Monte Carlo event generators are the central interface between theoretical calculations and experimental measurements in collider physics. Over several decades, a comprehensive and highly modular ecosystem of tools has developed around them, encompassing matrix-element calculations, parton showers, hadronisation models, and their integration with detector simulation, event-level analysis and statistical inference. While these tools are ubiquitous in modern research, the conceptual scope and technical structure of the full simulation chain can be challenging to navigate, particularly for researchers entering the field. In this primer, we provide a structured and up-to-date overview of the high-energy physics Monte Carlo ecosystem, focusing primarily on event-generator methodologies and their role within the broader collider workflow. We discuss the conceptual foundations of modern generators, the computational and organisational challenges of large-scale simulations, and the principles that enable interoperability and reproducibility across theory and experiment. We also examine the evolving computing landscape and sustainability considerations that will shape the future development of these tools. Aimed primarily at early-stage doctoral researchers while serving as a reference for the broader community, this article seeks to clarify architecture, methodology, and long-term trajectory of Monte Carlo event generation in collider physics.

We propose a new way to impose four-momentum conservation on timelike parton-shower branchings, allowing for recoil to be imparted not only to individual partons but also to groups of partons, "jets". In this work we present an explicit realisation of this idea for a dipole parton-shower, using angular ordering to decide which partons are grouped into jets in a way that does not require explicit jet clustering at each stage of the evolution. We verify that the algorithm satisfies next-to-leading logarithmic (NLL) accuracy criteria, from numerical fixed-order tests as well as resummation tests across a range of observables. Our conclusion is that jet recoils provide a viable path for adapting existing dipole/antenna-type showers to achieve NLL accuracy.

Measurements of hadronic final states in e^{+}e^{-} e + e − collisions at centre-of-mass (CM) energies below the Z peak can notably extend the FCC-ee physics reach in terms of precision quantum chromodynamics (QCD) studies. Hadronic final states can be studied over a range of hadronic energies \sqrt{s_\mathrm{had}} ≈ 20-80\,\mathrm{GeV} s h a d ≈ 20 − 80 G e V by exploiting events with hard initial- and final-state QED radiation (ISR/FSR) during the high-luminosity Z-pole run, as well as in dedicated short (about one month long) e^{+}e^{-} e + e − runs at CM energies \sqrt{s} ≈ 40\,\mathrm{GeV} s ≈ 40 G e V and 60\,\mathrm{GeV} 60 G e V . Using realistic estimates and fast detector simulations, we show that data samples of about 10^{9} 10 9 hadronic events can be collected at the FCC-ee at each of the low-CM-energy points. Such datasets can be exploited in a variety of precision QCD measurements, including studies of light-, heavy-quark and gluon jet properties, hadronic event shapes, fragmentation functions, and nonperturbative dynamics. This will offer valuable insights into strong interaction physics, complementing data from nominal FCC-ee runs at higher center-of-mass energies, \sqrt{s} ≈ 91, 160, 240, s ≈ 91 , 160 , 240 , and 365\,\mathrm{GeV} 365 G e V .

Measurements at LHC show an increased production of strange hadrons with charged multiplicity in pp collisions, which is not described by the Lund String Model (with the Monash tune) implemented in PYTHIA. This work investigates string closepacking, a mechanism invoked during hadronization where overlapping strings create a background field that increases the effective string tension. This reduces strangeness suppression, effectively enhancing production. The model also incorporates an option for "popcorn destructive interference", which suppresses baryon production, to address the non-strange p/π ratio, utilizing color algebra arguments; and an option for "strange junctions", which enhances strangeness specifically within the baryon sector. The Trieste tunes of this model to LHC data are presented. The closepacking model is in qualitative agreement with many of the salient particle ratios, although the Ξ_c/D ratio and the shape of p_⊥ spectra remain challenging to account for. Overall, the closepacking model with the Trieste tunes provides a competitive description of enhanced strangeness production in pp collisions, improving upon existing PYTHIA models while avoiding excessive proton yields.

We present a method for sampling singular functions defined on (nested) multiparticle phase spaces, based on a generalisation of parton-shower phase-space generation techniques. At the heart of the method are three key ingredients: (1) the Sudakov sampling by which shower-style calculations sweep across phase space in an ordered manner, from hard to soft; (2) the sequential nesting of multiparticle phase spaces; and (3) the factorisations obeyed by singular multiparton amplitudes on the edges of these phase spaces. We demonstrate a C++ implementation of the proposed algorithm, dubbed Sunshine (loosely derived from Sudakov Nesting of Hard Integrals), for hadronic Z decays, and use it to test the tree-level accuracy of the Vincia sector shower through 𝒪(α _s^2) .

