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Event Generation with Sherpa 2.2

Enrico Bothmann, Gurpreet Singh Chahal, Stefan Höche, Johannes Krause, Frank Krauss, Silvan Kuttimalai, Sebastian Liebschner, Davide Napoletano, Marek Schönherr, Holger Schulz, Steffen Schumann, Frank Siegert

arXiv:1905.09127v2hep-phhep-ex

TL;DR

Collider analyses require general-purpose event generators that combine realistic event simulation with increasingly precise theoretical predictions. This paper reviews SHERPA 2.2’s components and improvements, including showers, matching, merging, and reweighting, and reports a decade of development used extensively for LHC Run 1 and Run 2. The framework is being extended toward SHERPA 3.0 with further perturbative and non-perturbative improvements.

  • Problem

    Collider experiments need general-purpose event generators for realistic event simulation and precision predictions of scattering processes and event topologies.

  • Method

    The paper reviews SHERPA 2.2’s modular physics components, including matrix elements, parton showers, matching and merging, and internal reweighting.

  • Results

    SHERPA 2.2 represents a decade of developments toward higher-precision event simulation and has been extensively used for LHC Run 1 and Run 2 event generation.

  • Takeaways & Limitations

    SHERPA is a full-fledged multipurpose generator for modelling scattering events at past, current, and future collider experiments.

  • Takeaways & Limitations

    Including hundreds of reweighting variations can still slow event production significantly, especially with parton-shower reweighting enabled.

Abstract

from arXiv · show

Sherpa is a general-purpose Monte Carlo event generator for the simulation of particle collisions in high-energy collider experiments. We summarize essential features and improvements of the Sherpa 2.2 release series, which is heavily used for event generation in the analysis and interpretation of LHC Run 1 and Run 2 data. We highlight a decade of developments towards ever higher precision in the simulation of particle-collision events.

1. Introduction

SHERPA is a general-purpose Monte Carlo framework for simulating high-energy collider events and supporting precision analyses. The SHERPA 2.2 series combines broad physics components, automated setup, and extensive use in LHC Run 1 and Run 2 studies.

  • Motivation: Monte Carlo event generators support collider design, detector studies, cross-section extrapolation, and detailed final-state simulation.They also provide precision predictions for cross sections, differential distributions, and event topologies through higher-order corrections.
  • Framework: SHERPA provides a factorised and probabilistic description of collisions at hadron-hadron, lepton-hadron, and lepton-lepton colliders.Its components cover the stages needed for general-purpose event simulation.
  • Scope: SHERPA 2.2 was used extensively for analysing LHC Run 1 and Run 2 data.The paper summarises the framework’s current abilities and components.
  • Configuration and components: Generator setups are defined through text files specifying non-default settings for the process, beams, physics model, and event evolution.The framework includes AMEGIC and COMIX for tree-level matrix elements and interfaces to one-loop providers for NLO virtual corrections.
  • Paper scope: The paper reviews SHERPA physics implementations, tuning aspects, selected simulation results, and future outlook.It directs readers to separate reviews for more detailed treatments of general Monte Carlo event-generation techniques.

2. Highlighting SHERPA Components

SHERPA’s modular framework organizes event generation through configurable physics modules, automated matrix-element tools, and phase-space integration methods. Its components support Standard Model and beyond-the-Standard-Model processes while exposing detailed run controls.

  • Framework and configuration: SHERPA uses a modular C++ structure whose core initializes physics modules and iterates the event-generation steps.Run settings, model parameters, and switches are read from an ASCII Run.dat file using named parameter blocks.
  • Physics reach: SHERPA supports a wide range of fixed-order calculations and external model interfaces, including UFO files through FEYNRULES.AMEGIC limits vertices to four external particles, while COMIX is limited by computing power for more complicated theories.
  • Matrix-element generation: AMEGIC and COMIX provide automated tree-level matrix elements for multi-particle production, decays, and fixed-order cross sections.They support automated phase-space integration and infrared-subtraction algorithms, while COMIX uses recursive colour-dressed constructions.
  • Run controls: The event setup specifies hard processes, scales, selectors, particle containers, coupling orders, and matrix-element providers through text configuration.Examples include VAR and FASTJET scale setters, jet-based selectors, and separate choices for loop and real-subtraction generators.
  • Scope boundary: SHERPA no longer supports the ADD model realization since version 2.0.This is an explicit scope boundary for the available physics models.
  • Phase-space integration: COMIX reduces the factorial growth of phase-space channels to exponential growth through a recursive algorithm.AMEGIC typically constructs one channel per diagram, whereas both generators further optimize decay integrations using VEGAS-based remappings.

