Tree-level Matrix Elements Research Articles

WHIZARD—simulating multi-particle processes at LHC and ILC

We describe the universal Monte-Carlo event generator WHIZARD. The program automatically computes complete tree-level matrix elements, integrates them over phase space, evaluates distributions of observables, and generates unweighted event samples that can be used directly in detector simulation. There is no principal limit on the process complexity; using current hardware, the program has successfully been applied to hard scattering processes with up to eight particles in the final state. Matrix elements are computed as helicity amplitudes, so spin and color correlations are retained. The Standard Model, the MSSM, and many alternative models such as Little Higgs, anomalous couplings, or effects of extra dimensions or noncommutative SM extensions have been implemented. Using standard interfaces to PDF, beamstrahlung, parton shower and hadronization programs, WHIZARD generates complete physical events and covers physics at hadron, lepton, and photon colliders.

NLO matrix elements and truncated showers

In this publication, an algorithm is presented that combines the ME+PS approach to merge sequences of tree-level matrix elements into inclusive event samples with the POWHEG method, which combines exact next-to-leading order matrix element results with the parton shower. It was developed in parallel to the MENLOPS technique and has been implemented in the event generator Sherpa. The benefits of this approach are exemplified by some first predictions for a number of processes, namely the production of jets in e+ e- annihilation, in deep-inelastic ep scattering, in association with single W, Z or Higgs bosons, and with vector boson pairs at hadron colliders.

Double parton scattering singularity in one-loop integrals

We present a detailed study of the double parton scattering (DPS) singularity, which is a specific type of Landau singularity that can occur in certain one-loop graphs in theories with massless particles. A simple formula for the DPS singular part of a four-point diagram with arbitrary internal/external particles is derived in terms of the transverse momentum integral of a product of light cone wavefunctions with tree-level matrix elements. This is used to reproduce and explain some results for DPS singularities in box integrals that have been obtained using traditional loop integration techniques. The formula can be straightforwardly generalised to calculate the DPS singularity in loops with an arbitrary number of external particles. We use the generalised version to explain why the specific MHV and NMHV six-photon amplitudes often studied by the NLO multileg community are not divergent at the DPS singular point, and point out that whilst all NMHV amplitudes are always finite, certain MHV amplitudes do contain a DPS divergence. It is shown that our framework for calculating DPS divergences in loop diagrams is entirely consistent with the `two-parton GPD' framework of Diehl and Schafer for calculating proton-proton DPS cross sections, but is inconsistent with the `double PDF' framework of Snigirev.

CAMORRA: A C++ library for recursive computation of particle scattering amplitudes

We present a new Monte Carlo tool that computes full tree-level matrix elements in high-energy physics. The program accepts user-defined models and has no restrictions on the process multiplicity. To achieve acceptable performance, CAMORRA evaluates the matrix elements in a recursive way by combining off-shell currents. Furthermore, CAMORRA can be used to compute amplitudes involving continuous color and helicity final states. Program summary Program title: CAMORRA Catalogue identifier: AEHN_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEHN_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPL version 2 No. of lines in distributed program, including test data, etc.: 252 572 No. of bytes in distributed program, including test data, etc.: 1 711 469 Distribution format: tar.gz Programming language: C++ Computer: All Operating system: Tested on Linux and Mac OS, but should work on any system Classification: 4.4 Nature of problem: Current recursive matrix element computation programs are confined to standard model amplitudes, whereas many new physics signatures and backgrounds at hadron colliders are associated with multi-parton final states. Solution method: The library applies the Berends–Giele/Caravaglios–Moretti recursive algorithm in a generic way applicable to a wide range of quantum field theories. It allows the user to define a new physics model and consequently compute its predicted scattering amplitudes with exponential growth of the computing time with process multiplicity rather than factorial growth. Restrictions: There are no built-in restrictions on process complexity. Unusual features: CAMORRA can cope with Majorana fermions. Running time: A ten-gluon amplitude typically takes 9 ms per event.

Vector Boson + Jets with BlackHat and SHERPA

We review recent NLO QCD results for W,Z + 3-jet production at hadron colliders, computed using BlackHat and SHERPA. We also include some new results for Z + 3-jet production at the LHC at 7 TeV. We report new progress towards the NLO cross section for W + 4-jet production. In particular, we show that the virtual matrix elements produced by BlackHat are numerically stable. We also show that with an improved integrator and tree-level matrix elements from BlackHat, SHERPA produces well-behaved real-emission contributions. As an illustration, we present the real-emission contributions -- including dipole-subtraction terms -- to the p_T distribution of the fourth jet, for a single subprocess with the maximum number of gluons.

