A modified version of the CKKW matrix element merging algorithm is presented, suitable for use in an angular-ordered parton shower, using truncated showers and forced splittings. The algorithm is implemented in the Herwig++ Monte Carlo event generator for the benchmark process e+e- -> hadrons. Results are presented at parton and hadron levels, demonstrating a smooth merging between the matrix elements and parton shower and an improved description of LEP data.
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.
We here present an extension of the CKKW-L multi-jet merging technique to so-called sector showers as implemented in the Vincia antenna shower. The bijective nature of sector showers allows for efficient multi-jet merging at high multiplicities, as any given configuration possesses only a single "history", while retaining the accuracy of the CKKW-L technique. Our method reduces the factorial scaling of the number of parton shower histories to a constant of a single history per colour-ordered final state. We show that the complexity of constructing shower histories is reduced to an effective li…
We discuss extensions the CKKW-L and UMEPS tree-level matrix element and parton shower merging approaches to next-to-leading order accuracy. The generalisation of CKKW-L is based on the NL3 scheme previously developed for e+e- -annihilation, which is extended to also handle hadronic collisions by a careful treatment of parton densities. NL3 is further augmented to allow for more readily accessible NLO input. To allow for a more careful handling of merging scale dependencies we introduce an extension of the UMEPS method. This approach, dubbed UNLOPS, does not inherit problematic features of CKK…
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 scheme and one based on the so-called MLM scheme using different matrix element generators and different parton cascades. We find that although similar results are obtained in all cases, there are important differences.
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.
We revisit the CKKW-L method for merging tree-level matrix elements with parton showers, and amend it with an add/subtract scheme to minimise dependencies on the merging scale. The scheme is constructed to, as far as possible, recover the unitary nature of the underlying parton shower, so that the inclusive cross section is retained for each jet multiplicity separately.
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 …
We derive an improved prescription for the merging of matrix elements with parton showers, extending the CKKW approach. A flavour-dependent phase space separation criterion is proposed. We show that this new method preserves the logarithmic accuracy of the shower, and that the original proposal can be derived from it. One of the main requirements for the method is a truncated shower algorithm. We outline the corresponding Monte Carlo procedures and apply the new prescription to QCD jet production in e+e- collisions and Drell-Yan lepton pair production. Explicit colour information from matrix e…
We present an implementation of the so-called CKKW-L merging scheme for combining multi-jet tree-level matrix elements with parton showers. The implementation uses the transverse-momentum-ordered shower with interleaved multiple interactions as implemented in PYTHIA8. We validate our procedure using e+e--annihilation into jets and vector boson production in hadronic collisions, with special attention to details in the algorithm which are formally sub-leading in character, but may have visible effects in some observables. We find substantial merging scale dependencies induced by the enforced ra…
We propose an extension of matrix element plus parton shower merging at tree level to preserve inclusive cross sections obtained from the merged and showered sample. Implementing this constraint generates approximate next-to-leading order (NLO) contributions similar to the LoopSim approach. We then show how full NLO, or in principle even higher order, corrections can be added consistently, including constraints on inclusive cross sections to account for yet missing parton shower accuracy at higher logarithmic order. We also show how NLO accuracy below the merging scale can be obtained.
Higher order calculations are necessary to predict and describe measurements in high energy collider physics. In recent years multiple approaches to combine multiple next-to-leading (NLO) order corrections with parton showers had been presented. We present on recent developments and future perspective. We highlight similarities and ambiguities in the procedure of achieving a multijet merging at NLO.
We present a consistent way of combining associated weak boson radiation in hard dijet events with hard QCD radiation in Drell-Yan-like scatterings. This integrates multiple tree-level calculations with vastly different cross sections, QCD- and electroweak parton shower resummation into a single framework. The new merging strategy is implemented in the PYTHIA event generator and predictions are confronted with LHC data. Improvements over the previous strategy are observed. Results of the new electroweak-improved merging at a future 100 TeV proton collider are also investigated.
In this short note, I introduce to essential conceptual features and main building blocks of matrix element merging algorithms, operating on fixed order calculations both at leading order and next-to-leading order. The intention is purely pedagogical, i.e. to familiarize the reader with the essential basic concepts in a concise way, thus serving as an introduction to beginners and other interested readers. Unitarization is discussed briefly. The tutorial is highly biased towards transverse momentum ordered parton showers, and in particular towards merging schemes as they are implemented in the…
The merging of matrix elements and parton showers is an established calculational tool for the description of multi-jet final states at hadron colliders. These methods have recently been promoted to next-to-leading order accuracy in the description of hard well separated jets. This talk introduces such a method and discusses its application to phenomenologically relevant signal and background processes. The systematic assessment of its theoretical uncertainty is a prime focus.