2.2. Parton Showers

Parton showers evolve hard-scattering configurations toward low scales by modeling successive QCD and QED emissions before hadronisation. SHERPA provides two shower implementations with distinct construction and phase-space-evolution choices.

  • Role of showers: Parton showers evolve few-parton hard-scattering configurations from high scales to low scales through successive QCD or QED emissions.At low scales, hadronisation transforms the resulting partons into primary hadrons.
  • Resummation: Parton showers numerically approximate the all-orders resummation of large kinematical logarithms.Their logarithmic accuracy depends on the observable and shower algorithm.
  • Matching requirements: Matching showers to higher-order matrix elements must preserve fixed-order accuracy, singularity structure, colour structure, and shower resummation properties.These requirements have motivated shower algorithms based on NLO QCD infrared subtraction schemes.
  • Implementations: SHERPA contains CSSHOWER and DIRE, which use different construction paradigms and different ways to populate multi-emission phase space.CSSHOWER is the default SHERPA-2 shower and is based on Catani–Seymour dipole factorisation.
  • DIRE: DIRE combines a colour-dipole picture with standard collinear evolution and uses the inverse soft eikonal as its evolution variable.Its splitting functions can be negative, requiring a weighted Sudakov veto algorithm and analytic event weights.

2.3. Matching and Merging

SHERPA combines fixed-order matrix elements with parton showers through matching and multijet merging, extending accurate predictions across increasing jet multiplicities. Its framework includes LO, NLO, NNLO, and approximate electroweak applications across several collider processes.

  • Predictive scope: Matching and merging enable higher jet rates to be predicted at NLO or LO accuracy according to the underlying matrix-element calculation.Jet rates beyond the highest matrix-element multiplicity are supplied by the parton shower.
  • NLO matching: NLO matching uses a variant of MC@NLO that identifies the first shower emission with the infrared-subtracted real-emission contribution.This decomposes the calculation into finite real-emission and Born-like terms sharing consistent kinematics.
  • NNLO matching: NNLO+parton-shower calculations using UN2LOPS are available for Drell–Yan and Higgs production with colour-singlet final states.The method uses qT-slicing to regulate additional infrared singularities, while these facilities are not distributed with public code releases.
  • Multijet merging: Multijet merging combines matrix elements with increasing jet multiplicities and uses a separation scale to assign emissions to matrix elements or showers.The complementary classification avoids explicit double counting and preserves shower resummation in both regions.
  • MEPS@NLO: MEPS@NLO combines MC@NLO-matched samples of increasing jet multiplicity into an inclusive sample separated by Qcut.SHERPA applies the approach to processes including vector-boson, Higgs, four-lepton, triple-boson, and top-pair production.
  • Status: MEPS@NLO is described as SHERPA’s current standard for simulating QCD-associated Standard Model production processes.The approach has been continuously developed through applications of MC@NLO matching in Standard Model simulations.

2.4. Internal Reweighting

SHERPA supports on-the-fly reweighting for theoretical input variations, reducing the need to generate separate event samples while retaining broad fixed-order, matched, and merged-calculation coverage. Hundreds of variations can nevertheless significantly slow production, especially with parton-shower reweighting.

  • On-the-fly reweighting covers scale variations, PDF choices, coupling constants, and selected parton-shower effects without rerunning the shower.The shower-emission reweighting uses a generalised Sudakov Veto Algorithm.
  • SHERPA applies reweighting to LO and NLO fixed-order calculations and to matched or merged calculations using both CSSHOWER and DIRE.A lower bound on the shower evolution scale allows a speed–accuracy trade-off by omitting very soft-emission reweighting.
  • The example configuration combines 7-point scale variations, multiple PDF sets and error replicas, varied αS(mZ), electroweak contributions, and consistent shower-splitting variations.
  • Hundreds of variations can still slow production significantly, particularly when parton-shower reweighting is enabled.Reweighting remains considerably faster than producing separate event samples for each variation.

