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 linear scaling with the number of final-state particles. Moreover, we demonstrate that the overall event generation time and the memory footprint of our implementation remain approximately constant when including additional jets. We compare both to the conventional CKKW-L implementation in Pythia and gain a first estimate of renormalisation scale uncertainties at high merged multiplicities. As a proof of concept, we show parton-level predictions for vector boson production in proton-proton collisions with up to nine hard jets using the new implementation. Despite its much simpler nature, we dub the new technique MESS, in analogy to the conventional MEPS nomenclature.
We summarize recent developments in the VINCIA parton shower. After a brief review of the basics of the formalism, the extension of VINCIA to hadron collisions is sketched. We then turn to improvements of the efficiency of tree-level matching by making the shower history unique and by incorporating identified helicities. We conclude with an overview of matching to one-loop matrix elements.
We summarise the main features of VINCIA's antenna-based treatment of QCD initial- and final-state showers, which includes iterated tree-level matrix-element corrections and automated evaluations of perturbative shower uncertainties. The latter are computed on the fly and are cast as a set of alternative weights for each generated event. The resulting algorithm has been made publicly available as a plug-in to the PYTHIA 8 event generator.
We present an antenna-shower formalism that includes helicity dependence for massless partons. The formalism applies to both traditional (global) showers and to sector-based variants. We combine the shower with VINCIA's multiplicative approach to matrix-element matching, generalized to operate on each helicity configuration separately. The result is a substantial gain in computational speed for high parton multiplicities. We present an implementation of both sector and global showers, with min and max variations, and helicity-dependent tree-level matching applied for vector bosons or Higgs dec…
We present algorithms that interleave photon radiation from the final state and the initial state with the QCD evolution in the antenna-based Vincia parton shower. One of the algorithms incorporates the complete soft and collinear structure associated with photon emission, but may be computationally expensive, while the other approximates the soft structure at a lower cost. Radiation from fermions and W bosons is included, and a strategy for photon radiation off leptons below the hadronization scale is set up. We show results of the application of the shower algorithms to Drell-Yan and WW prod…
We propose a framework for high-energy interactions in which resonance decays and electroweak branching processes are interleaved with the QCD evolution in a single common sequence of decreasing resolution scales. The interleaved treatment of resonance decays allows for a new treatment of finite-width effects in parton showers. At scales above their offshellness, resonances participate explicitly as incoming and outgoing states in branching processes, while they are effectively "integrated out" of the description at lower scales. We implement this formalism, together with a full set of antenna…
We discuss and illustrate the properties of several parton-shower algorithms available in Pythia and Vincia, in the context of Higgs production via vector boson fusion (VBF). In particular, the distinctive colour topology of VBF processes allows to define observables sensitive to the coherent radiation pattern of additional jets. We study a set of such observables, using the Vincia sector-antenna shower as our main reference, and contrast it to Pythia's transverse-momentum-ordered DGLAP shower as well as Pythia's dipole-improved shower. We then investigate the robustness of these predictions a…
We present the first public implementation of antenna-based QCD initial- and final-state showers. The shower kernels are $2\to 3$ antenna functions, which capture not only the collinear dynamics but also the leading soft (coherent) singularities of QCD matrix elements. We define the evolution measure to be inversely proportional to the leading poles, hence gluon emissions are evolved in a $p_\perp$ measure inversely proportional to the eikonal, while processes that only contain a single pole (e.g., $g\to q\bar{q}$) are evolved in virtuality. Non-ordered emissions are allowed, suppressed by an …
We present a complete set of helicity-dependent 2->3 antenna functions for QCD initial- and final- state radiation. The functions are implemented in the Vincia shower Monte Carlo framework and are used to generate showers for hadron-collider processes in which helicities are explicitly sampled (and conserved) at each step of the evolution. Although not capturing the full effects of spin correlations, the explicit helicity sampling does permit a significantly faster evaluation of fixed-order matrix-element corrections. A further speed increase is achieved via the implementation of a new fast li…
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. …
A Markovian shower algorithm based on "sector antennae" is presented and its main properties illustrated. Tree-level full-color matrix elements can be automatically incorporated in the algorithm and are re-interpreted as process-dependent 2 -> n antenna functions. In hard parts of phase-space, these functions generate tree-level matrix-element corrections to the shower. In soft parts, they should improve the logarithmic accuracy of it. The number of matrix-element evaluations required per order of matching is 1, with an unweighting efficiency that remains very high for arbitrary numbers of leg…
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 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 outline a new technique for the fully-differential matching of final-state parton showers to NNLO calculations, focussing here on the simplest case of leptonic collisions with two final-state jets. The strategy is facilitated by working in the antenna formalism, making use of NNLO antenna subtraction on the fixed-order side and the sector-antenna framework on the shower side. As long as the combined real-virtual and double-real corrections do not overcompensate the real-emission term in the three-jet region, negative weights can be eliminated from the matching scheme. We describe the implem…
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.
