在味工厂中，$e^+ e^-$ 湮灭产生 π 介子对在确定 μ 子反常磁矩的强子贡献中起着至关重要的作用。最近 CMD-3 通过能量扫描对 π 介子形状因子的测量与先前的实验测定显示出显著差异。为了有助于改进能量扫描实验的理论描述和模拟，我们提出了一项在 QED 和 sQED 中匹配到 Parton Shower 算法的 $e^+ e^- \to π^+ π^- (γ)$ 强子道次领头阶计算。根据文献中的最新进展，我们特别关注在圈图中超出常用因子化 sQED 方法的 π 介子复合结构处理，以及通过 Parton Shower 算法对多重光子辐射的建模。具体而言，我们详细讨论了根据两种独立方法在虚 sQED 修正中纳入 π 介子形状因子，这两种方法分别受广义矢量介子主导模型和色散方法启发。我们发现这两种方法高度一致。我们展示了与精密能量扫描测量相关的包容性和微分可观测量的唯象结果，重点关注辐射修正的影响以及处理 π 介子形状因子的各种方法的效果。我们的计算已实现在 Monte Carlo 事件生成器 BabaYaga@NLO 的更新版本中，可用于数据分析中的完全排他性模拟。
英文摘要：
The pion pair production in $e^+ e^-$ annihilation at flavour factories plays a crucial role in the determination of the hadronic contribution to the muon anomalous magnetic moment. The recent CMD-3 measurement of the pion form factor via energy scan displays a significant difference with the previous experimental determinations. In order to contribute to an improved theoretical description and simulation of energy scan experiments, we present a calculation of the $e^+ e^- \to π^+ π^- (γ)$ hadronic channel at next-to-leading order matched to a Parton Shower algorithm in QED and sQED. According to the recent advances in the literature, particular attention is paid to the treatment of the pion composite structure in loop diagrams beyond the commonly used factorised sQED approach, as well as to the modelling of multiple photon radiation through the Parton Shower algorithm. In particular, we carry out a detailed discussion on the inclusion of the pion form factor in the virtual sQED corrections according to two independent methods, inspired by the generalised vector meson dominance model and the dispersive approach, respectively. We find the two methods to be in remarkable agreement. We show phenomenological results for inclusive and differential observables which are relevant for precision energy scan measurements, focusing on the impact of the radiative corrections and the effect of the various approaches for the treatment of the pion form factor. Our calculation is implemented in an updated version of the Monte Carlo event generator BabaYaga@NLO, that can be used for fully exclusive simulations in data analysis.
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.
Modern parton showers are built using one of two models: dipole showers or angular ordered showers. Both have distinct strengths and weaknesses. Dipole showers correctly account for wide-angle, soft gluon emissions and track the leading flows in QCD colour charge but they are known to mishandle partonic recoil. Angular ordered showers keep better track of partonic recoil and correctly include large amounts of wide-angle, soft physics but azimuthal averaging means they are known to mishandle some correlations. In this paper, we derive both approaches from the same starting point; linking our un…
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…
A new parton shower algorithm has been presented with the claim of providing soft-gluon resummation at `full colour' (arXiv:2001.11492). In this paper we show that the algorithm does not succeed in this goal. We show that full colour accuracy requires the Sudakov factors to be defined at amplitude level and that the simple parton-shower unitarity argument employed in arXiv:2001.11492 is not sufficient.
We present the implementation and validation of the techniques used to efficiently evaluate parametric and perturbative theoretical uncertainties in matrix-element plus parton-shower simulations within the Sherpa event-generator framework. By tracing the full $α_s$ and PDF dependences, including the parton-shower component, as well as the fixed-order scale uncertainties, we compute variational event weights on-the-fly, thereby greatly reducing the computational costs to obtain theoretical-uncertainty estimates.
