and to precision calculations, triggering the need for the development of new mathematical methods and software tools. A first workshop in 2018 had focused on the first FCC-ee stage, the Tera-Z, and confronted the theoretical status of precision Standard Model calculations on the Z-boson resonance to the experimental demands. The second workshop in January 2019, which is reported here, extended the scope to the next stages, with the production of W-bosons (FCC-ee-W), the Higgs boson (FCC-ee-H) and top quarks (FCC-ee-tt). In particular, the theoretical precision in the determination of the crucial input parameters, alpha_QED, alpha_QCD, M_W, m_t at the level of FCC-ee requirements is thoroughly discussed. The requirements on Standard Model theory calculations were spelled out, so as to meet the demanding accuracy of the FCC-ee experimental potential. The discussion of innovative methods and tools for multi-loop calculations was deepened. Furthermore, phenomenological analyses beyond the Standard Model were discussed, in particular the effective theory approaches. The reports of 2018 and 2019 serve as white papers of the workshop results and subsequent developments., Comment: Published version

A detailed study of Higgs interference effects at the one-loop level in the 1-Higgs-Singlet extension of the Standard Model (1HSM) is presented for the WW and tt decay modes with fully leptonic WW decay. We explore interference effects for benchmark points with a heavy Higgs mass that significantly exceeds 2*m_t. In the WW channel, the Higgs signal and the interfering continuum background are loop induced. In the tt channel, which features a tree-level background, we also calculate the interference with the one-loop background, which, due to the appearance of the absorptive part, is found to dominate the normalisation and shape of differential Higgs distributions and should therefore be considered in experimental analyses. The commonly used geometric average K-factor approximation K_interference ~ (K_Higgs*K_background)^(1/2) is not appropriate. We calculate with massive top and bottom quarks. Our 1HSM and SM implementation in Sherpa+OpenLoops is publicly available and can be used as parton-level integrator or event generator., Comment: 42 pages, 29 figures, 12 tables; added references, published version

We present the first computation of the full next-to-leading-order QCD and electroweak corrections to the WZ scattering process at the LHC. All off-shell, gauge-boson-decay, and interference effects are taken into account for the process $\mathrm{p} \mathrm{p} \to \mu^+\mu^-\mathrm{e}^+\nu_\mathrm{e} \mathrm{j} \mathrm{j} + X$ at the orders $\mathcal{O}{\left( \alpha_\mathrm{s} \alpha^6 \right)}$ and $\mathcal{O}{\left( \alpha^7 \right)}$. The electroweak corrections feature the typical Sudakov behaviour towards high energy and amount to $-16\%$ relative to the electroweak contribution to the integrated cross section. Moreover, the corrections induce significant shape distortions in differential distributions. The next-to-leading-order analysis of the quark- and gluon-induced channels is supplemented by a leading-order study of all possible contributions to the full $4\ell+2\mbox{jets}$ production cross section in a realistic fiducial phase-space volume., Comment: 28 pages, 44 pdf figures; added more comments on the size of the EW corrections, improved readability of the figures, added $p_\mathrm{T}$ distributions of $\mathrm{W}$ and $\mathrm{Z}$, added comment on $\mathrm{tZj}$ background, version to appear in JHEP

We present the Feynman integral reduction program Kira 1.2 and describe its new features and other changes w.r.t. the previous versions. The main new features include a much faster equation generator, more flexible seed specification options, several predefined integral orderings, the reduction of systems of user-provided equations and a new technique to simplify coefficients by sampling variables over integers. Furthermore, we provide a collection of recommendations on how to use the program efficiently. This version has overall improvements in runtime for all reduction tasks compared to the previous versions of Kira., Comment: 21 pages

This Report summarizes the proceedings of the 2017 Les Houches workshop on Physics at TeV Colliders. Session 1 dealt with (I) new developments relevant for high precision Standard Model calculations, (II) theoretical uncertainties and dataset dependence of parton distribution functions, (III) new developments in jet substructure techniques, (IV) issues in the theoretical description of the production of Standard Model Higgs bosons and how to relate experimental measurements, (V) phenomenological studies essential for comparing LHC data from Run II with theoretical predictions and projections for future measurements, and (VI) new developments in Monte Carlo event generators., Comment: Proceedings of the Standard Model Working Group of the 2017 Les Houches Workshop, Physics at TeV Colliders, Les Houches 5-23 June 2017. 314 pages

