An Introduction to PYTHIA 8.2

Torbjörn Sjöstrand; Stefan Ask; Jesper R. Christiansen; Richard Corke; Nishita Desai; Philip Ilten; Stephen Mrenna; Stefan Prestel; Christine O. Rasmussen; Peter Z. Skands

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An Introduction to PYTHIA 8.2

Torbjörn Sjöstrand, Stefan Ask, Jesper R. Christiansen, Richard Corke, Nishita Desai, Philip Ilten, Stephen Mrenna, Stefan Prestel, Christine O. Rasmussen, Peter Z. Skands

arXiv:1410.3012v1Oct 11, 2014hep-ph

TL;DR

High-energy collision studies need event-generation models that connect hard processes to complex multiparticle final states. This paper introduces PYTHIA 8.2 as a mature C++ framework integrating these models and associated utilities for phenomenological and experimental studies.

Problem
High-energy collision studies require coherent event-generation models spanning hard scattering, particle evolution, and multiparticle final states.
Method
The paper presents PYTHIA 8.2’s integrated physics models, event-generation components, utilities, and external interfaces.
Results
PYTHIA 8.2 is presented as a mature C++ event generator for high-energy collision studies, including LHC applications.
Takeaways & Limitations
PYTHIA 8.2 provides a standard framework for exploring theoretical models, developing search strategies, and interpreting experimental data.
Takeaways & Limitations
PYTHIA is not reliable below roughly 10 GeV centre-of-mass energy, where its continuum final-state approximations break down.

Abstract

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The PYTHIA program is a standard tool for the generation of events in high-energy collisions, comprising a coherent set of physics models for the evolution from a few-body hard process to a complex multiparticle final state. It contains a library of hard processes, models for initial- and final-state parton showers, matching and merging methods between hard processes and parton showers, multiparton interactions, beam remnants, string fragmentation and particle decays. It also has a set of utilities and several interfaces to external programs. PYTHIA 8.2 is the second main release after the complete rewrite from Fortran to C++, and now has reached such a maturity that it offers a complete replacement for most applications, notably for LHC physics studies. The many new features should allow an improved description of data.

NEW VERSION PROGRAM SUMMARY

PYTHIA 8.2 is a C++ event generator for high-energy collisions, distributed under GPL version 2 and designed for commodity PCs and Macs. It supersedes the previous version and addresses the complexity of multiparticle final states.

Implementation: PYTHIA 8.2 is a C++ event generator licensed under GPL version 2 for Linux and OS X systems.It uses approximately 10 megabytes of RAM and should also work on other operating systems.
Versioning: The new version supersedes the previous PYTHIA release.The cited previous version is Sjöstrand, Mrenna, and Skands, Computer Physics Communications 178 (2008) 852.
Physics scope: PYTHIA addresses high-energy collisions that produce complex final states with many hadrons, leptons, photons, and neutrinos.The passage identifies the relation between these final states and the underlying physics description as non-simple.

1. Introduction

PYTHIA is a mature, standard event generator for high-energy collisions that models the evolution from hard processes to complex multiparticle final states. PYTHIA 8.2 completes the transition to C++ and expands features, interfaces, and documentation to support LHC studies and other applications.

Program scope: PYTHIA provides a coherent set of models evolving few-body hard-scattering processes into complex multiparticle final states.Its physics combines rigorously derived components with phenomenological models whose parameters are determined from data.
Interfaces: PYTHIA is intended both for standalone physics studies and for integration with external packages through interfaces such as the Les Houches Accord and Les Houches Event Files.These interfaces allow matrix-element-based calculations from different sources to be combined with PYTHIA-specific components.
Article scope: The article explains the evolution of the current program and clarifies how its online manual and other resources should be used.It summarizes PYTHIA 8 physics, emphasizing limitations and aspects new since PYTHIA 8.100, and outlines the program code and user interaction methods.

2. Physics Summary · 2.1. Limitations · 2.2. Hard processes

PYTHIA’s physics models target high-energy hadron–hadron and lepton–lepton collisions, with limitations in energy range, beam types, and detector-material simulation. Its hard-process coverage is broad, combining many internal processes with external LHA/LHEF inputs and user- or MadGraph-generated matrix elements.