Spin correlations are an important, but often neglected, effect in modern Monte Carlo event generators. We show that they can be fully incorporated in Herwig 7 using the algorithm originally proposed by Collins and Knowles in all stages of the event generation process and between the different stages of the event generation. In this paper we present the final missing ingredient, correlations in both the angular-ordered and dipole shower algorithms and between the parton shower and hard production and decay processes.
We present the matching of NLO QCD and NLO EW corrections to parton showers for vector-boson pair production at the LHC. We consider leptonic final states, including resonant and non-resonant diagrams, spin correlations and off-shell effects. Our results are obtained interfacing the Recola2-Collier one-loop provider with the POWHEG-BOX-RES framework. We discuss our implementation, we validate it at fixed order, and we show our final results matched to parton shower. A by-product of our work is also a general interface between Recola2-Collier and POWHEG-BOX-RES. This is the first time that EW a…
In these proceedings we present three possible interpretations of the ordering variable implemented in the Herwig7 angular-ordered parton shower. Each interpretation determines a different recoil-scheme prescription and we show how it can impact the logarithmic accuracy of the algorithm. We also present comparisons with LEP data.
We implement matrix-element corrections to HERWIG parton shower simulations for Standard Model Higgs boson production at hadron colliders. We study the Higgs transverse momentum distribution and compare different versions of HERWIG and resummed calculations. The HERWIG results exhibit a remarkable improvement as many more events are generated at large transverse momentum after the inclusion of matrix-element corrections.
For the first time, differential cross sections for the production of W-bosons in conjunction with up to three jets, computed at next-to leading order in QCD and including parton shower corrections, are presented and compared to recent experimental data from the Large Hadron Collider.
We present a set of NLO SUSY-QCD calculations for the pair production of neutralinos and charginos at the LHC, and their matching to parton-shower programs in the framework of the POWHEG-BOX program package. The code we have developed provides a SUSY Les Houches Accord interface for setting supersymmetric input parameters. Decays of the neutralinos and charginos and parton-shower effects can be simulated with PYTHIA. To illustrate the capabilities of our program, we present phenomenological results for a representative SUSY parameter point. We find that NLO-QCD corrections increase the product…
In this paper, we present the next-to-leading order predictions for diphoton production in the ADD model, matched to the HERWIG parton shower using the MC@NLO formalism. A selection of the results is presented for d=2-6 extra dimensions, using generic cuts as well as analysis cuts mimicking the search strategies as pursued by the ATLAS and CMS experiments.
Modified Altarelli-Parisi splitting functions were recenty proposed to model multi-parton radiation in a dense medium and describe jet quenching, one of most striking features of heavy-ion collisions. We implement medium-modified splitting functions in the HERWIG parton shower algorithm, which satisfies the angular ordering prescription, and present a few parton-level results, such as transverse momentum, angle and energy-fraction distributions, which exhibit remarkable medium-induced effects. We also comment on the comparison with respect to the results yielded by other implementations of med…
We present a calculation of the next-to-leading order QCD corrections to slepton pair production in association with a jet at the LHC together with their implementation in the POWHEG BOX. For the simulation of parton-shower effects and the decays of the sleptons we employ the multi-purpose Monte-Carlo program PYTHIA. We discuss the impact of next-to-leading order QCD corrections on experimentally accessible distributions and illustrate how the parton shower can modify observables that are sensitive to QCD radiation effects. Having full control on the hard jet in the process, we provide precise…
We present results for the Higgsstrahlung process within the GENEVA Monte Carlo framework. We combine the fully differential NNLO calculation with the higher-order resummation in the 0-jettiness resolution variable (beam-thrust). The resulting parton-level events are further showered and hadronised by Pythia8. The beam-thrust resummation is carried out to NNLL$'$ accuracy, which consistently incorporates all singular virtual and real NNLO corrections. It thus provides a natural perturbative connection between the NNLO calculation and the parton shower regime, including a systematic assessment …
We present an implementation of $WZjj$ production via vector-boson fusion in the POWHEG BOX, a public tool for the matching of next-to-leading order QCD calculations with multi-purpose parton-shower generators. We provide phenomenological results for electroweak $WZjj$ production with fully leptonic decays at the LHC in realistic setups and discuss theoretical uncertainties associated with the simulation. We find that beyond the leading-order approximation the dependence on the unphysical factorization and renormalization scales is mild. The two tagging jets are furthermore very stable against…
We present the implementation of electroweak Zjj and Wjj production via vector boson fusion with fully leptonic decays at NLO QCD in the POWHEG framework. These processes represent an important background to Higgs searches in vector boson fusion, but they also can be seen as signal processes to study anomalous triple vector boson couplings as well as the impact of a central jet veto. Observables related to the third jet are sensitive to the parton shower which is used, a fact which is demonstrated by a comparison between PYTHIA, the standard angular-ordered HERWIG++ shower and the new p_T-orde…
We present the determination of Transverse Momentum Dependent (TMD) parton distributions from Monte Carlo parton showers. We investigate the effective TMD distributions obtained from the PYTHIA8 and HERWIG6 parton showers and compare them to the TMD distributions determined within the Parton Branching method.