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

High-energy jets recoiling against missing transverse energy (MET) are powerful probes of dark matter at the LHC. Searches based on large MET signatures require a precise control of the $Z(\nu\bar\nu)+$jet background in the signal region. This can be achieved by taking accurate data in control regions dominated by $Z(\ell^+\ell^-)+$jet, $W(\ell\nu)+$jet and $\gamma+$jet production, and extrapolating to the $Z(\nu\bar\nu)+$jet background by means of precise theoretical predictions. In this context, recent advances in perturbative calculations open the door to significant sensitivity improvements in dark matter searches. In this spirit, we present a combination of state-of-the art calculations for all relevant $V+$jets processes, including throughout NNLO QCD corrections and NLO electroweak corrections supplemented by Sudakov logarithms at two loops. Predictions at parton level are provided together with detailed recommendations for their usage in experimental analyses based on the reweighting of Monte Carlo samples. Particular attention is devoted to the estimate of theoretical uncertainties in the framework of dark matter searches, where subtle aspects such as correlations across different $V+$jet processes play a key role. The anticipated theoretical uncertainty in the $Z(\nu\bar\nu)+$jet background is at the few percent level up to the TeV range., Comment: 32 pages + appendices, 21 figures. V2: NNLO QCD predictions and uncertainties included troughout; improved methodology for mixed QCD-EW uncertainties; more realistic NLO EW uncertainty in eq. (57); photon-induced processes estimated at NLO QCD; PDF uncertainties made publicly available; discussion of numerical results extended; overall presentation improved and streamlined

This Report summarizes the results of the activities of the LHC Higgs Cross Section Working Group in the period 2014-2016. The main goal of the working group was to present the state-of-the-art of Higgs physics at the LHC, integrating all new results that have appeared in the last few years. The first part compiles the most up-to-date predictions of Higgs boson production cross sections and decay branching ratios, parton distribution functions, and off-shell Higgs boson production and interference effects. The second part discusses the recent progress in Higgs effective field theory predictions, followed by the third part on pseudo-observables, simplified template cross section and fiducial cross section measurements, which give the baseline framework for Higgs boson property measurements. The fourth part deals with the beyond the Standard Model predictions of various benchmark scenarios of Minimal Supersymmetric Standard Model, extended scalar sector, Next-to-Minimal Supersymmetric Standard Model and exotic Higgs boson decays. This report follows three previous working-group reports: Handbook of LHC Higgs Cross Sections: 1. Inclusive Observables (CERN-2011-002), Handbook of LHC Higgs Cross Sections: 2. Differential Distributions (CERN-2012-002), and Handbook of LHC Higgs Cross Sections: 3. Higgs properties (CERN-2013-004). The current report serves as the baseline reference for Higgs physics in LHC Run 2 and beyond., Comment: 869 pages, 295 figures, 248 tables and 1645 citations. Working Group web page: https://twiki.cern.ch/twiki/bin/view/LHCPhysics/LHCHXSWG

In this contribution recent results regarding the NLO electroweak corrections for vector boson production in association with jets are presented. Besides discussing the phenomenology of the fixed-order results, their corporation in existing NLO QCD parton shower matched and merged calculations, which can directly be used in experimental analyses, will be shown., Comment: Talk presented at Fourth Annual Large Hadron Collider Physics conference (LHCP2016), 13-18 June 2016, Lund, Sweden (10 pages, 5 figures)

We present theoretical predictions for the production of top-quark pairs with up to three jets at the next-to leading order in perturbative QCD. The relevant calculations are performed with Sherpa and OpenLoops. To address the issue of scale choices and related uncertainties in the presence of multiple scales, we compare results obtained with the standard scale HT/2 at fixed order and the MINLO procedure. Analyzing various cross sections and distributions for tt+0,1,2,3 jets at the 13 TeV LHC we find a remarkable overall agreement between fixed-order and MINLO results. The differences are typically below the respective factor-two scale variations, suggesting that for all considered jet multiplicities, missing higher-order effects should not exceed the ten percent level., Comment: 10 pages, 6 figures, 2 tables