2.1. Limitations: PYTHIA targets collisions above 10 GeV CM energy, using continuum final-state approximations especially for hadron–hadron cross sections and string fragmentation.This corresponds to a pp fixed-target beam energy of at least 50 GeV; the supplied passage is truncated before stating the lower-energy consequence.
2.1. Limitations: Explicit physics-model tests extend to roughly 100 TeV CM energy, so higher-energy extrapolations require careful cross-checks and are not advised for novice users.This corresponds to a pp fixed-target beam energy of at most 10^10 GeV.
2.1. Limitations: PYTHIA supports hadron–hadron and lepton–lepton collisions, but not lepton–hadron collisions, incoming photon beams, or internally handled proton–nucleus and nucleus–nucleus collisions.Supported hadrons include (anti)protons, (anti)neutrons, pions, and, specially, the Pomeron.
2.1. Limitations: Produced particles are simulated in vacuum without detector-material interactions, although users can interface external detector simulation through direct code or HepMC.Pythia events can be analyzed at parton or particle level, with examples distributed alongside the code.
2.2. Hard processes: PYTHIA combines many internal hard processes with a rapidly expanding set imported through the LHA/LHEF standards, while retaining specialized internal processes.Specialized cases include long-lived coloured particles and other processes with particular requirements.
2.2. Hard processes: Beyond QCD and electroweak production, internal processes cover Higgs, SUSY, new gauge bosons, left-right symmetry, leptoquarks, compositeness, hidden sectors, and extra dimensions.Examples include CP-violating Higgs decays, long-lived SUSY R-hadrons, Z′/W′ production, leptoquarks, hidden-sector radiation, and Randall–Sundrum or Unparticle states.
2.2. Hard processes: Users can code unavailable matrix elements for one, two, or three final-state hard partons or particles, or generate such code automatically with MadGraph 5.The full BSM process and parameter list is available in the distributed HTML manual.

2.3. Soft processes

PYTHIA models elastic, diffractive, and non-diffractive components of the hadronic total cross section, with special emphasis on non-diffractive events and increasingly capable diffraction modeling. Its soft-process framework includes several diffractive topologies, while some cross-section updates and exclusive diffractive processes remain outstanding.

2.3. Soft processes: PYTHIA describes elastic, diffractive, and non-diffractive topologies, with non-diffractive events constituting the major part of the total cross section.Diffraction modeling has improved to a comparable level, although related parameter tuning lags behind.
2.3. Soft processes: Total, elastic, and inelastic cross sections are obtained from Regge fits, with the default pp model using the 1992 Donnachie–Landshoff parametrisation.The parametrisation contains one Pomeron and one Reggeon term.
2.3. Soft processes: The inelastic cross section is decomposed into single-, double-, central-diffractive, and non-diffractive components using one of five parametrisations, currently defaulting to Schuler–Sjöstrand.The central-diffractive component is a new addition and is parametrised by default using a simple scaling assumption.
2.3. Soft processes: Precision measurements indicate that σTOT(s) and σEL(s) grow faster at large s, while σINEL(s) remains in the right ballpark; updating Pythia 8 formulas is planned.More recent fits support a Pomeron term proportional to s^0.096.
2.3. Soft processes: Single, double, and central diffraction use the Ingelman–Schlein model, with Pomeron flux determining diffractive-system masses and internal structure simulated as a Pomeron–proton non-diffractive collision.Low-mass diffractive systems are assumed to have no perturbative effects.
2.3. Soft processes: Exclusive diffractive processes such as pp → pph are not implemented.Such processes would not benefit from the full Pythia machinery.

2.4. Parton distributions

PYTHIA 8.2 provides built-in and externally accessible parton distribution functions, with an emphasis on LO sets because its machinery is primarily leading order. The section highlights the importance of small-x PDFs for minimum-bias, underlying-event, and multiparton-interaction modeling, while allowing separate PDF choices for hard interactions and subsequent evolution.

Parton distributions: Sixteen proton PDF sets are built in, with additional sets for pions, the Pomeron, and leptons; larger selections are accessible through LHAPDF5 and LHAPDF6.Most built-in sets use interpolation of a grid for Q2 evolution.
Parton distributions: LO PDFs are preferred internally because they retain a parton-number-density interpretation and remain suitable for the low-x, low-Q regime probed by minimum-bias and underlying-event phenomena.These models probe x values down to around 10^-8 and Q scales below 1 GeV.
Parton distributions: NLO PDFs can become negative at small x and Q, making them unsuitable for showers or multiparton interactions despite their use in tunes describing collider data.Their small-x corrections are proportional to ln(1/x).
Parton distributions: NLO tunes require a significantly smaller p⊥0 scale to compensate for their low small-x gluon density, affecting the number and kinematics of multiparton interactions.Small-x partons determine integrated QCD cross sections through the parton density fi(x, Q2), while asymmetric collisions are suppressed when NLO PDFs are tiny at small x.
Parton distributions: Pythia permits separate PDF sets for the hard interaction and for subsequent showers and multiparton interactions, enabling an NLO hard-process choice alongside LO evolution inputs.Standard backward-evolution ISR uses PDF ratios, so many differences between PDF sets divide out away from the low-x region.