We present a Monte-Carlo approach to prompt-photon production, where photons and QCD partons are treated democratically. The photon fragmentation function is modelled by an interleaved QCD+QED parton shower. This known technique is improved by including higher-order real-emission matrix elements. To this end, we extend a recently proposed algorithm for merging matrix elements and truncated parton showers. We exemplify the quality of the Monte-Carlo predictions by comparing them to measurements of the photon fragmentation function at LEP and to measurements of prompt photon and diphoton product…
With Run-II of the LHC starting its final year of data-taking, high precision theoretical predictions through Monte-Carlo event generators whose uncertainties match that of the recorded data are of highest importance. This talk summarises the progress of the field and highlight a number of recent developments.
QCD predictions for final states with multiple jets in hadron collisions make use of multi-jet merging methods, which allow one to combine consistently the contributions from hard scattering matrix elements with different parton multiplicities and parton showers. In this article I consider a multi-jet merging method that has recently been proposed to take into account the effects of transverse momentum dependent (TMD) evolution and parton shower, and present studies focusing on the application of this method to jets associated with Drell-Yan (DY) production in the region of high masses.
One of the main theoretical systematics in studies of final states with large jet multiplicities at high-energy hadron colliders is associated with the merging of QCD parton showers and hard-scattering matrix elements. We present a method to incorporate the physics of transverse momentum recoils due to initial-state shower evolution into multi-jet merging algorithms by using the concept of transverse momentum dependent (TMD) distributions and the associated parton branching. We investigate the dependence on the merging scale and illustrate the impact of the new method at the level of both excl…
We present an algorithm to combine multiple matrix elements at LO and NLO with a parton shower. We build on the unitarized merging paradigm. The inclusion of higher orders and multiplicities reduce the scale uncertainties for observables sensitive to hard emissions, while preserving the features of inclusive quantities. The combination allows further soft and collinear emissions to be predicted by the all-order parton shower approximation. We inspect the impact of terms that are formally but not parametrically negligible. We present results for a number of collider observables where multiple j…
We discuss an extension of matrix element plus parton shower merging at leading and next-to-leading order. The algorithm does preserve inclusive cross sections at the respective input order. This constraint avoids potentially large logarithmic contributions, which would require approximate (N)NLO contributions to cancel against.
We present results for the QCD production of Z/γ + 2 jets matched with parton showers using the POWHEG method. Some technicalities relevant for the merging of NLO corrections for this process with parton showers are discussed, and results for typical distributions are shown, in presence of different sets of cuts. A comparison with ATLAS data is also presented, and good agreement is found.
The method to merge matrix elements for multi particle production and parton showers in electron-positron annihilations and hadronic collisions and its implementation into the new event generator SHERPA is described in detail. Examples highlighting different aspects of it are thoroughly discussed, some results for various cases are presented. In addition, a way to extend this method to general electroweak interactions is presented.
We consider the POWHEG generator for a H/W/Z boson plus one jet, augmented with the recently proposed MiNLO method for the choice of scales and the inclusion of Sudakov form factors. Within this framework, the generator covers all the transverse-momentum region of the H/W/Z boson, i.e. no generation cuts are needed to obtain a finite result. By construction, the generator achieves NLO accuracy for distributions involving a finite (and relatively large) transverse momentum of the boson. We examine the conditions under which also the totally inclusive distributions (e.g. the boson rapidity distr…
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 st…
We present a parameter-free scheme to combine fixed-order multi-jet results with parton-shower evolution. The scheme produces jet cross sections with leading-order accuracy in the complete phase space of multiple emissions, resumming large logarithms when appropriate, while not arbitrarily enforcing ordering on momentum configurations beyond the reach of the parton-shower evolution equation. This requires the development of a matrix-element correction scheme for complex phase-spaces including ordering conditions as well as a systematic scale-setting procedure for unordered phase-space points. …
We make the connection between certain deep learning architectures and the renormalisation group explicit in the context of QCD by using a deep learning network to construct a toy parton shower model. The model aims to describe proton-proton collisions at the Large Hadron Collider. A convolutional autoencoder learns a set of kernels that efficiently encode the behaviour of fully showered QCD collision events. The network is structured recursively so as to ensure self-similarity, and the number of trained network parameters is low. Randomness is introduced via a novel custom masking layer, whic…
In conventional parton showers (including ones based on dipoles/antennae), a given $(\mathrm{Born}+m)$-parton configuration can typically be reached via ${\mathcal O}(m!)$ different "shower histories". In the context of matrix-element-correction and merging procedures, accounting for these histories mandates fairly complex and resource-intensive algorithms. A so far little-explored alternative in the shower context is to divide the branching phase spaces into distinct "sectors", each of which only receives contributions from a single branching kernel. This has a number of consequences includin…
Calculations of Drell-Yan (DY) production at next-to-leading (NLO) order have been combined with Transverse Momentum Dependent (TMD) distributions obtained with the Parton Branching (PB). The predictions show a remarkable agreement with DY measurement from E605 experiment, consistent with previous results we obtained for R209, PHENIX, CMS and ATLAS experiments. We also present predictions for Z+jet measurements showing the importance of TMD parton shower contributions to the jet multiplicity. We show that PB-TMD parton density and the corresponding PB-TMD parton shower can be combined with lea…
Recent developments in QCD phenomenology have spurred on several improved approaches to Monte Carlo event generation, relative to the post--LEP state of the art. In this brief review, the emphasis is placed on approaches for 1) consistently merging fixed--order matrix element calculations with parton showers, 2) improving the parton shower algorithms themselves, and 3) improving the description of the underlying event in hadron collisions.