This report summarises the properties of Standard Model processes at the 100 TeV pp collider. We document the production rates and typical distributions for a number of benchmark Standard Model processes, and discuss new dynamical phenomena arising at the highest energies available at this collider. We discuss the intrinsic physics interest in the measurement of these Standard Model processes, as well as their role as backgrounds for New Physics searches., Comment: 253 pages, 198 figures. Chapter 1 of the "Physics at the FCC-hh" Report

We report on the first fully differential calculation for double Higgs boson production through gluon fusion in hadron collisions up to next-to-next-to-leading order (NNLO) in QCD perturbation theory. The calculation is performed in the heavy-top limit of the Standard Model, and in the phenomenological results we focus on pp collisions at 14 TeV. We present differential distributions through NNLO for various observables including the transverse-momentum and rapidity distributions of the two Higgs bosons. NNLO corrections are at the level of 10%-25% with respect to the next-to-leading order (NLO) prediction with a residual scale uncertainty of 5%-15% and an overall mild phase-space dependence. Only at NNLO the perturbative expansion starts to converge yielding overlapping scale uncertainty bands between NNLO and NLO in most of the phase-space. The calculation includes NLO predictions for pp -> HH+jet+X. Corrections to the corresponding distributions exceed 50% with a residual scale dependence of 20%-30%., Comment: 16 pages, 7 figures

Higgs boson production in association with a $Z$-boson at the LHC is analysed, both in the Standard Model and in Simplified Model extensions for Dark Matter. We focus on $H\rightarrow$invisibles searches and show that loop-induced components for both the signal and background present phenomenologically relevant contributions to the $\mathcal{BR}(H\rightarrow\textit{inv})$ limits. In addition, the constraining power of this channel to Simplified Models for Dark Matter with scalar and pseudo-scalar mediators $\phi$ and $A$ is discussed and compared with non-collider constraints. We find that with $100~fb^{-1}$ of LHC data, this channel provides competitive constraints to the non-collider bounds, for most of the parameter space we consider, bounding the universal Standard Model fermion-mediator strength at $g_v < 1$ for moderate masses in the range of ${100~\text{GeV}

This Report summarizes the proceedings of the 2015 Les Houches workshop on Physics at TeV Colliders. Session 1 dealt with (I) new developments relevant for high precision Standard Model calculations, (II) the new PDF4LHC parton distributions, (III) issues in the theoretical description of the production of Standard Model Higgs bosons and how to relate experimental measurements, (IV) a host of phenomenological studies essential for comparing LHC data from Run I with theoretical predictions and projections for future measurements in Run II, and (V) new developments in Monte Carlo event generators., Comment: Proceedings of the Standard Model Working Group of the 2015 Les Houches Workshop, Physics at TeV Colliders, Les Houches 1-19 June 2015. 227 pages

We present next-to-leading order (NLO) predictions including QCD and electroweak (EW) corrections for the production and decay of off-shell electroweak vector bosons in association with up to two jets at the 13 TeV LHC. All possible dilepton final states with zero, one or two charged leptons that can arise from off-shell W and Z bosons or photons are considered. All predictions are obtained using the automated implementation of NLO QCD+EW corrections in the OpenLoops matrix-element generator combined with the Munich and Sherpa Monte Carlo frameworks. Electroweak corrections play an especially important role in the context of BSM searches, due to the presence of large EW Sudakov logarithms at the TeV scale. In this kinematic regime, important observables such as the jet transverse momentum or the total transverse energy are strongly sensitive to multijet emissions. As a result, fixed-order NLO QCD+EW predictions are plagued by huge QCD corrections and poor theoretical precision. To remedy this problem we present an approximate method that allows for a simple and reliable implementation of NLO EW corrections in the MEPS@NLO multijet merging framework. Using this general approach we present an inclusive simulation of vector-boson production in association with jets that guarantees NLO QCD+EW accuracy in all phase space regions involving up to two resolved jets., Comment: 42 pages, 24 figures. V2: version accepted for publication in JHEP, results unchanged, appendix added discussing in detail multijet merging systematic uncertainties in the TeV range

