We show how a careful analysis of the behaviour of a parton shower Monte Carlo in the vicinity of the soft and collinear regions allows one to formulate a modified MC@NLO-matching prescription that reduces the number of negative-weight events with respect to that stemming from the standard MC@NLO procedure. As a first practical application of such a prescription, that we dub MC@NLO-$Δ$, we have implemented it in the MadGraph5_aMC@NLO framework, by employing the Pythia8 Monte Carlo. We present selected MC@NLO-$Δ$ results at the 13 TeV LHC, and compare them with MC@NLO ones. We find that the former predictions are consistent with the latter ones within the typical matching systematics, and that the reduction of negative-weight events is significant.
We present the matching between a next-to-leading order computation in QCD and the PYTHIA parton shower Monte Carlo, according to the MC@NLO formalism. We study the case of initial-state radiation, and consider in particular single vector boson hadroproduction.
We give a prescription for attaching parton showers to next-to-leading order (NLO) partonic jet cross sections in electron-positron annihilation. Our method effectively extends to NLO the scheme of Catani, Krauss, Kuhn, and Webber for matching between m hard jets and (m+1) hard jets. The matching between parton splitting as part of a shower and parton splitting as part of NLO matrix elements is based on the Catani-Seymour dipole subtraction method that is commonly used for removing the singularities from the NLO matrix elements.}
We report on the implementation of a coherent dipole shower algorithm along with an automated implementation for dipole subtraction and for performing POWHEG- and MC@NLO-type matching to next-to-leading order (NLO) calculations. Both programs are implemented as add-on modules to the event generator Herwig++. A preliminary tune of parameters to data acquired at LEP, HERA and Drell-Yan pair production at the Tevatron has been performed, and we find an overall very good description which is slightly improved by the NLO matching.
The MC@NLO and MEPS@NLO methods, as implemented in the Monte-Carlo event generator framework Sherpa, are used to estimate the perturbative and non-perturbative uncertainties in various processes such as dijet production and the production of a W boson in association with (multiple) jets.
In this review a new method is presented for attaching parton shower algorithms to NLO partonic jet cross sections in electron-positron annihilation. Our method is based on the Catani-Seymour dipole subtraction method and also uses an adaptation of the matching scheme of Catani, Krauss, Kuhn, and Webber.
We compare a NLO W gamma matrix element generator with the leading order calculation in Pythia . A matching scheme between a next-to-leading order W gamma matrix element generator by Baur et. al. and the Pythia parton shower is presented. The NLO package produces W gamma+0 jet and W gamma+1jet final states in the hard scattering and the objective is to consistently match these to the initial state radiation from Pythia parton shower. The proposed methodology preserves both the rate of the hard scattering process as well as various kinematic distributions of experimental interest.
We perform a detailed study of NLO parton shower matching uncertainties in Higgs boson pair production through gluon fusion at the LHC based on a generic and process independent implementation of NLO subtraction and parton shower matching schemes for loop-induced processes in the Sherpa event generator. We take into account the full top-quark mass dependence in the two-loop virtual corrections and compare the results to an effective theory approximation. In the full calculation, our findings suggest large parton shower matching uncertainties that are absent in the effective theory approximatio…
We apply the MC@NLO approach to the process of heavy flavour hadroproduction. MC@NLO is a method for matching next-to-leading order (NLO) QCD calculations and parton shower Monte Carlo (MC) simulations, with the following features: fully exclusive events are generated, with hadronisation according to the MC model; total rates are accurate to NLO; NLO results for distributions are recovered upon expansion in $\as$; hard emissions are treated as in NLO computations while soft/collinear emissions are handled by the MC simulation, with the same logarithmic accuracy as the MC; matching between the …
We propose a method for matching the next-to-leading order (NLO) calculation of a given QCD process with a parton shower Monte Carlo (MC) simulation. The method has the following features: fully exclusive events are generated, with hadronization according to the MC model; total exclusive rates are accurate to NLO; NLO results for distributions are recovered upon expansion in $α_S$; hard emissions are treated as in NLO computations while soft/collinear emissions are handled by the MC simulation, with the same logarithmic accuracy as the MC; and matching between the hard- and soft/collinear-emis…
The aim of this work is to describe in detail the POWHEG method, first suggested by one of the authors, for interfacing parton-shower generators with NLO QCD computations. We describe the method in its full generality, and then specify its features in two subtraction frameworks for NLO calculations: the Catani-Seymour and the Frixione-Kunszt-Signer approach. Two examples are discussed in detail in both approaches: the production of hadrons in e+e- collisions, and the Drell-Yan vector-boson production in hadronic collisions.