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 …
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.
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 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 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.
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.
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 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…
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 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.
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…
The theoretical description of the physics of multi-jets in hadronic collisions at high energies is based on "merging" methods, which combine short-timescale production of jets with long-timescale evolution of partonic showers. We point out potential implications of the evolution of transverse momentum dependent (TMD) distributions on the structure of multi-jet states at high energies, and in particular on the theoretical systematics associated with multi-jet merging. To analyze this, we propose a new merging methodology, and illustrate its impact by comparing our theoretical results with expe…
We propose a novel technique for the combination of multi-jet merged simulations in the five-flavor scheme with calculations for the production of b-quark associated final states in the four-flavor scheme. We show the equivalence of our algorithm to the FONLL method at the fixed-order and logarithmic accuracy inherent to the matrix-element and parton-shower simulation employed in the multi-jet merging. As a first application we discuss Zbb production at the Large Hadron Collider.
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…
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.
In this article we generalise POWHEG next-to-leading order parton shower (NLOPS) simulations of vector boson production and vector boson production in association with a single jet, to give matrix element corrected MENLOPS simulations. In so doing we extend and provide, for the first time, an exact and faithful implementation of the MENLOPS formalism in hadronic collisions. We also consider merging the resulting event samples according to a phase space partition defined in terms of an effective jet clustering scale. The merging scale is restricted such that the component generated by the assoc…
We present precise predictions for four-lepton plus jets production at the LHC obtained within the fully automated Sherpa+OpenLoops framework. Off-shell intermediate vector bosons and related interferences are consistently included using the complex-mass scheme. Four-lepton plus 0- and 1-jet final states are described at NLO accuracy, and the precision of the simulation is further increased by squared quark-loop NNLO contributions in the gg -> 4l, gg -> 4l+g, gq -> 4l+q, and qq -> 4l+g channels. These NLO and NNLO contributions are matched to the Sherpa parton shower, and the 0- and 1-jet fina…
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 simulation program for the production of a pair of W bosons in association with a jet, that can be used in conjunction with general-purpose shower Monte Carlo generators, according to the POWHEG method. We have further adapted and implemented the MINLO' method on top of the NLO calculation underlying our WW+jet generator. Thus, the resulting simulation achieves NLO accuracy not only for inclusive distributions in WW+jet production but also WW production, i.e. when the associated jet is not resolved, without the introduction of any unphysical merging scale. This work represents the…
We consider the production of a single $Z$ or $W$ boson in association with jets at the LHC. We compute the corresponding cross sections by matching NLO QCD predictions with the Herwig++ and Pythia8 parton showers, and by merging all of the underlying matrix elements with up to two light partons at the Born level. We compare our results with several 7-TeV measurements by the ATLAS and CMS collaborations, and overall we find a good agreement between theory and data.
We present a generator for the production of a Higgs boson H in association with a vector boson V=W or Z (including subsequent V decay) plus zero and one jet, that can be used in conjunction with general-purpose shower Monte Carlo generators, according to the POWHEG method, as implemented within the POWHEG BOX framework. We have computed the virtual corrections using GoSam, a program for the automatic construction of virtual amplitudes. In order to do so, we have built a general interface of the POWHEG BOX to the GoSam package. With this addition, the construction of a POWHEG generator within …
Measurements of $t\bar{t} H$ production in the $H\to b\bar{b}$ channel depend in a critical way on the theoretical uncertainty associated with the irreducible $t\bar{t}+b$-jet background. In this paper, analysing the various topologies that account for $b$-jet production in association with a $t\bar{t}$ pair, we demonstrate that the process at hand is largely driven by final-state $g\to b\bar{b}$ splittings. We also show that in five-flavour simulations based on $t\bar{t}+$multi-jet merging $b$-jet production is mostly driven by the parton shower, while matrix elements play only a marginal rol…