2.5. Parton showers

PYTHIA 8.2 uses p⊥-ordered dipole-style ISR and FSR showers with expanded radiation options and a single interleaved ISR–FSR–MPI evolution. The showers use LO DGLAP kernels with mass and polarization treatments, configurable effective couplings, and matrix-element corrections for first hard emissions.

2.5. Parton showers: PYTHIA 8.2 extends dipole-style p⊥-ordered ISR and FSR with photon, weak-boson, Hidden Valley, flexible-colour, alternative-recoil, and onium-emission options.Weak gauge-boson emission is available in both ISR and FSR, while Hidden Valley bremsstrahlung and flexible colour strengths extend the framework to specialized models and decays.
2.5. Parton showers: ISR, FSR, and MPI are interleaved in one decreasing-p⊥ sequence, preventing hard-FSR phase space from depending on dipoles created by soft ISR.The interleaving can be switched on or off for cross checks; some FSR can recoil against colour dipoles connected to a beam-remnant hole.
2.5. Parton showers: Both showers use LO DGLAP splitting kernels, with approximate gluon-polarization effects from non-isotropic azimuths and generally included parton-mass corrections.The evolution equations describe radiation probabilities as the evolution variable decreases; FSR proceeds through timelike branchings, whereas ISR involves spacelike virtualities.
2.5. Parton showers: Radiation strength is controlled by separate effective αs(MZ) values for ISR and FSR, evaluated by default at the shower scale p⊥evol with kµR = 1.The scale factor can be varied for uncertainty estimates, and shower αs(MZ) values are not directly comparable to the PDG MS αs(MZ) = 0.1185(6).
2.5. Parton showers: Automated matrix-element corrections upgrade the first jet emission to the full LO matrix element across many production and decay processes.The underlying shower is primarily intended for collinear or soft radiation with strongly ordered successive p⊥ scales.

2.6. Multiparton interactions

Pythia 8 models soft and hard multiparton interactions in a unified framework, with expanded process coverage and correlations enforcing energy, momentum, and flavour constraints. MPI are interleaved with initial- and final-state radiation, while optional components extend the model to rescattering and x-dependent impact-parameter profiles.

Process coverage: Pythia 8 extends MPI beyond QCD 2 →2 scattering to include photon-associated processes, quarkonium production, s-channel γ exchange, and t-channel γ/Z0/W± exchange.Users can also request two distinct hard interactions in one event, with further MPI occurring as usual.
Model regulation: The model regulates the low-p⊥ divergence through an effective p⊥0 parameter, with MPI rates also controlled by αs(MZ), its running order, and the MPI PDF set.The hadron mass distribution in impact-parameter space and colour-reconnection modeling are additional important tunable aspects.
Correlations and conservation: MPI correlations account for energy conservation by squeezing PDFs into the remaining x range and enforcing momentum and flavour sum rules.Flavour conservation tracks preceding valence and sea-quark interactions, while companion PDFs account for sea quarks produced through g →q q̄ splitting.
Interleaved evolution: MPI, ISR, and FSR are combined into one interleaved p⊥-ordered sequence, forming Pythia 8’s master evolution equation.The sequence uses the corresponding MPI, ISR, and FSR evolution kernels.
Optional components: Two optional components, off by default, model partonic rescattering and an x-dependent impact-parameter shape.The latter places high-momentum partons closer to the hadron center than low-momentum partons.

2.7. Beam remnants and colour reconnection

PYTHIA 8.2 models complex beam remnants, scale-dependent primordial k⊥, and colour reconnection among multiple parton interactions. Its core includes three colour-reconnection models, while additional models remain less supported or unimplemented.