The theory talks at Moriond QCD and High-Energy Interactions 2025 covered the full range of scales from BSM, top, Higgs, EW, and hard QCD physics, through resummation, factorisation, and PDFs, to hadronic, heavy-ion, nonperturbative, and lattice QCD. A few talks also touched on methodologies. We here summarise main points of most of these contributions.

AbstractThe formation of hadrons is a fundamental process in nature that can be investigated at particle colliders. As several recent findings demonstrate, with $$\textrm{e}^{+}\textrm{e}^{-}$$ e + e - collisions as a “vacuum-like” reference at one extreme, and central nucleus–nucleus as a dense, extended size system characterized by flow and local equilibrium at the opposite extreme, different collision systems offer a lever arm that can be exploited to probe with a range of heavy-flavour hadron species the onset of various hadronization processes. In this review, we present an overview of the theoretical and experimental developments. The focus is on open-heavy-flavour measurements. The comparison with model predictions and connections among the results in electron–positron, proton–proton, proton–nucleus, nucleus–nucleus collisions are discussed. After reviewing the current state, we suggest some prospects and future developments.

In dark-matter annihilation channels to hadronic final states, stable particles — such as positrons, photons, antiprotons, and antineutrinos — are produced via complex sequences of phenomena including QED/QCD radiation, hadronisation, and hadron decays. These processes are normally modelled by Monte Carlo (MC) event generators whose limited accuracy imply intrinsic QCD uncertainties on the predictions for indirect-detection experiments like Fermi-LAT, Pamela, IceCube or Ams–02. In this article, we perform a comprehensive analysis of QCD uncertainties, meaning both perturbative and nonperturbative sources of uncertainty are included — estimated via variations of MC renormalization-scale and fragmentation-function parameters, respectively — in antimatter spectra from dark-matter annihilation, based on parametric variations of the Pythia 8 event generator. After performing several retunings of light-quark fragmentation functions, we define a set of variations that span a conservative estimate of the QCD uncertainties. We estimate the effects on antimatter spectra for various annihilation channels and final-state particle species, and discuss their impact on fitted values for the dark-matter mass and thermally-averaged annihilation cross section. We find dramatic impacts which can go up to 𝒪 (40) GeV for uncertainties on the dark-matter mass and up to 𝒪 (10

We document several recent updates to the MCPLOTS event-generator validation resource. The project is based on the RIVET analysis library and harnesses volunteer computing provided by LHC@home to generate high-statistics MC comparisons to data. Users interact with the resource via a simple website, http://mcplots.cern.ch/ , which provides flexible options for requesting comparison plots and comprehensive statistical analyses on demand, all in a few clicks. The project has been structured to enable community-driven developments, and we discuss the computational back end, the web front end, and how to add new data analyses, generators, and tunes that would be accessible on the website for comparison.

We report on a new formalism for parton showers whose fixed-order expansion can be corrected through next-to-next-to-leading order (NNLO) in QCD. It is the first such formalism we are aware of that has no dependence on any auxiliary scales or external resummations and which is fully differential in all of the relevant phase spaces. Since the shower acts as the phase-space generator, the dominant singularity structures are encoded by construction and the method can generate unweighted events with very high efficiency without any significant initialisation time. We argue that the the method should be capable of achieving (at least) NNLO+NNDL accuracy for the shower evolution variable and use hadronic Z decays as a specific example.

The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 2,717 new measurements from 869 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. Particle properties and search limits are listed in Summary Tables. We give numerous tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. Most of the 120 reviews are updated, including many that are heavily revised. The Review is divided into two volumes. Volume 1 includes the Summary Tables and 97 review articles. Volume 2 consists of the Particle Listings and contains also 23 reviews that address specific aspects of the data presented in the Listings. The complete Review (both volumes) is published online on the website of the Particle Data Group (pdg.lbl.gov) and in a journal. Volume 1 is available in print as the PDG Book. A Particle Physics Booklet with the Summary Tables and essential tables, figures, and equations from selected review articles is available in print, as a web version optimized for use on phones, and as an Android app.

This paper is a write-up of the ideas that were presented, developed and discussed at the fourth International Workshop on QCD Challenges from pp to AA, which took place in February 2023 in Padua, Italy. The goal of the workshop was to focus on some of the open questions in the field of high-energy heavy-ion physics and to stimulate the formulation of concrete suggestions for making progresses on both the experimental and theoretical sides. The paper gives a brief introduction to each topic and then summarizes the primary results.