We present the status of the automation of NLO processes within the event generator WHIZARD. The program provides an automated FKS subtraction and phase space integration over the FKS regions, while the (QCD) NLO matrix element is accessed via the Binoth Les Houches Interface from an externally linked one-loop program. Massless and massive test cases and validation are shown for several e+e- processes. Furthermore, we discuss work in progress and future plans. The second part covers the matching of the NRQCD prediction with NLL threshold resummation to the NLO continuum top pair production at …
We give a status report on the automation of next-to-leading order processes within the Monte Carlo event generator WHIZARD, using GoSam and OpenLoops as provider for one-loop matrix elements. To deal with divergences, WHIZARD uses automated FKS subtraction, and the phase space for singular regions is generated automatically. NLO examples for both scattering and decay processes with a focus on e+e- processes are shown. Also, first NLO-studies of observables for collisions of polarized leptons beams, e.g. at the ILC, will be presented. Furthermore, the automatic matching of the fixed-order NLO …
We propose a new approach for combining next-to-leading order (NLO) and parton shower (PS) calculations so as to obtain three core features: (a) applicability to general showers, as with the MCatNLO and POWHEG methods; (b) positive-weight events, as with the KrkNLO and POWHEG methods; and (c) all showering attributed to the parton shower code, as with the MCatNLO and KrkNLO methods. This is achieved by using multiplicative matching in phase space regions where the shower overestimates the matrix element and accumulative (additive) matching in regions where the shower underestimates the matrix …
We present a calculation of the NLO QCD corrections to the loop-induced production of a photon pair through gluon fusion, including massive top quarks at two loops, where the two-loop integrals are calculated numerically. Matching the fixed-order NLO results to a threshold expansion, we obtain accurate results around the top quark pair production threshold. We analyse how the top quark threshold corrections affect distributions of the photon pair invariant mass and comment on the possibility of determining the top quark mass from precision measurements of the diphoton invariant mass spectrum.
Building on the new automatic subtraction of NLO amplitudes in WHIZARD, we present our implementation of the POWHEG scheme to match radiative corrections consistently with the parton shower. We apply this general framework to two linear collider processes, $e^+e^-\,\to\,t\bar{t}$ and $e^+e^-\,\to\,t\bar{t}H$.
Next steps in development of the KrkNLO method of implementing NLO QCD corrections to hard processes in parton shower Monte Carlo programs are presented. This new method is a simpler alternative to other well-known approaches, such as MC@NLO and POWHEG. The KrkNLO method owns its simplicity to the use of parton distribution functions (PDFs) in a new, so-called Monte Carlo (MC), factorization scheme which was recently fully defined for the first time. Preliminary numerical results for the Higgs-boson production process are also presented.
A new method to construct event-generators based on next-to-leading order QCD matrix-elements and leading-logarithmic parton showers is proposed. Matrix elements of loop diagrams as well as those of a tree level can be generated using an automatic system. A soft/collinear singularity is treated using a leading-log subtraction method. Higher order re-summation of the soft/collinear correction by the parton shower method is combined with the NLO matrix-element without any double-counting in this method.
In this talk, I show the automated Monte Carlo simulations at next-to-leading order in QCD as well as its matching to parton showers are already feasible within the framework of \MG5aMC. I briefly overview the recent activities and take the colored particle production at the LHC as examples. The tools and the models are ready for using by both phenomenologists and experimentalists.
The next-to-leading order accuracy for MC@NLO results exclusive in J light jets is achieved if the computation is based on matrix elements that feature J and J+1 QCD partons. The simultaneous prediction of observables which are exclusive in different light-jet multiplicities cannot simply be obtained by summing the above results over the relevant range in J; rather, a suitable merging procedure must be defined. We address the problem of such a merging, and propose a solution that can be easily incorporated into existing MC@NLO implementations. We use the automated aMC@NLO framework to illustra…
One of the most important developments in Monte Carlo simulation of collider events for the LHC has been the arrival of schemes and codes for matching of parton showers to matrix elements calculated at next-to-leading order in the QCD coupling. The POWHEG scheme, and particularly its implementation in the POWHEG-BOX code, has attracted most attention due to ease of use and effective portability between parton shower algorithms. But formal accuracy to NLO does not guarantee predictivity, and the beyond-fixed-order corrections associated with the shower may be large. Further, there are open ques…
In this publication, uncertainties in and differences between the MC@NLO and POWHEG methods for matching next-to-leading order QCD calculations with parton showers are discussed. Implementations of both algorithms within the event generator Sherpa and based on Catani-Seymour subtraction are employed to assess the impact on a representative selection of observables. In the case of MC@NLO a substantial simplification is achieved by using dipole subtraction terms to generate the first emission. A phase space restriction is employed, which allows to vary in a transparent way the amount of non-sing…
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) analy…
The resummed differential thrust rate in e+e- annihilation is calculated using Soft-Collinear Effective Theory (SCET). The resulting distribution in the two-jet region T~1 is found to agree with the corresponding expression derived by the standard approach. A matching procedure to account for finite corrections at T < 1 is then described. There are two important advantages of the SCET approach. First, SCET manifests a dynamical seesaw scale q = p^2/Q in addition to the center-of-mass energy Q and the jet mass scale p ~ Q ~ sqrt(1 - T). Thus, the resummation of logs of p/q can be cleanly distin…
We briefly summarize the Nagy-Soper parton shower and the MC@NLO-like matching scheme. Results obtained using HELAC-NLO framework in conjunction with DEDUCTOR for top quark pair production in association with one hard jet at the LHC are presented. A comparison of our results with other matching schemes and other parton showers is also discussed for various observables.
