We present a detailed technical derivation of matching conditions at next-to-next-to-leading order in the sectorised VINCIA parton shower, by considering leading-colour 2-, 3- and 4-jet rates in hadronic Z-boson decays. In particular, we introduce 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 higher-order mixing between Born states with different flavour contents. Finally, we briefly comment on higher-order uncertainty estimates.

Australia

Basem El-Menoufi

Germany

Christian Preuss

Ludovic Scyboz

Peter Skands

Matching Z

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.

Javira Altmann

France

Carlota Andres

Anton Andronic

Italy

Federico Antinori

Pietro Antonioli

Andrea Beraudo

Eugenio Berti

Livio Bianchi

United States

Thomas Boettcher

Lorenzo Capriotti

Sweden

Peter Christiansen

Czechia

Jesus Contreras Nuño

Leticia Cunqueiro Mendez

Cesar Silva

Andrea Dainese

Hans Dembinski

Brazil

Austria

David Dobrigkeit Chinellato

Andrea Dubla

Mattia Faggin

Chris Flett

Vincenzo Greco

Ilia Grishmanovskii

Jack Holguin

Finland

Yuuka Kanakubo

Dong Kim

Ramona Lea

South Korea

Su Lee

CERN

Saverio Mariani

Poland

Adam Matyja

Aleksas Mazeliauskas

Vincenzo Minissale

Andreas Morsch

Lucia Oliva

Luca Orusa

Petja Paakkinen

Spain

Daniel Pablos

Mexico

Guy Paić

Tanguy Pierog

Salvatore Plumari

Francesco Prino

Andrea Rossi

Lorenzo Sestini

Olga Soloveva

Francesca Soramel

Alba Soto Ontoso

Martin Spousta

Andre Stahl Leiton

Jiayin Sun

Norway

Adam Takacs

Stefano Trogolo

Rosario Turrisi

Netherlands

Marta Verweij

Vytautas Vislavicius

Jing Wang

Klaus Werner

Valentina Zaccolo

China

Mingyu Zhang

Jianhui Zhu

Davide Zuliani

QCD challenges from pp to AA collisions: 4th edition

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   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (40) GeV for uncertainties on the dark-matter mass and up to   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (10%) for the annihilation cross section. We provide the spectra in tabulated form including QCD uncertainties and code snippets to perform fast dark-matter fits, in this github repository.

Adil Jueid

Jochem Kip

Roberto Ruiz de Austri

United Kingdom

The Strong Force meets the Dark Sector: a robust estimate of QCD uncertainties for anti-matter dark matter searches

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.

John M. Campbell

Stefan Höche

Hai Tao Li

Christian T. Preuss

Towards NNLO+PS matching with sector showers

We present algorithms that interleave photon radiation from the final state and the initial state with the QCD evolution in the antenna-based Vincia parton shower. One of the algorithms incorporates the complete soft and collinear structure associated with photon emission, but may be computationally expensive, while the other approximates the soft structure at a lower cost. Radiation from fermions and W bosons is included, and a strategy for photon radiation off leptons below the hadronization scale is set up. We show results of the application of the shower algorithms to Drell-Yan and <math><msup><mrow><mi>W</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>W</mi></mrow><mrow><mo>−</mo></mrow></msup></math> production at the LHC, showing the impact of the inclusion of the full soft structure and treatment of radiation off W bosons.

Rob Verheyen

Multipole photon radiation in the Vincia parton shower

Motivated by recent theoretical arguments that expanding strings can be regarded as having a temperature that is inversely proportional to the proper time,  $$\tau $$  <math> <mi>τ</mi> </math>  , we investigate the consequences of adding a term  $$\propto 1/\tau $$  <math> <mrow> <mo>∝</mo> <mn>1</mn> <mo>/</mo> <mi>τ</mi> </mrow> </math>   to the string tension in the Lund string-hadronization model. The lattice value for the tension,  $$\kappa _0 \sim 0.18\,{\mathrm {GeV}}^2\sim 0.9\,{\mathrm {GeV}}/{\mathrm {fm}}$$  <math> <mrow> <msub> <mi>κ</mi> <mn>0</mn> </msub> <mo>∼</mo> <mn>0.18</mn> <mspace width="0.166667em"></mspace> <msup> <mrow> <mi>GeV</mi> </mrow> <mn>2</mn> </msup> <mo>∼</mo> <mn>0.9</mn> <mspace width="0.166667em"></mspace> <mi>GeV</mi> <mo>/</mo> <mi>fm</mi> </mrow> </math>  , is then interpreted as the late-time/equilibrium limit. A generic prediction of this type of model is that early string breaks should be associated with higher strangeness (and baryon) fractions and higher fragmentation  $$\langle p_\perp \rangle $$  <math> <mrow> <mo>⟨</mo> <msub> <mi>p</mi> <mo>⊥</mo> </msub> <mo>⟩</mo> </mrow> </math>   values. It should be possible to use archival ee data sets to provide model-independent constraints on this type of scenario, and we propose a few simple key measurements to do so.