General-purpose Monte Carlo event generators have become important tools in particle physics, allowing the simulation of exclusive hadronic final states. In this article we examine the Pythia 8 generator, in particular focusing on its parton-shower algorithms. Some relevant new additions to the code are introduced, that should allow for a better description of data. We also implement and compare with 2 to 3 real-emission QCD matrix elements, to check how well the shower algorithm fills the phase space away from the soft and collinear regions. A tuning of the generator to Tevatron data is perfo…
We present an implementation of Higgs boson production via vector-boson fusion in association with three jets at hadron colliders in the POWHEG-BOX, a framework for the matching of NLO-QCD calculations with parton-shower programs. Our work provides the means to precisely describe the properties of extra jet activity in vector-boson fusion reactions that are used for the suppression of QCD backgrounds by central jet veto techniques. For a representative setup at the CERN LHC we verify that uncertainties related to parton-shower effects are mild for distributions related to the third jet, in con…
We formulate some first fundamental elements of an approach for assessing the logarithmic accuracy of parton-shower algorithms based on two broad criteria: their ability to reproduce the singularity structure of multi-parton matrix elements, and their ability to reproduce logarithmic resummation results. We illustrate our approach by considering properties of two transverse momentum ordered final-state showers, examining features up to second order in the strong coupling. In particular we identify regions where they fail to reproduce the known singular limits of matrix elements. The characteri…
We present a general method to match fully differential next-to-next-to-leading (NNLO) calculations to parton shower programs. We discuss in detail the perturbative accuracy criteria a complete NNLO+PS matching has to satisfy. Our method is based on consistently improving a given NNLO calculation with the leading-logarithmic (LL) resummation in a chosen jet resolution variable. The resulting NNLO$+$LL calculation is cast in the form of an event generator for physical events that can be directly interfaced with a parton shower routine, and we give an explicit construction of the input "Monte Ca…
In this study we tried to emphasize the role parton shower plays in event generation, and in the physics of high energy event generation. We achieved this task by comparing the next-to-leading order and next-to-next-to-leading order results from EERAD3 with the next-to-leading order plus parton shower results from Vincia, and comparing both with real data.
This paper presents a novel quantum walk approach to simulating parton showers on a quantum computer. We demonstrate that the quantum walk paradigm offers a natural and more efficient approach to simulating parton showers on quantum devices, with the emission probabilities implemented as the coin flip for the walker, and the particle emissions to either gluons or quark pairs corresponding to the movement of the walker in two dimensions. A quantum algorithm is proposed for a simplified, toy model of a 31-step, collinear parton shower, hence significantly increasing the number of steps of the pa…
When the initial state evolution of a parton shower is organized according to the standard "backward evolution'' prescription, ratios of parton distribution functions appear in the splitting probabilities. The shower thus organized evolves from a hard scale to a soft cutoff scale. At the end of the shower, one expects that only the parton distributions at the soft scale should affect the results. The other effects of the parton distributions should have cancelled. This means that the kernels for parton evolution should be related to the shower splitting functions. If the initial state partons …
In this paper we outline a new parton shower algorithm based on the Catani-Seymour dipole factorization. Our motivation is to have an algorithm which can naturally cooperate with the NLO calculations.