Beam remnants: Beam remnants can occupy complex, high-colour representations after multiple initiators are extracted, with a new option supporting arbitrary representations and suppressing higher-charge states.The default model attaches gluon initiators to other colour lines to reduce remnant colour charge without forming a singlet.
Beam remnants: Primordial k⊥ is modeled with a hard-process-dependent width, allowing low-p⊥ multiparton-interaction systems to receive less primordial transverse momentum.Although intrinsic motion is expected to be a few hundred MeV, low-end Z-boson p⊥ studies prefer average values around 2 GeV, possibly reflecting incompletely simulated low-p⊥ initial-state radiation.
Colour reconnection: Three colour-reconnection models are implemented: MPI-based, QCD-based, and gluon-move, with reconnections generally chosen to reduce total string length.The QCD-based model also allows junction formation, while the gluon-move model optionally flips connections between string systems.
Colour reconnection: Additional colour-reconnection models are available only as less well-supported plugins, while Pythia 6 hadron-collider models and the LEP W+W− machinery are not implemented.The latter machinery is described as not yet implemented.

2.8. Hadronisation

PYTHIA 8.2 models hadronisation solely with the Lund string-fragmentation framework, retaining its core machinery while improving the treatment of multijunction configurations. The model represents confinement through strings that break into colour-singlet systems and ultimately on-shell hadrons, with fragmentation constrained by left–right symmetry and parameters fitted to data.

Framework: Hadronisation uses only the Lund string-fragmentation framework, with improved handling of more complicated multijunction string configurations.The core string-fragmentation machinery remains unchanged from earlier Jetset/Pythia implementations.
String model: The string model starts from linear confinement, in which the energy between a charge and anticharge increases linearly with separation.The flux tube has typical transverse dimensions of roughly 1 fm and string tension κ ≈1 GeV/fm.
String fragmentation: As partons separate, strings can break through new q′q′ pair production into colour-singlet pieces, with repeated breaks producing on-shell hadrons.Each hadron corresponds to a small piece of string once the remaining string-piece invariant masses are sufficiently low.
String fragmentation: Causally disconnected string breaks permit convenient fragmentation ordering, while physical hadron masses and left–right symmetry constrain the fragmentation functions.The remaining free parameters in the fragmentation-function shape are determined from data.
Pair production: Tunneling suppresses heavy-quark pair production with u : d : s : c ≈1 : 1 : 0.3 : 10−11, allowing charm and bottom production to be neglected during hadronisation.The same mechanism gives a flavour-independent Gaussian transverse-momentum spectrum for produced quarks.

2.9. Resonance and particle decays

PYTHIA distinguishes resonances, particles, and partons by lifetime and colour, with resonance decays integrated into the hard process and particle decays performed after hadronisation. The release improves decay modelling, especially for tau spin correlations and dedicated multibody tau decay models, while updating particle data.

Resonance and particle decays: States above 20 GeV are generally treated as resonances; colourless leptons and hadrons are particles, while quarks and gluons are partons.Exceptions include some light hypothetical weakly interacting or stable states, such as the gravitino.
Resonance and particle decays: Resonance decay channels affect Pythia’s total cross-section, whereas particle decay channels are applied after hadronisation and leave it unchanged.Resonances are decayed sequentially as part of the hard process; particle decays occur afterward.
Tau decays: Tau decays support full spin correlations for most standard production mechanisms and can use polarisation information.The treatment also uses generic matrix-element weights for many decays, including Dalitz and weak decays.
Tau decays: Tau helicity-density calculations correlate the decays of two taus produced by the same mechanism.The decay matrix from the first decayed tau is used when calculating the helicity density matrix for the second.
Tau decays: Dedicated models cover tau decays with up to six bodies and all channels with branching fractions greater than 0.04%.New tau decay models require only the hadronic current Jµ to be provided.

2.10. Matching and merging

Pythia combines matrix-element descriptions at high momentum transfer with parton showers at low scales through process-specific matching and process-independent multi-jet merging techniques. These include first-order ME corrections, POWHEG and MC@NLO matching, and the native CKKW–L merging method.