We analyse the production of a Higgs boson in association with a Z boson at hadron colliders in the Standard Model and some simple extensions. We show how multi-jet merging algorithms at leading and next-to-leading order for the loop-induced gluon fusion and the Drell-Yan like quark-induced processes, respectively, improve the descriptions for various differential distributions, in particular those that involve the production of additional jets. The phenomenological studies focus on two relevant channels of Higgs boson decays, namely $H\rightarrow invisible$ and $H\rightarrow b\bar{b}$. We find sizable and phenomenologically relevant corrections to the transverse momentum and invariant mass distributions for the Higgs boson candidate. Thanks to the large destructive interference for the top Yukawa terms, this process is very sensitive to the magnitude and sign of a possible non-standard top-Higgs coupling. We analyse the impact of this anomalous interaction on distributions and estimate constraints from LHC Run II., Comment: 13 pages, 12 figures and 3 tables

In this talk we present a fully automated implementation of next-to-leading order electroweak (NLO EW) corrections in OpenLoops together with Sherpa and Munich. As a first application, we present NLO QCD+EW predictions for the production of positively charged W bosons in association with up to three jets and for the production of a Z boson or photon in association with one jet., Comment: 4 pages, 3 figures, proceedings for Moriond QCD 2015

We present a fully automated implementation of next-to-leading order electroweak (NLO EW) corrections in the OpenLoops matrix-element generator combined with the Sherpa and Munich Monte Carlo frameworks. The process-independent character of the implemented algorithms opens the door to NLO QCD+EW simulations for a vast range of Standard Model processes, up to high particle multiplicity, at current and future colliders. As a first application, we present NLO QCD+EW predictions for the production of positively charged on-shell W bosons in association with up to three jets at the Large Hadron Collider. At the TeV energy scale, due to the presence of large Sudakov logarithms, EW corrections reach the 20-40% level and play an important role for searches of physics beyond the Standard Model. The dependence of NLO EW effects on the jet multiplicity is investigated in detail, and we find that W+multijet final states feature genuinely different EW effects as compared to the case of W+1jet., Comment: 46 pages, 23 Figures; V2: Original results unchanged. Extra plots on electroweak and photon-induced Born contributions added. References added. Various minor modifications. Version accepted for publication in JHEP

Charged gauge boson pair production at the Large Hadron Collider allows detailed probes of the fundamental structure of electroweak interactions. We present precise theoretical predictions for on-shell $W^+W^-$ production that include, for the first time, QCD effects up to next-to-next-to-leading order in perturbation theory. As compared to next-to-leading order, the inclusive $W^+W^-$ cross section is enhanced by 9% at 7 TeV and 12% at 14 TeV. The residual perturbative uncertainty is at the 3% level. The severe contamination of the $W^+W^-$ cross section due to top-quark resonances is discussed in detail. Comparing different definitions of top-free $W^+W^-$ production in the four and five flavour number schemes, we demonstrate that top-quark resonances can be separated from the inclusive $W^+W^-$ cross section without significant loss of theoretical precision., Comment: 7 pages, 3 figures

We report on the first calculation of next-to-next-to-leading order (NNLO) QCD corrections to the inclusive production of ZZ pairs at hadron colliders. Numerical results are presented for pp collisions with centre-of-mass energy ($\sqrt{s}$) ranging from 7 to 14 TeV. The NNLO corrections increase the NLO result by an amount varying from $11\%$ to $17\%$ as $\sqrt{s}$ goes from 7 to 14 TeV. The loop-induced gluon fusion contribution provides about $60\%$ of the total NNLO effect. When going from NLO to NNLO the scale uncertainties do not decrease and remain at the $\pm 3\%$ level., Comment: Reference added, version published on Physics Letters B

We present the computation of the double real and real-virtual contributions to top-antitop pair production in the quark-antiquark channel at leading colour. The $q \bar q \to t \bar{t} g$ amplitudes contributing to the real-virtual part are computed with OpenLoops, and their numerical stability in the soft and collinear regions is found to be sufficiently high to perform a realistic NNLO calculation in double precision. The subtraction terms required at real-real and real-virtual levels are constructed within the antenna subtraction formalism extended to deal with the presence of coloured massive final state particles. We show that those subtraction terms approximate the real-real and real-virtual matrix elements in all their singular limits., Comment: 54 pages, 10 figures