2.5. Initial State Radiation and PDFs

SHERPA models initial states across several collider configurations by separating beam spectra and possible particle conversion from the subsequent hard interaction. It provides built-in and external-library PDF options with consistent αS handling.

  • SHERPA supports pp, e+e−, ep, γγ, and µ+µ− collider setups, requiring beam-spectrum and partonic-substructure modelling.
  • Beam particles can receive energy spectra or be converted into bunch particles before their substructure enters the hard interaction.
  • Available beam treatments include laser backscattering into photons and equivalent photons in the Weizsäcker–Williams approximation.Initial beams are monochromatic by default before the second-stage substructure treatment.
  • SHERPA supplies PDFs for protons, photons, and leptons, and can interface with LHAPDF for additional proton sets and their variation or error sets.
  • PDF-based setups use a consistent αS value and running order throughout event generation, with an option to use the PDF library’s running implementation.

2.6. Higher-Order QED and EW Corrections to Decays

SHERPA computes higher-order QED and electroweak corrections to decays using YFS soft-photon resummation while retaining mass effects and preserving resonance structures. Its resummation is targeted at colourless decays, with coloured particles treated by a regular parton shower.

  • YFS resummation constructs an all-order approximation for universal soft real and virtual photon emissions while retaining mass effects.The implementation focuses on higher-order corrections to elementary-particle and hadron decays.
  • Soft-photon resummation is applied to colourless decays, whereas decays involving quarks or gluons use a regular parton shower.
  • SHERPA identifies possible resonances by ordering invariant-mass differences normalized by resonance widths, with configurations above Δres classified as non-resonant.The default value is Δres = 10.
  • Radiation from identified resonant decays preserves the invariant mass of the resonant system, while non-resonant final states receive universal YFS corrections.
  • The YFS controls select QED correction activation, the resonance-clustering threshold, soft or hard photons, and exact first-order matrix-element corrections.

2.7. Underlying Event and Beam Remnants

SHERPA models the underlying event through multiple parton interactions, beam-remnant treatment, and intrinsic transverse momentum. Its MPI evolution is ordered in transverse momentum and regulated at low scales, while the model is tuned to reference data and excludes SHERPA’s Minimum Bias implementation.

  • Underlying Event: The underlying event includes non-perturbative parton transverse momentum, hadron breakup, additional colour charges, and multiple parton interactions.
  • Underlying Event: SHERPA’s MPI model interprets partonic 2 → 2 QCD scatters above roughly 2–5 GeV as multiple scatters within one hadronic collision.
  • Underlying Event: MPI scatters are ordered by transverse momentum, which serves as the underlying-event evolution parameter dressing the primary interaction with secondary scatters.
  • Underlying Event: A transverse-momentum regulator controls the small-transfer singularity, and MPI evolution stops below p⊥,min, typically a few GeV.The parameter ξ rescales the non-diffractive cross section.
  • Underlying Event: SHERPA implements all partonic MPI channels, supplements scatters with a shower beginning at the scatter transverse momentum, and precalculates cross-section tables.
  • Underlying Event: The MPI profile parameters, cutoff, regulator, and ξ are tuned to reference data, while the extended Minimum Bias model is not implemented in SHERPA.
  • Underlying Event: Intrinsic parton kT, up to a few ΛQCD, washes out the unwanted zero-transverse-momentum peak in low-pT Drell–Yan production.
  • Beam Remnants: For hadronic beams, remnant modelling enforces flavour sum rules and compensating colour assignments; lepton-beam remnants are simpler and remain collinear with reduced energy.

2.8. Hadronisation

SHERPA models the parton-to-hadron transition through cluster fragmentation in AHADIC, while also interfacing with the Lund string model. Its cluster procedure uses non-perturbative flavour production, kinematic splitting, and mass-dependent cluster decays.