In the algorithm presented here, the ME+PS approach to merge samples of tree-level matrix elements into inclusive event samples is combined with the POWHEG method, which includes exact next-to-leading order matrix elements in the parton shower. The advantages of the method are discussed and the quality of its implementation in Sherpa is exemplified by results for e+e- annihilation into hadrons at LEP, for deep-inelastic lepton-nucleon scattering at HERA, for Drell-Yan lepton-pair production at the Tevatron and for W+W- production at LHC energies.
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 W/Z+jets production at the Tevatron. Comparisons with results obtained from other approaches and programs and with experimental results clearly show that the merging procedure yields relevant and correct results at both the hadron and parton levels.
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.
We discuss the theoretical bases that underpin the automation of the computations of tree-level and next-to-leading order cross sections, of their matching to parton shower simulations, and of the merging of matched samples that differ by light-parton multiplicities. We present a computer program, MadGraph5_aMC@NLO, capable of handling all these computations -- parton-level fixed order, shower-matched, merged -- in a unified framework whose defining features are flexibility, high level of parallelisation, and human intervention limited to input physics quantities. We demonstrate the potential …
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 lead…
We present a new algorithm for an analytic parton shower. While the algorithm for the final-state shower has been known in the literature, the construction of an initial-state shower along these lines is new. The aim is to have a parton shower algorithm for which the full analytic form of the probability distribution for all branchings is known. For these parton shower algorithms it is therefore possible to calculate the probability for a given event to be generated, providing the potential to reweight the event after the simulation. We develop the algorithm for this shower including scale cho…
The new version of the parton shower module APACIC++ for the SHERPA event generator framework is presented. It incorporates some features, that are specific for the consistent merging with multi-particle matrix elements at tree-level. This publication also includes some exemplary results and a short description of the upgraded class structure of APACIC++, version 2.0.
Triple gauge boson hadroproduction, in particular the production of three $W$-bosons at the LHC, is considered at next-to leading order accuracy in QCD. The NLO matrix elements are combined with parton showers. Multijet merging is invoked such that NLO matrix elements with one additional jet are also included. The studies here incorporate both the signal and all relevant backgrounds for $VH$ production with the subsequent decay of the Higgs boson into $W$-- or $τ$--\-pairs. They have been performed using \SherpaOpenLoops in combination with Collier.
We present a novel method to combine QCD calculations at next-to-next-to-leading order (NNLO) with parton shower (PS) simulations, that can be applied to the production of heavy systems in hadronic collisions, such as colour singlets or a $t\bar{t}$ pair. The NNLO corrections are included by connecting the MiNLO$^\prime$ method with transverse-momentum resummation, and they are calculated at generation time without any additional reweighting, making the algorithm considerably efficient. Moreover, the combination of different jet multiplicities does not require any unphysical merging scale, and…
We detail a simulation of Higgs boson production via gluon fusion, accurate at next-to-next-to-leading order in the strong coupling, including matching to a parton shower, yielding a fully exclusive, hadron-level description of the final-state. The approach relies on the POWHEG method for merging the NLO Higgs plus jet cross-section with the parton shower, and on the MINLO method to simultaneously achieve NLO accuracy for inclusive Higgs boson production. The NNLO accuracy is reached by a reweighting procedure making use of the HNNLO program.
An azimuthal angle correlation between the two hardest jets is studied in the ttbar production process at the 14 TeV LHC. The event samples are generated by merging the tree level matrix elements for the ttbar plus up to 2 or 3 partons with parton showers. The generated event samples show a strong correlation in the azimuthal angle difference between the two hardest jets, as predicted in the analysis based on the tree level matrix elements for the ttbar+2 partons. The effects of merging the matrix elements for the ttbar+3 partons on the correlation are studied in detail. It is found that they …
In the present work we consider the assignment of the factorization and renormalization scales in hadron collider processes with associated jet production, at next-to-leading order (NLO) in perturbation theory. We propose a simple, definite prescription to this end, including Sudakov form factors to consistently account for the distinct kinematic scales occuring in such collisions. The scheme yields results that are accurate at NLO and, for a large class of observables, it resums to all orders the large logarithms that arise from kinematic configurations involving disparate scales. In practica…
Lund University（隆德大学）；University of Bern（伯尔尼大学）；Simrhythmia Research（Simrhythmia研究公司）；Ruijl Research（Ruijl研究公司）；Uppsala University（乌普萨拉大学）；ELTE Eötvös Loránd University（厄特沃什·罗兰大学）