Improving NLO-parton shower matched simulations with higher order matrix elements

In recent times the algorithms for the simulation of hadronic collisions have been subject to two substantial improvements: the inclusion, within parton showering, of exact higher order tree level matrix elements (MEPS) and, separately, next-to-leading order corrections (NLOPS). In this work we examine the key criteria to be met in merging the two approaches in such a way that the accuracy of both is preserved, in the framework of the POWHEG approach to NLOPS. We then ask to what extent these requirements may be fulfilled using existing simulations, without modifications. The result of this study is a pragmatic proposal for merging MEPS and NLOPS events to yield much improved MENLOPS event samples. We apply this method to W boson and top quark pair production. In both cases results for distributions within the remit of the NLO calculations exhibit no discernible changes with respect to the pure NLOPS prediction; conversely, those sensitive to the distribution of multiple hard jets assume, exactly, the form of the corresponding MEPS results.

Hadronic final states in deep-inelastic scattering with Sherpa

We extend the multi-purpose Monte-Carlo event generator Sherpa to include processes in deeply inelastic lepton-nucleon scattering. Hadronic final states in this kinematical setting are characterised by the presence of multiple kinematical scales, which were up to now accounted for only by specific resummations in individual kinematical regions. Using an extension of the recently introduced method for merging truncated parton showers with higher-order tree-level matrix elements, it is possible to obtain predictions which are reliable in all kinematical limits. Different hadronic final states, defined by jets or individual hadrons, in deep-inelastic scattering are analysed and the corresponding results are compared to HERA data. The various sources of theoretical uncertainties of the approach are discussed and quantified. The extension to deeply inelastic processes provides the opportunity to validate the merging of matrix elements and parton showers in multi-scale kinematics inaccessible in other collider environments. It also allows to use HERA data on hadronic final states in the tuning of hadronisation models.

Observing strongly interacting vector boson systems at the CERN Large Hadron Collider

We explore the potential of the CERN Large Hadron Collider to access a strongly interacting electroweak symmetry breaking sector via weak boson scattering with ${W}^{+}{W}^{\ensuremath{-}}jj$, $ZZjj$, and ${W}^{\ifmmode\pm\else\textpm\fi{}}Zjj$ final states. As examples of models with scalar or vector resonances we concentrate on a scenario with a heavy Higgs boson and on a warped Higgsless Kaluza-Klein model of narrow spin-one resonances. The signal and the most prominent background processes are evaluated using exact tree-level matrix elements including full off-shell and finite width effects for final states with two tagging jets and four leptons. Using double forward jet-tagging techniques, we derive dedicated cuts on the observable jets and charged leptons to suppress standard model backgrounds. We demonstrate that the LHC has substantial sensitivity to strong interactions in the electroweak symmetry breaking sector.

Measurements of differential cross sections of [formula omitted] events in [formula omitted] collisions at [formula omitted

We present cross section measurements for Z/γ∗+jets+X production, differential in the transverse momenta of the three leading jets. The data sample was collected with the DØ detector at the Fermilab Tevatron pp¯ collider at a center-of-mass energy of 1.96 TeV and corresponds to an integrated luminosity of 1 fb−1. Leading and next-to-leading order perturbative QCD predictions are compared with the measurements, and agreement is found within the theoretical and experimental uncertainties. We also make comparisons with the predictions of four event generators. Two parton-shower-based generators show significant shape and normalization differences with respect to the data. In contrast, two generators combining tree-level matrix elements with a parton shower give a reasonable description of the shapes observed in data, but the predicted normalizations show significant differences with respect to the data, reflecting large scale uncertainties. For specific choices of scales, the normalizations for either generator can be made to agree with the measurements.

Higgs boson production in association with multiple hard jets

We elucidate a new technique for estimating the production of multiple (at least two) hard jets in Higgs production via gluon-gluon fusion. The approach is based upon high energy factorisation, with the region of applicability extended by constraints on the analytic behaviour of the scattering amplitudes stemming from known all-order results. The method approximates both real and virtual corrections, and allows for the resummation in an n-parton inclusive event sample of the terms dominant in the high energy limit. The resulting approximation is matched to the known tree level matrix elements for the production of a Higgs boson in association with 2 and 3 jets, and implemented in a Monte Carlo generator. Example results are presented and characteristic radiation patterns discussed.