  • Underlying principles: The non-perturbative decays insert light flavour–antiflavour pairs into colour-connected singlets, repeatedly producing singlets with reduced masses.Only light u, d, and s quarks, and possibly corresponding diquarks, are allowed in this pair production.
  • Fragmentation models: SHERPA supports both its native AHADIC cluster model and an interface to PYTHIA 6.4’s Lund string fragmentation model.The Lund-model parameters can be set through SHERPA run cards.
  • Cluster fragmentation: AHADIC begins with non-perturbative gluon decays that produce quark–antiquark or diquark–antidiquark pairs, selected using available phase space and flavour-suppression weights.The term “quark” includes diquarks in this description.
  • Cluster fragmentation: Gluon splitting is constructed in a dipole frame with massless gluons, spectator recoil, and tunable distributions for the splitting variables y and z.The invariant mass of the resulting quark–antiquark system constrains the allowed constituent flavours.
  • Cluster decays: After gluon decay, colour-connected quarks and antiquarks form colour-neutral clusters that either decay directly into hadrons or split into further clusters.Further cluster formation introduces a non-perturbatively produced quark–antiquark pair and energy-sharing variables x and y.
  • Cluster decays: Clusters below a critical mass decay into two hadrons, with the critical value combining the lightest and heaviest allowed hadron-pair masses.Channel probabilities include flavour-popping probabilities, hadron wave-function and multiplet weights, phase space, and a mass-dependent factor.

2.9. Hadron Decays

SHERPA handles unstable hadrons and τ leptons through recursive decay cascades. HADRONS simulates on-shell 1 → n decays, can include spin correlations, and subsequently imposes off-shell kinematics, while decay tables rely primarily on measured branching ratios.

  • Decay chains: Unstable primary hadrons, τ leptons, and subsequent unstable decay products generate recursive cascades of secondary hadrons.The cascade continues because decay products may themselves be unstable.
  • Decay chains: The HADRONS module recursively simulates individual on-shell 1 → n decays and can account for spin correlations across the decaying particle’s propagator.Off-shell kinematics is imposed afterward using a relativistic Breit–Wigner distribution and a reverse Rambo algorithm.
  • Decay widths and kinematics: SHERPA bases decay tables on measured branching ratios, rescaling incomplete observed totals within uncertainties when necessary.Known decay modes may still be insufficient, particularly for heavy mesons.

2.10. Tuning non-perturbative model parameters

SHERPA tunes non-perturbative model parameters by iteratively comparing predictions with data in three consecutive stages: cluster hadronisation, intrinsic transverse momentum, and the underlying event.

  • Tuning strategy: SHERPA tunes non-perturbative parameters through iterative comparisons of predictions with experimental data, assuming the three event-generation phases can be tuned consecutively.The procedure addresses hadronisation, intrinsic constituent motion, and the underlying event.
  • Cluster hadronisation: Cluster hadronisation is tuned primarily to LEP 1 data using charged multiplicities, hadron yields, particle distributions, B-hadron fragmentation, and event shapes.The cluster model has about 20 parameters, so tuning is largely automated with PROFESSOR.
  • Intrinsic transverse momentum: Intrinsic transverse-momentum parameters are adjusted using Drell–Yan lepton-pair transverse-momentum distributions in proton–proton collisions at 7 TeV.The two proton beams are assigned identical parameter values in this procedure.
  • Underlying event: Underlying-event parameters are tuned with PROFESSOR against dedicated Tevatron and LHC measurements after hadronisation and intrinsic transverse momentum have been adjusted.The parameters belong to the impact-parameter-dependent multiple-parton-interaction model.
  • Underlying event: The underlying-event reference parameters are evolved to the actual collider energy, using a power α set to 0.244.The quoted pT,min and pT,0 values refer to a reference collision energy before this evolution.

3. Highlighting SHERPA Applications

SHERPA 2.2 is illustrated across collider processes and non-perturbative phenomena, with predictions compared against data or alternative calculations. These applications demonstrate multijet merging, higher-order corrections, loop-induced contributions, and decay modelling across varied observables.