We present differential cross sections for the production of top-quark pairs in conjunction with up to two jets, computed at next-to leading order in perturbative QCD and consistently merged with a parton shower in the Sherpa+OpenLoops framework. Top quark decays including spin correlation effects are taken into account at leading order accuracy. The calculation yields a unified description of top-pair plus multi-jet production, and detailed results are presented for various key observables at the Large Hadron Collider. A large improvement with respect to the multi-jet merging approach at leading order is found for the total transverse energy spectrum, which plays a prominent role in searches for physics beyond the Standard Model., Comment: 6 pages, 1 table, 3 figures. Comments on merging scale choice added. Distributions in the kT jet resolution variables added. Decomposition into individual jet multiplicities added. Comments on the uncertainty associated with the 3rd jet emission added. Reduced statistical uncertainties. Accepted for publication in Phys. Lett. B

We develop a Monte Carlo event generator for Higgs Boson pair production merged to exact one-jet matrix elements. The matrix elements are generated with OpenLoops and event generation is performed with the HERWIG++ general-purpose event generator. This allows us to simulate fully-exclusive hadronic final states with accurate description of the kinematics of the leading jet in conjunction with a parton shower. We use the implementation to examine in detail the systematic uncertainties which result from the merging procedure. We assess the magnitude of the impact of the merging on experimental searches of Standard Model di-Higgs production that aim to constrain the Higgs boson self-coupling. We find that the use of a merged sample can reduce theoretical systematic uncertainties in the efficiencies of cuts on certain observables. This constitutes the most accurate simulation of the process available to date. The Monte Carlo event generator developed for this project is available as an add-on to the HERWIG++ event generator at http://www.itp.uzh.ch/~andreasp/hh, Comment: 19 pages, 10 figures, updated URL

We present an NLO simulation of WWbb production with massive b-quarks at the LHC. Off-shell and non-resonant contributions associated with top-pair and single-top channels and with leptonic W-boson decays are consistently taken into account using the complex-mass scheme. Thanks to the finite b-quark mass, WWbb predictions can be extended to the whole b-quark phase space, thereby including Wt-channel single-top contributions that originate from collinear g->bb splittings in the four-flavour scheme. This provides a consistent NLO description of tt and Wt production and decay, including quantum interference effects. The simulation is also applicable to exclusive 0- and 1-jet bins, which is of great importance for Higgs-boson studies in the H->WW channel and for any other analysis with large top backgrounds and jet vetoes or jet bins., Comment: 8pp. Minor revision, results unchanged

Theoretical uncertainties in the simulation of ttbb production represent one of the main obstacles that still hamper the observation of Higgs-boson production in association with top-quark pairs in the H->bb channel. In this letter we present a next-to-leading order (NLO) simulation of ttbb production with massive b-quarks matched to the Sherpa parton shower. This allows one to extend NLO predictions to arbitrary ttbb kinematics, including the case where one or both b-jets arise from collinear g->bb splittings. We find that this splitting mechanism plays an important role for the ttH(bb) analysis., Comment: 4 pages, 3 figures. v2: b-jet momenta replaced by b-quark momenta in the dynamical QCD scale; related technical cut removed; numerical results updated accordingly and conclusions unchanged. References and various comments on the resummation of b-mass logarithms and on the consistency of double-splitting contributions added. Version to appear in Phys. Lett B

We present the result for the three-loop singlet QCD corrections to the decay of a Higgs boson into two photons and improve the calculation for the non-singlet case. With the new result presented, the decay width Gamma(H -> \gamma \gamma) is completely known at O(G_F \alpha ^2 \alpha_s^2, G_F \alpha ^3)., Comment: 11 pages

We introduce a new technique to generate scattering amplitudes at one loop. Traditional tree algorithms, which handle diagrams with fixed momenta, are promoted to generators of loop-momentum polynomials that we call open loops. Combining open loops with tensor-integral and OPP reduction results in a fully flexible, very fast, and numerically stable one-loop generator. As demonstrated with non-trivial applications, the open-loop approach will permit to obtain precise predictions for a very wide range of collider processes., Comment: 5 pages, 3 figures; v2: Comment on ordering added after eq. (6); typos in eqs. (14,16,17) corrected; various cosmetic changes; reference added. Accepted for publication in PRL