Event generation with SHERPA 1.1

In this paper the current release of the Monte Carlo event generator Sherpa, version 1.1, is presented. Sherpa is a general-purpose tool for the simulation of particle collisions at high-energy colliders. It contains a very flexible tree-level matrix-element generator for the calculation of hard scattering processes within the Standard Model and various new physics models. The emission of additional QCD partons off the initial and final states is described through a parton-shower model. To consistently combine multi-parton matrix elements with the QCD parton cascades the approach of Catani, Krauss, Kuhn and Webber is employed. A simple model of multiple interactions is used to account for underlying events in hadron-hadron collisions. The fragmentation of partons into primary hadrons is described using a phenomenological cluster-hadronisation model. A comprehensive library for simulating tau-lepton and hadron decays is provided. Where available form-factor models and matrix elements are used, allowing for the inclusion of spin correlations; effects of virtual and real QED corrections are included using the approach of Yennie, Frautschi and Suura.

Extending CKKW-merging to one-loop matrix elements

We extend earlier schemes for merging tree-level matrix elements with parton showers to include also merging with one-loop matrix elements. In this paper we make a first study on how to include one-loop corrections, not only for events with a given jet multiplicity, but simultaneously for several different jet multiplicities. Results are presented for the simplest non-trivial case of hadronic events at LEP as a proof-of-concept.

Comix, a new matrix element generator

We present a new tree-level matrix element generator, based on the color dressed Berends-Giele recursive relations. We discuss two new algorithms for phase space integration, dedicated to be used with large multiplicities and color sampling.

GenEvA (II): a phase space generator from a reweighted parton shower

We introduce a new efficient algorithm for phase space generation. A parton shower is used to distribute events across all of multiplicity, flavor, and phase space, and these events can then be reweighted to any desired analytic distribution. To verify this method, we reproduce the e+e- -> n jets tree-level result of traditional matrix element tools. We also show how to improve tree-level matrix elements automatically with leading-logarithmic resummation. This algorithm is particularly useful in the context of a new framework for event generation called GenEvA. In a companion paper [arXiv:0801.4026], we show how the GenEvA framework can address contemporary issues in event generation.

Merging parton showers and matrix elements—back to basics

We make a thorough comparison between different schemes of merging fixed-order tree-level matrix element generators with parton-shower models. We use the most basic benchmark of the O(alpha_S) correction to e+e- -> jets, where the simple kinematics allows us to study in detail the transition between the matrix-element and parton-shower regions. We find that the CKKW-based schemes give a reasonably smooth transition between these regions, although problems may occur if the parton shower used is not ordered in transverse momentum. However, the so-called Pseudo-Shower and MLM schemes turn out to have potentially serious problems due to different scale definitions in different regions of phase space, and due to sensitivity to the details in the initial conditions of the parton shower programs used. (Less)

Comparative study of various algorithms for the merging of parton showers and matrix elements in hadronic collisions

We compare different procedures for combining fixed-order tree-level matrix-element generators with parton showers. We use the case of W-production at the Tevatron and the LHC to compare different implementations of the so-called CKKW and MLM schemes using different matrix-element generators and different parton cascades. We find that although similar results are obtained in all cases, there are important differences.

Improving Jet Distributions with Effective Field Theory

We obtain perturbative expressions for jet distributions using soft-collinear effective theory (SCET). By matching SCET onto QCD at high energy, tree level matrix elements and higher order virtual corrections can be reproduced in SCET. The resulting operators are then evolved to lower scales, with additional operators being populated by required threshold matchings in the effective theory. We show that the renormalization group evolution and threshold matchings reproduce the Sudakov factors and splitting functions of QCD, and that the effective theory naturally combines QCD matrix elements and parton showers. The effective theory calculation is systematically improvable and any higher order perturbative effects can be included by a well-defined procedure.

SimulatingW/Z+jetsproduction at the CERN LHC

The merging procedure of tree-level matrix elements and the subsequent parton shower as implemented in the new event generator SHERPA will be validated for the example of single gauge boson production at the CERN LHC. The validation includes consistency checks and comparisons to results obtained from other event generators. In particular, comparisons with full next-to-leading order QCD calculations prove SHERPA's ability to correctly account for additional hard QCD radiation present in these processes.

StudyingW+W−production at the Fermilab Tevatron with SHERPA

The merging procedure of tree-level matrix elements with the subsequent parton shower as implemented in SHERPA will be studied for the example of W boson pair production at the Fermilab Tevatron. Comparisons with fixed order calculations at leading and next-to-leading order in the strong coupling constant and with other Monte Carlo simulations validate once more the impact and the quality of the merging algorithm and its implementation.

W+jets matrix elements and the dipole cascade

We extend the algorithm for matching fixed-order tree-level matrix element generators with the Dipole Cascade Model in Ariadne to apply to processes with incoming hadrons. We test the algoritm on for the process W+n jets at the Tevatron, and find that the results are fairly insensitive to the cutoff used to regularize the soft and collinear divergencies in the tree-level matrix elements. We also investigate a few observables to check the sensitivity to the matrix element correction.