  • Z+jets production: SHERPA models Z+jets jet multiplicities well through six jets, while MEPS@NLO describes the azimuthal correlation between the two hardest jets.Up to four jets are seeded by hard matrix-element partons; higher multiplicities originate from the parton shower.
  • W production: Approximate NLO electroweak corrections produce a substantial Sudakov suppression in W production at large transverse momentum.The corresponding one-loop virtual amplitudes cover up to W + 2j production.
  • Higgs production: Finite quark-mass corrections suppress the Higgs transverse-momentum spectrum by up to −60% around 500 GeV, with little jet-multiplicity dependence except for HT.The comparison covers inclusive 0-, 1-, 2- and 3-jet distributions in gluon-fusion production.
  • Top-pair production: For top-pair production, MEPS@NLO and globally rescaled MEPS@LO predictions agree closely, while higher-order corrections chiefly reduce scale uncertainty.At high HT, the prediction is almost entirely from the t¯tjj component.
  • Loop-induced diboson production: Loop-induced gg →ℓνℓν contributions reach 5% near pT(j1) ≈20 GeV and require one-jet matrix elements to describe the high-pT region.A pure parton shower does not fully account for the high-pT one-jet contribution.
  • Comparisons with data: Across several measured processes, SHERPA predictions show good agreement with data, including photon and diphoton spectra, hadronisation models, and semileptonic B0 decays.For B0 →π−e+νe, the BGL parametrisation reproduces data well, whereas the original ISGW2 and ISGW parameter sets do not.
  • New Physics sensitivity: New Physics signals can exceed the Standard Model uncertainty band at around ST ≳40 TeV in the illustrated comparison.The uncertainty band is based on perturbative-scale variations.
  • Hadron and tau decays: Including spin correlations in tau decay chains can dramatically change decay-product correlations and yields excellent agreement with exact-matrix-element results.The effect is exemplified by the decay-plane angle in H →τ(→πν)τ(→πν).

4. Conclusions

SHERPA 2.2 combines broad event-generation components with improvements aimed at higher-precision simulation and has been extensively used for LHC Run 1 and Run 2 analyses. Development toward SHERPA 3.0.0 targets further perturbative and non-perturbative improvements for future LHC data analysis.

  • SHERPA 2.2 has been extensively used for event generation during LHC Run 1 and Run 2, reflecting a decade of development toward higher-precision simulation.
  • Its full-event description combines automated matrix-element generators, parton showers, hadronisation, multiple-parton interactions, particle decays, QED corrections, and multiple interfaces.
  • Development toward SHERPA 3.0.0 includes improved perturbative treatments, phase-space sampling, QCD soft-gluon resummation, and non-perturbative modelling.
  • SHERPA 3.0.0 is intended to support future analyses of LHC data as Run 3 preparations proceed and full Run 2 measurements appear.

A. Default-tune non-perturbative model parameters

Sherpa’s default non-perturbative model is specified by tuned parameters for cluster fragmentation, intrinsic initial-state transverse momentum, and multiple-parton interactions. These parameters use reference collision energies and are evolved to the actual collider energy where stated.

  • Cluster fragmentation: Cluster-fragmentation defaults include a strange-quark fraction of 0.6049, baryon fraction of 1.0, and several flavour-selection weights.The parameters were obtained by tuning, particularly to LEP data.
  • Cluster fragmentation: The cluster-fragmentation model uses gluon-splitting, cluster-splitting, spectral, and decay parameters, with α specified by TURNOFF EXPONENT.Listed defaults include G2QQ_EXPONENT 1.08, PT^2_0 1.56, SPLIT_EXPONENT 0.1608, and DECAY_OFFSET 1.202.
  • Intrinsic transverse momentum: For initial-state protons, both beams use K_PERP_MEAN 1.1 and K_PERP_SIGMA 0.85 in the default Gaussian intrinsic-k_T distribution.In proton–proton collisions, the corresponding mean and width values are assumed equal for the two beams.
  • Energy-dependent parameters: The intrinsic-k_T values reference Eref = 7 TeV, while the MPI model defines pT,min and pT,0 at Eref = 1.8 TeV and evolves them to the actual collider energy.The MPI defaults include SCALE_MIN 2.895, TURNOFF 0.7549, and TURNOFF_EXPONENT 0.244; the latter specifies α.
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