Presented here is a technique of propagating uncertainties through the parton shower by means of an alternate event weight. This technique provides a mechanism to systematically quantify the effect of variations of certain components of the parton shower leading to a novel approach to probing the physics implemented in a parton shower code and understanding its limitations. Further, this approach can be applied to a large class of parton shower algorithms and requires no changes to the underlying implementation.
A new calculation using off-shell matrix elements with TMD parton densities supplemented with a newly developed initial state TMD parton shower is described. The calculation is based on the KaTie package for an automated calculation of the partonic process in high-energy factorization, making use of TMD parton densities implemented in TMDlib. The partonic events are stored in an LHE file, similar to the conventional LHE files, but now containing the transverse momenta of the initial partons. The LHE files are read in by the CASCADE package for the full TMD parton shower, final state shower and…
We report on the possibility of reweighting parton-shower Monte Carlo predictions for scale variations in the parton-shower algorithm. The method is based on a generalization of the Sudakov veto algorithm. We demonstrate the feasibility of this approach using example physical distributions. Implementations are available for both the parton-shower modules in the Herwig 7 event generator.
One can use more than one scale variable to define the family of surfaces in the space of parton splitting parameters that define the evolution of a parton shower. In an earlier paper, we developed this idea for electron-positron annihilation. Here, we use multiple scale variables for a parton shower with initial state partons. Then we need a more sophisticated analysis because the evolution of parton distribution functions must be coordinated with the parton shower evolution. We make the needed connections more precise than in our earlier work, even for the case of just one scale variable. Th…
We present an algorithm for improving subsequent parton shower emissions by full SU(3) colour correlations in the framework of a dipole-type shower. As a proof of concept, we present results from the first implementation of such an algorithm for a final state shower.
We present an implementation of a parton shower algorithm for hadron colliders and electron-positron colliders based on the dipole factorisation formulae. The algorithm treats initial-state partons on equal footing with final-state partons. We implemented the algorithm for massless and massive partons.
Parton showers are widely used to generate fully exclusive final states needed to compare theoretical models to experimental observations. While, in general, parton showers give a good description of the experimental data, the precise functional form of the probability distribution underlying the event generation is generally not known. The reason is that realistic parton showers are required to conserve four-momentum at each vertex. In this paper we investigate in detail how four-momentum conservation is enforced in a standard parton shower and why this destroys the analytic control of the pr…
We derive a new method for initial-state collinear showering in Monte-Carlo event generators which is based on the use of unintegrated parton correlation functions. Combined with a previously derived method for final-state showering, the method solves the problem of treating both the hard scattering and the evolution kernels to be used in arbitrarily non-leading order. Although we only treat collinear showering, so that further extensions are needed for QCD, we have discovered several new results: (1) It is better to generate exact parton kinematics in the hard scattering rather than with the …
We present a systematic study of differences between NLL resummation and parton showers. We first construct a Markovian Monte-Carlo algorithm for resummation of additive observables in electron-positron annihilation. Approximations intrinsic to the pure NLL result are then removed, in order to obtain a traditional, momentum and probability conserving parton shower based on the coherent branching formalism. The impact of each approximation is studied, and an overall comparison is made between the parton shower and pure NLL resummation. Differences compared to modern parton-shower algorithms for…
We perform a detailed analysis of next-to-leading order plus parton-shower matching in vector-boson-fusion WW production including leptonic decays. The study is performed in the Herwig 7 framework interfaced to VBFNLO 3, using the angular-ordered and dipole-based parton-shower algorithms combined with the subtractive and multiplicative matching algorithms.
We report on re-calculation of the next-to-leading order DGLAP evolution kernels performed in a scheme suited for Monte Carlo simulations of parton cascades (parton showers).