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 QCD $t\bar{t}+b$-jet background. We introduce a new $pp\to t\bar{t}b\bar{b}$ POWHEG generator in the 4F scheme based on POWHEG-BOX-RES and on OpenLoops for fast evaluation of the scattering amplitudes. We present predictions and uncertainties for $t\bar{t}+b$-jet observables at the 13 TeV LHC. We also consider theoretical uncertainties related to the POWHEG matching method and to the parton shower (PS) modelling, with emphasis on $g\to b…
An MC@NLO-like matching of NLO QCD calculations with the Nagy-Soper parton shower is briefly summarised. Uncertainties and ambiguities of the matching scheme are shortly discussed. A few results for the pp -> ttj + X production process at the LHC with sqrt(s) = 8 TeV are also shown. All results have been obtained using the Nagy-Soper parton shower implementation in the DEDUCTOR program together with the HELAC-NLO framework.
We demonstrate that the ambiguity of the low-x evolution kernels in the next-to-leading order (NLO) permits one to match the Mobius form of the BFKL kernel and the kernel of the colour dipole model and to construct the Mobius invariant NLO BFKL kernel in N=4 supersymmetric Yang-Mills theory.
We present theoretical predictions for the hadroproduction of t tbar W+, t tbar W- and t tbar Z at LHC as obtained by matching numerical computations at NLO accuracy in QCD with Shower Monte Carlo programs. The calculation is performed by PowHel, relying on the POWHEG-BOX framework, that allows for the matching between the fixed order computation, with input of matrix elements produced by the HELAC-NLO collection of event generators, and the Parton Shower evolution, followed by hadronization and hadron decays as described by PYTHIA and HERWIG. We focus on the dilepton and trilepton decay chann…
We report on a calculation of $ε_K'/ε_K$ at next-to-leading in the $1/N_c$ expansion and to lowest order in Chiral Perturbation Theory. We discuss the short-distance matching, the scale and scheme dependence as well as the long-distance short-distance matching. We include the two known chiral corrections to our result and discuss further order $p^4$ corrections to it.
A new method of including the complete NLO QCD corrections to hard processes in the LO parton-shower Monte Carlo (PSMC) is presented. This method, called KrkNLO, requires the use of parton distribution functions in a dedicated Monte Carlo factorization scheme, which is also discussed in this paper. In the future, it may simplify introduction of the NNLO corrections to hard processes and the NLO corrections to PSMC. Details of the method and numerical examples of its practical implementation, as well as comparisons with other calculations, such as MCFM, MC@NLO, POWHEG, for single $Z/γ^*$-boson …
We use the POWHEG method to perform parton-shower matching for Drell-Yan production of W and Z bosons at the LHC at NLO QCD and NLO electroweak accuracy. In particular, we investigate an improved treatment of the vector-boson resonances within the POWHEG method. We employ an independent implementation of the POWHEG method and compare to earlier results within the POWHEGBOX. On the technical side, we provide the FKS formalism for photon-radiation off fermions within mass regularization.
This is the user's manual of MC@NLO.1.0. This package is a practical implementation, based upon the HERWIG event generator, of the recently proposed MC@NLO formalism for matching the next-to-leading order calculation of a QCD process with a parton-shower Monte Carlo simulation. The processes of standard-model vector boson pair production in hadronic collisions are available.
The pair production of squarks is one of the main search channels for supersymmetry at the LHC. We present a fully differential calculation of the next-to-leading order (NLO) SUSY-QCD corrections to the on-shell production of a pair of squarks in the Minimal Supersymmetric Standard Model (MSSM), supplemented by the leading-order decay of the squarks to the lightest neutralino and a quark. In addition, we use the Powheg method to match our NLO calculation with parton showers. To this end, the process was implemented in the Powheg-Box framework and interfaced with Pythia6 and Herwig++. We study …
We study the matching of multijet matrix elements and shower evolution in the case of top production in hadronic collisions at the Tevatron and at the LHC. We present the results of the matching algorithm implemented in the ALPGEN Monte Carlo generator, and compare them with results obtained at the parton level, and with the predictions of the MC@NLO approach. We highlight the consistency of the matching algorithm when applied to these final states, and the excellent agreement obtained with MC@NLO for most inclusive quantities. We nevertheless identify also a remarkable difference in the rapid…
We present an MC@NLO-like matching of next-to-leading order QCD calculations with the Nagy-Soper parton shower. An implementation of the algorithm within the HELAC-DIPOLES Monte Carlo generator is used to address the uncertainties and ambiguities of the matching scheme. First results obtained using the Nagy-Soper parton shower implementation in DEDUCTOR in conjunction with the HELAC-NLO framework are given for the pp -> top anti-top j + X process at the LHC with sqrt(s)=8 TeV. Effects of resummation are discussed for various observables.