Nicholas Hunt-Smith

String fragmentation with a time-dependent tension

In conventional parton showers (including ones based on dipoles/antennae), a given (Born + m)-parton configuration can typically be reached via O(m!) different “shower histories”. In the context of matrix-element-correction and merging procedures, accounting for these histories mandates fairly complex and resource-intensive algorithms. A so far little-explored alternative in the shower context is to divide the branching phase spaces into distinct “sectors”, each of which only receives contributions from a single branching kernel. This has a number of consequences including making the shower operator bijective; i.e., each parton configuration now has a single unique “inverse”. As a first step towards developing a full-fledged matrix-element-correction and merging procedure based on such showers, we here extend the sector approach for antenna showers to hadron-hadron collisions, including mass and helicity dependence.

Helen Brooks

Sector showers for hadron collisions

We present a new approach to coherent parton showers in the decays of colored resonances, based on the notion of “resonance-final” (RF) QCD antennae. A full set of mass- and helicity-dependent <math><mn>2</mn><mo>→</mo><mn>3</mn></math> antenna functions are defined, with the additional requirement of positivity over the respective branching phase spaces. Their singularity structure is identical to that of initial-final (IF) antennae in <math><mn>2</mn><mo>→</mo><mi>N</mi></math> hard processes (once mass terms associated with the incoming legs are allowed for), but the phase-space factorizations are different. The consequent radiation patterns respect QCD coherence (at leading color) and reduce to Dokshitzer-Gribov-Lipatov-Altarelli-Parisi and eikonal kernels in the respective collinear and soft limits. The main novelty in the phase-space factorization is that branchings in RF antennae impart a collective recoil to the other partons within the same decay system. An explicit implementation of these ideas, based on the Sudakov veto algorithm, is provided in the vincia antenna-shower plug-in to the pythia 8 Monte Carlo event generator. We apply our formalism, matched to next-to-leading order accuracy using powheg, to top quark production at the LHC, and investigate implications for direct measurement of the top quark mass. Finally, we make recommendations for assessing theoretical uncertainties arising from parton showers in this context.

Coherent showers in decays of colored resonances

In the context of design studies for future pp colliders, we present a set of predictions for average soft-QCD event properties for pp collisions at $$E_\text {CM} = 14$$ <math><mrow><msub><mi>E</mi><mtext>CM</mtext></msub><mo>=</mo><mn>14</mn></mrow></math> , 27, and 100 TeV. The current default Monash 2013 tune of the Pythia 8.2 event generator is used as the baseline for the extrapolations, with uncertainties evaluated via variations of cross-section parametrisations, PDFs, MPI energy-scaling parameters, and colour-reconnection modelling, subject to current LHC constraints. The observables included in the study are total and inelastic cross sections, inelastic average energy and track densities per unit pseudorapidity (inside $$|\eta |\le 6$$ <math><mrow><mo>|</mo><mi>η</mi><mo>|</mo><mo>≤</mo><mn>6</mn></mrow></math> ), average track $$p_\perp $$ <math><msub><mi>p</mi><mo>⊥</mo></msub></math> , and jet cross sections for 50- and 100-GeV anti-$$k_T$$ <math><msub><mi>k</mi><mi>T</mi></msub></math>  jets with $$\Delta R=0.4$$ <math><mrow><mi>Δ</mi><mi>R</mi><mo>=</mo><mn>0.4</mn></mrow></math> , using aMC@Nlo in conjunction with Pythia 8 for the latter.

Average event properties from LHC to FCC-hh

We present a complete set of helicity-dependent $$2\rightarrow 3$$ <math><mrow><mn>2</mn><mo>→</mo><mn>3</mn></mrow></math>  antenna functions for QCD initial- and final-state radiation. The functions are implemented in the Vincia shower Monte Carlo framework and are used to generate showers for hadron-collider processes in which helicities are explicitly sampled (and conserved) at each step of the evolution. Although not capturing the full effects of spin correlations, the explicit helicity sampling does permit a significantly faster evaluation of fixed-order matrix-element corrections. A further speed increase is achieved via the implementation of a new fast library of analytical MHV amplitudes, while matrix elements from Madgraph are used for non-MHV configurations. A few examples of applications to QCD $$2\rightarrow 2$$ <math><mrow><mn>2</mn><mo>→</mo><mn>2</mn></mrow></math>  processes are given, comparing the newly released Vincia 2.200 to Pythia 8.226.

Nadine Fischer

Switzerland

Andrew Lifson

Helicity antenna showers for hadron colliders