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.
In this talk, we discuss recent developments in combining parton showers and fixed-order calculations. We focus on the UNNLOPS method for matching next-to-next-to-leading order computations to the parton shower, and we present results from Sherpa for Drell-Yan lepton-pair and Higgs-boson production at the LHC.
Parton showers in Monte Carlo event generators reflect to a certain accuracy our understanding of QCD radiation at all orders. For observables sensitive to interjet energy flow in well defined regions of phase space, it has been known for some time that relevant all-order dynamics is substantially more complicated than that encoded via angular ordering in parton shower algorithms, even to leading logarithmic accuracy. Here we investigate the extent of the numerical mismatch between leading logarithmic analytical estimates (resummation) and parton showers in an effort to better understand the a…
This lecture discusses the physics implemented by Monte Carlo event generators for hadron colliders. It details the construction of parton showers and the matching of parton showers to fixed-order calculations at higher orders in perturbative QCD. It also discusses approaches to merge calculations for a varying number of jets, the interface to the underlying event and hadronization.
We perform a detailed study of the sources of perturbative uncertainty in parton shower predictions within the Herwig 7 event generator. We benchmark two rather different parton shower algorithms, based on angular-ordered and dipole-type evolution, against each other. We deliberately choose leading order plus parton shower as the benchmark setting to identify a controllable set of uncertainties. This will enable us to reliably assess improvements by higher-order contributions in a follow-up work.
Motivated by asking how to combine parton showers with nonleading QCD matrix elements, we discuss a subtractive technique based on gauge-invariant Wilson-line operators and how this can be used to treat the soft region.
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 consider idealized parton shower event generators that treat parton spin and color exactly, leaving aside the choice of practical approximations for spin and color. We investigate how the structure of such a parton shower generator is related to the structure of QCD. We argue that a parton shower with splitting functions proportional to $α_s$ can be viewed not just as a model, but as the lowest order approximation to a shower that is defined at any perturbative order. To support this argument, we present a formulation for a parton shower at order $α_s ^k$ for any $k$. Since some of the inpu…
Initial state evolution in parton shower event generators involves parton distribution functions. We examine the probability for the system to evolve from a higher scale to a lower scale without an initial state splitting. A simple argument suggests that this probability, when multiplied by the ratio of the parton distributions at the two scales, should be independent of the parton distribution functions. We call this the PDF property. We examine whether the PDF property actually holds using Pythia and Deductor. We also test a related property for the Deductor shower and discuss the physics be…
When parton distributions are falling steeply as the momentum fractions of the partons increases, there are effects that occur at each order in $α_s$ that combine to affect hard scattering cross sections and need to be summed. We show how to accomplish this in a leading approximation in the context of a parton shower Monte Carlo event generator.
We describe an algorithm for improving subsequent parton shower emissions by full SU(3) color correlations in the framework of a dipole-type shower. As a proof of concept, we present results from the first implementation of such an algorithm for a final state shower. The corrections are found to be small for event shapes and jet rates but can be more significant for tailored observables.
We have previously described a mathematical formulation for a parton shower based on the approximation of strongly ordered virtualities of successive parton splittings. Quantum interference, including interference among different color and spin states, is included. In this paper, we add the further approximations of taking only the leading color limit and averaging over spins, as is common in parton shower Monte Carlo event generators. Soft gluon interference effects remain with this approximation. We find that the leading color, spin averaged shower in our formalism is similar to that in othe…
A method is suggested to combine tree level QCD matrix for the production of multi jet final states and the parton shower in hadronic interactions. The method follows closely an algorithm developed recently for the case of $e^+e^-$ annihilations.
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 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 …
The parton splittings in a parton shower are ordered according to an ordering variable, for example the transverse momentum of the daughter partons relative to the direction of the mother, the virtuality of the splitting, or the angle between the daughter partons. We analyze the choice of the ordering variable and conclude that one particular choice has the advantage of factoring softer splittings from harder splittings graph by graph in a physical gauge.