The energy dependence of the total hadroproduction cross section of pseudo-scalar quarkonia is computed via matching Next-to-Leading Order (NLO) Collinear-Factorisation (CF) results with resummed higher-order corrections, proportional to $α_s^{n}\ln^{n-1}(1/z)$, to the CF hard-scattering coefficient, where $z=M^2/\hat{s}$ with $M$ and $\hat{s}$ being the quarkonium mass and the partonic center-of-mass energy squared. The resummation is performed using High-Energy Factorisation (HEF) in the Doubly-Logarithmic (DL) approximation, which is a subset of the leading logarithmic $\ln (1/z)$ approxima…
I show that with simple extensions of the shower algorithms in Monte Carlo programs, one can implement NLO corrections to the hardest emission that overcome the problems of negative weighted events found in previous implementations. Simple variants of the same method can be used for an improved treatment of matrix element corrections in Shower Monte Carlo programs.
The decay $B \to X_s γ$ is studied at the Next to Leading Order in QCD in a class of models containing at least two Higgs doublets and with only one charged Higgs boson non-decoupled at low-energy. The two-loop matching condition is calculated and it is found to agree with existing results. The complete dependence of the Wilson coefficients on the matching scale is given. The size of the Next to Leading Order corrections is extensively discussed. Results for branching ratios, possible CP asymmetries and lower bounds on the charged Higgs mass are presented when the convergence of the perturbati…
In the case of the gluon-fusion process in deep-inelastic leptoproduction, I explicitly show how to incorporate NLO corrections in a Monte-Carlo event generator by a subtraction method. I calculate the parton densities to be used by the event generator in terms of MSbar densities. The method is generalizable. A particular motivation for treating the gluon-fusion process is to treat diffractive deep-inelastic scattering properly, since in diffractive scattering the gluon density dominates the quark densities. I also propose a modified algorithm for treating parton kinematics in event generators…
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…
We present numerical tests and predictions of the KrkNLO method for matching of NLO QCD corrections to hard processes with LO parton shower Monte Carlo generators (NLO+PS). This method was described in detail in our previous publications, where it was also compared with other NLO+PS matching approaches (MC@NLO and POWHEG) as well as fixed-order NLO and NNLO calculations. Here we concentrate on presenting some numerical results (cross sections and distributions) for $Z/γ^*$ (Drell-Yan) and Higgs-boson production processes at the LHC. The Drell--Yan process is used mainly to validate the KrkNLO …
Exclusive rare decays mediated by $b\to s\ell\ell$ transitions receive contributions from four-quark operators that cannot be naively expressed in terms of local form factors. Instead, one needs to calculate a matrix element of a bilocal operator. In certain kinematic regions, this bilocal operator obeys some type of Operator Product Expansion, with coefficients that can be calculated in perturbation theory. We review the formalism and, focusing on the dominant SM operators ${\cal O}_{1,2}$, we perform an improved calculation of the NLO matching for the leading dimension-three operators. This …
We discuss top-quark physics at the ILC with a focus on the full off-shell processes for $t\bar{t}$ and $t\bar{t}H$ production, including top-quark decays and also leptonic $W$ decays. A special focus is on the matching of the resummed vNRQCD threshold calculation and the fixed-order NLO QCD continuum calculation, where we present an update on the validation of the matching. All of the calculations have been performed in the \wz event generator framework.
We present an extension of the Monte Carlo Event Generator Whizard which includes chargino production at the ILC at NLO. We include photons using both a fixed order and a resummation approach. While the fixed order approach suffers from negative event weights, the resummation method solves this problem and automatically includes leading higher order corrections. We present results for cross sections and event generation for both methods and evaluate the systematic errors due to soft and collinear approximations. In the resummation approach, the residual uncertainty can be brought down to the p…
We show how many contemporary issues in event generation can be recast in terms of partonic calculations with a matching scale. This framework is called GenEvA, and a key ingredient is a new notion of phase space which avoids the problem of phase space double-counting by construction and includes a built-in definition of a matching scale. This matching scale can be used to smoothly merge any partonic calculation with a parton shower. The best partonic calculation for a given region of phase space can be determined through physics considerations alone, independent of the algorithmic details of …