Matching and merging: Matching and merging combine matrix-element calculations at high momentum-transfer scales with parton showers at low scales, using external ME events in many implementations.The methods internally accept or reject external events before combining them with parton showers.
Process-specific matching: Process-specific schemes improve the first-emission radiation pattern and, often, the inclusive cross section through first-order ME corrections, POWHEG, or MC@NLO matching.These methods target specific physics processes rather than supplementing showers independently of the core process.
Process-specific matching: First-order ME corrections upgrade shower emission probabilities to reproduce the full +1-parton inclusive tree-level cross section for selected decays and production processes.The improved splitting kernels provide a better approximation to QCD emission cross sections than regular kernels in the applicable cases.
NLO matching: POWHEG replaces Born-level event selection with the differential NLO cross section and generates exactly one hard emission, while using distinct phase-space mapping and hardness ordering variables.Pythia interfaces to Powheg-Box events to complete NLO+PS event generation.
NLO matching: MC@NLO separates soft/collinear shower-like contributions from hard real radiation, but can require negative-weight events when the shower emission rate exceeds the matrix-element rate away from the soft/collinear limit.aMC@NLO generates LHE files containing soft n-body and hard n + 1-body events for common showers, including Pythia.
Multi-jet merging: Multi-jet merging uses showers for soft or collinear partons and fixed-order matrix elements for well-separated partons, combining states with any numbers of each.Pythia’s native CKKW–L method combines LHEF samples of any parton multiplicity and process into a LO merged inclusive sample, removing overlaps with shower-generated Sudakov factors.

2.11. Other program components

PYTHIA 8.2 provides standardised procedures for linking to external programs and includes several analysis utilities. These utilities include old jet finders, other analysis routines, and simple one-dimensional histogram generation, display, and saving.

External interfaces: Standardised procedures link PYTHIA 8.2 to external programs for specific tasks.These procedures are discussed in subsection 3.8.
Analysis utilities: The program retains some old jet finders and other analysis routines.
Analysis utilities: A utility generates, displays, and saves simple one-dimensional histograms.

2.12. Tunes

Pythia tunes calibrate model parameters against data, with Monash 2013 as the new default covering LEP, Tevatron, and LHC measurements. Tuning emphasizes global agreement across complementary distributions while increasingly using automation, though parameter uncertainties and effects of matrix-element matching remain unresolved.

Early pre-LHC tunes under-predicted LHC minimum-bias and underlying-event activity by (10-20)%.
Monash 2013 varies many parameters, covers LEP, Tevatron, and LHC data, and became the default in Pythia 8.2.
Tuning should assess simultaneous agreement across many mutually complementary distributions rather than optimize a single distribution.MCPLOTS supports these comparisons using the Rivet analysis toolkit.
Automated tools reduce computing and human effort by sampling limited parameter points and interpolating generator results between them.Professor is cited as an example of this approach.
Comprehensive parameter uncertainties are still lacking, and tuning effects after matrix-element matching are poorly known and computationally demanding to study.

3. Program Overview

PYTHIA 8.2 is organized as a modular C++ codebase with core physics classes, plugins, documentation, examples, and a three-phase event-generation workflow. Its top-level architecture separates process generation, parton-level evolution, and hadronisation and decays, with event records and databases mediating user control and information flow.

Code organization: The codebase is organized mainly by physics task into paired header and source files, with non-core extensions in include/Pythia8Plugins.Each file typically contains one main class and related helper classes.
Documentation and examples: The distribution includes documentation and examples, while matching code and xmldoc subversions are required for the library to use settings and particle data correctly.The examples illustrate how to write main programs, and xmldoc contains settings, particle data, and PDF data grids.
Program architecture: The top-level Pythia class coordinates ProcessLevel, PartonLevel, and HadronLevel to construct complete events.ProcessLevel generates the hard process; PartonLevel handles ISR, FSR, MPI, and beam remnants; HadronLevel performs string fragmentation and unstable-particle decays.
User interaction: User interaction follows three phases: initialisation, event generation in an event loop, and finishing for final statistics.The subdivision is not strict, and many utilities and tasks span phase boundaries.
Information flow: The Event class carries the main information flow through separate process and event objects representing the hard process and the full collision history.The process object covers the few hard-process partons, while event covers incoming beams through final hadrons.
User interface: Settings and ParticleData provide user-adjustable databases, while the Pythia object exposes methods for modifying values before generator initialisation.readString changes one variable, whereas readFile reads multiple variables from an input file.

4. Outlook

PYTHIA 8.2 is a mature, tried code that completely replaces PYTHIA 6.4 for hadron-collider applications and e+e− annihilation, with several improvements. PYTHIA 6.4 may still be useful for ep, γp, and γγ processes, which remain lacking in 8.2.

4. Outlook: PYTHIA 8.2 offers a complete replacement for PYTHIA 6.4 in hadron-collider applications and e+e− annihilation, with several improvements.The 8.200 release is described as much more mature and tried than the 8.100 release.
4. Outlook: PYTHIA 6.4 may still be useful for ep, γp, and γγ applications because these areas remain lacking in PYTHIA 8.2.The passage states that these areas will be added when time permits.