Recent theoretical and experimental improvements in the determination of charm and bottom quark masses are discussed. A new and improved evaluation of the contribution from the gluon condensate $< \frac{\alpha_s}{\pi} G^2>$ to the charm mass determination and a detailed study of potential uncertainties in the continuum cross section for $b\bar b$ production is presented, together with a study of the parametric uncertainty from the $\alpha_s$-dependence of our results. The final results, $m_c(3 \text{GeV})=986(13) $MeV and $m_b(m_b)=4163(16) $MeV, represent, together with a closely related lattice determination $m_c(3\;{\rm GeV})=986(6) $MeV, the presently most precise determinations of these two fundamental Standard Model parameters. A critical analysis of the theoretical and experimental uncertainties is presented., Comment: 12 pages, presented at Quarks~2010, 16th International Seminar of High Energy Physics, Kolomna, Russia, June 6-12, 2010; v2: references added

Using new four-loop results for the heavy quark vacuum polarization and new data for bottom quark production in electron-positron annihilation, an update on the determination of charm- and bottom-quark masses through sum rules has been performed. The previous result for the charm-quark mass, $m_c(3 {\rm GeV})= 0.986(13) {\rm GeV}$, based on the lowest moment, is supported by the new results from higher moments which lead to consistent values with comparable errors. The new value for the bottom quark, $m_b(10 {\rm GeV})= 3.610(16) {\rm GeV}$, corresponding to $m_b(m_b)= 4.163(16) {\rm GeV}$, makes use both of the new data and the new perturbative results and is consistent with the earlier determination., Comment: 5 pages, v2: formula for mb(mb) in eq.(14) corrected

We construct approximate formulas for the O(\alpha_s^3) QCD contributions to vector, axial-vector, scalar and pseudo-scalar quark current correlators, which are valid for arbitrary values of momenta and masses. The derivation is based on conformal mapping and the Pade approximation procedure and incorporates known expansions in the low energy, threshold and high energy regions. We use our results to estimate additional terms in these expansions., Comment: 24 pages, 4 figures

We describe several techniques for the calculation of multi-loop integrals and their application to heavy quark current correlators. As new results, we present the four-loop correction to the second and third physical moment in the low-energy expansions of vector, axial-vector and scalar quark current correlators. Using a Ward identity, we obtain the third and fourth moment for the pseudo-scalar correlator. We briefly discuss the impact of these results on the determination of the charm quark mass and the strong coupling constant using lattice simulations for the current correlators and of the charm- and bottom-quark mass from experimental data for \sigma(e^+ e^- -> hadrons)., Comment: 21 pages

The second moment of the heavy quark vector correlator at O(alpha_s^3) is presented. The implications of this result on recent determinations of the charm and bottom quark mass are discussed., Comment: 9 pages, physics discussion extended

We present the first 30 moments of the low energy expansions of the vector, axial-vector, scalar and pseudo-scalar heavy quark correlation functions at three-loop order, including the singlet contribution which appears for the first time at three loops. In addition we compare the behavior of the moments for large n with the prediction from threshold calculations., Comment: 32 pages, 7 figures

We have constructed an epsilon-finite basis of master integrals for all new types of one-scale tadpoles which appear in the calculation of the four-loop QCD corrections to the electroweak rho-parameter. Using transformation rules from the epsilon-finite basis to the standard minimal-number-of-lines basis, we obtain as a by-product analytical expressions for few leading terms of the epsilon-expansion of all members of the standard basis. The new master integrals have been computed with the help of the Pade method and by use of difference equations independently., Comment: 26 pages

The four-loop QCD corrections to the electroweak $\rho$-parameter arising from top and bottom quark loops are computed. Specifically we evaluate the missing ``non-singlet'' piece. Using algebraic methods the amplitude is reduced to a set of around 50 new master integrals which are calculated with various analytical and numerical methods. Inclusion of the newly completed term halves the final value of the four-loop correction for the minimally renormalized top-quark mass. The predictions for the shift of the weak mixing angle and the W-boson mass is thus stabilized., Comment: 3 pages, 1 figure. Few references are added.The final text published in Phys. Rev. Lett