We consider leading-colour 2-, 3- and 4-jet rates in hadronic Z-boson decay to derive matching conditions at next-to-next-to-leading order in the sectorised VINCIA parton shower. In particular, we present a full subtraction-based calculation of the matching coefficient required to obtain the NLO 3-jet rate. This is achieved through a judicious choice of the counter-terms, which optimises the numerical evaluation of the subtracted double-real matrix element. We additionally give a consistent prescription for incorporating interference effects due to multiple Born states. Finally, we briefly comment on higher-order uncertainty estimates.

Recent measurements at the LHC have revealed heavy-flavour baryon fractions much larger than those observed at LEP, with e.g., LambdaC+/D0 and LambdaB0/B0 reaching ~ 0.5 at low pT. One scenario that has been at least partly successful in predicting observed trends is QCD colour reconnections with string junctions. In previous work, however, the limit of a low-pT heavy quark was not well defined. We reconsider the string equations of motion for junction systems in this limit, and find that the junction effectively becomes bound to the heavy quark, a scenario we refer to as a "pearl on a string". We extend string-junction fragmentation in Pythia with a dedicated modelling of this limit for both light- and heavy-quark "pearls".

In this talk, we discuss the physics modeling of antiproton spectra arising from dark matter (DM) annihilation or decay in a model-independent manner. The modeling of antiproton spectra contains some intrinsic uncertainties related to QCD parton showers and hadronisation of baryons. We briefly assess the sources of these uncertainties and their impact on antiproton energy spectra for a few selected DM scenarios. The results are provided in tabulated form for future analyses.

EW Higgs plus multi-jet event samples at parton level in HDF5 event format \(\sqrt{s}=14\,{\rm TeV}\) \(m_H=125\,{\rm GeV}\) \(\mu_R=\mu_F=\frac{1}{2}\Big(m_{\perp,H}+\sum_{jets}p_{\perp,j}\Big)\) Generated with Sherpa using the attached setup files

Reducing resource usage will improve the environmental impact of high-performance computing — but doing so can clash with the science goals of funders. Computational physicist Peter Skands explains how he approached the conflict.

We outline a new technique for the fully-differential matching of final-state parton showers to NNLO calculations, focussing here on the simplest case of leptonic collisions with two final-state jets. The strategy is facilitated by working in the antenna formalism, making use of NNLO antenna subtraction on the fixed-order side and the sector-antenna framework on the shower side. As long as the combined real-virtual and double-real corrections do not overcompensate the real-emission term in the three-jet region, negative weights can be eliminated from the matching scheme. We describe the implementation of all necessary components in the VINCIA antenna shower in PYTHIA 8.3.

This manual describes the PYTHIA 8.3 event generator, the most recent version of an evolving physics tool used to answer fundamental questions in particle physics. The program is most often used to generate high-energy-physics collision"events", i.e. sets of particles produced in association with the collision of two incoming high-energy particles, but has several uses beyond that. The guiding philosophy is to produce and reproduce properties of experimentally obtained collisions as accurately as possible. The program includes a wide ranges of reactions within and beyond the Standard Model, and extending to heavy ion physics. Emphasis is put on phenomena where strong interactions play a major role. The manual contains both pedagogical and practical components. All included physics models are described in enough detail to allow the user to obtain a cursory overview of used assumptions and approximations, enabling an informed evaluation of the program output. A number of the most central algorithms are described in enough detail that the main results of the program can be reproduced independently, allowing further development of existing models or the addition of new ones. Finally, a chapter dedicated fully to the user is included towards the end, providing pedagogical examples of standard use cases, and a detailed description of a number of external interfaces. The program code, the online manual, and the latest version of this print manual can be found on the PYTHIA web page: https://www.pythia.org/

Beauty and charm quarks are ideal probes of pertubative Quantum Chromodymanics in proton-proton collisions, owing to their large masses. In this paper the role of multi-parton interactions in the production of doubly-heavy hadrons is studied using simulation samples generated with Pythia, a Monte Carlo event generator. Comparisons are made to the stand-alone generators BcVegPy and GenXicc. New methods of speeding up Pythia simulations for events containing heavy quarks are described, enabling the production of large samples with multiple heavy-quark pairs. We show that significantly higher production rates of doubly-heavy hadrons are predicted in models that allow heavy quarks originating from different parton-parton interactions (within the same hadron-hadron collision) to combine to form such hadrons. Quantitative predictions are sensitive to the modelling of colour reconnections. We suggest a set of experimental measurements capable of differentiating these additional contributions.