Providing accurate theoretical predictions in the Standard Model for processes with polarised electroweak bosons is crucial to understand more in-depth the electroweak-symmetry breaking mechanism and to enhance the sensitivity to potential new-physics effects. Motivated by the rapidly increasing number of polarisation analyses of di-boson processes with LHC data, we carry out a comprehensive study of the inclusive production of two polarised Z bosons in the decay channel with four charged leptons. We perform a detailed comparison of fixed-order predictions obtained with various Monte Carlo programs which rely on different signal-definition strategies, assessing non-resonant and interference effects by contrasting polarised results with unpolarised and full off-shell ones. For the first time, we accomplish the combination of NNLO QCD and NLO EW corrections, setting the new state-of-the-art perturbative accuracy for polarised Z-boson pairs at the LHC. The impact of parton-shower matching and multi-jet merging is investigated by scrutinising calculations obtained with event generators that are typically used in experimental analyses. Integrated and differential results are discussed in a realistic fiducial setup and compared to publicly available ATLAS results.

Italy

Costanza Carrivale

Roberto Covarelli

Germany

Ansgar Denner

China

Dongshuo Du

Christoph Haitz

Mareen Hoppe

United States

Martina Javurkova

Vietnam

Duc Le

Jakob Linder

Rafael Sa

Belgium

Olivier Mattelaer

Susmita Mondal

Giacomo Ortona

Giovanni Pelliccioli

Poland

Rene Poncelet

United Kingdom

Karolos Potamianos

Richard Ruiz

Marek Schönherr

Frank Siegert

Lailin Xu

Xingyu Wu

Giulia Zanderighi

Precise standard-model predictions for polarised Z-boson pair production and decay at the LHC

<p>Motivated by the ion-collision program at the Large Hadron Collider, plans for its high-luminosity upgrade, and ongoing discussions for multi-TeV future hadron colliders, we systematically investigate hard-scattering, Standard Model processes in many-TeV ion-ion collisions. We focus on the symmetric beam configurations <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><mmultiscripts><mrow><mi>Pb</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>208</mn></mrow></mmultiscripts></mrow><mtext>−</mtext><mrow><mmultiscripts><mrow><mi>Pb</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>208</mn></mrow></mmultiscripts></mrow></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><mmultiscripts><mrow><mi>Xe</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>131</mn></mrow></mmultiscripts></mrow><mtext>−</mtext><mrow><mmultiscripts><mrow><mi>Xe</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>131</mn></mrow></mmultiscripts></mrow></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><mmultiscripts><mrow><mi mathvariant="normal">C</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>12</mn></mrow></mmultiscripts></mrow><mtext>−</mtext><mrow><mmultiscripts><mrow><mi mathvariant="normal">C</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>12</mn></mrow></mmultiscripts></mrow></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math>, and we catalog total and fiducial cross sections for dozens of processes, ranging from associated-Higgs and multiboson production to associated-top pair production, at next-to-leading order in QCD for nucleon-nucleon collision energies from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>1</mn></math> to 100 TeV. We report the residual scale uncertainties at this order as well as the uncertainties originating from fits of nuclear parton densities. We also discuss the propagation of nuclear dynamics (as encoded in nuclear parton densities) into parton luminosities and ultimately into predictions for cross sections. Finally, we report on the emergence of trends and the reliability of extrapolating cross sections across different nuclei. For Pb-Pb collisions at a hypothetical Future Circular Collider with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>N</mi><mi>N</mi></mrow></msub></mrow></msqrt><mo>=</mo><mn>39</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mn>10</mn><mn>8</mn></msup><mo stretchy="false">)</mo></math> weak bosons, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mn>10</mn><mn>5</mn></msup><mo stretchy="false">)</mo></math> diboson pairs, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mn>10</mn><mn>4</mn></msup><mo stretchy="false">)</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>W</mi><mi>H</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><mi>H</mi></math> pairs, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mn>10</mn><mn>3</mn></msup><mo stretchy="false">)</mo></math> triboson events, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mn>10</mn><mn>5</mn></msup><mo stretchy="false">)</mo></math> high-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>p</mi><mi>T</mi></msub></math> photons events, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mn>10</mn><mn>7</mn></msup><mo stretchy="false">)</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi><mover accent="true"><mi>t</mi><mo stretchy="false">¯</mo></mover></math> pairs can be produced with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">L</mi><mo>=</mo><mn>33</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>nb</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math> of data. At <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>N</mi><mi>N</mi></mrow></msub></mrow></msqrt><mo>=</mo><mn>5.52</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></mrow></math>, one can expect <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mn>10</mn><mi>–</mi><msup><mrow><mn>10</mn></mrow><mrow><mn>6</mn></mrow></msup><mo stretchy="false">)</mo></mrow></math> single, multiboson, and top events per <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mtext> </mtext><mtext> </mtext><msup><mi>nb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. Decay rates and experimental selection/acceptance rates will impact final event yields and merit further study; as an illustrative example, we focus on select diboson and triboson channels in lead-lead collisions and discuss their observability at the high-luminosity phase of the Large Hadron Collider and the Future Circulate Collider.</p>

France

Benjamin Fuks

Greece

Fotios Marougkas

Alicja Sztandera

Hard processes in multi-TeV ion collisions

Pair production of helicity-polarized weak bosons <math><mo>(</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>=</mo><msubsup><mrow><mi>W</mi></mrow><mrow><mi>λ</mi></mrow><mrow><mo>±</mo></mrow></msubsup><mo>,</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>)</mo></math> from gluon fusion <math><mo>(</mo><mi>g</mi><mi>g</mi><mo>→</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>λ</mi></mrow></msub><msubsup><mrow><mi>V</mi></mrow><mrow><msup><mrow><mi>λ</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow><mrow><mo>′</mo></mrow></msubsup><mo>)</mo></math> and weak boson fusion <math><mo>(</mo><msub><mrow><mi>V</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>V</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>→</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>λ</mi></mrow></msub><msubsup><mrow><mi>V</mi></mrow><mrow><msup><mrow><mi>λ</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow><mrow><mo>′</mo></mrow></msubsup><mo>)</mo></math> are powerful probes of the Standard Model, new physics, and properties of quantum systems. Measuring cross sections of polarized processes is a chief objective of the Large Hadron Collider's (LHC) Run 3 and high luminosity programs, but progress is limited by the simulation tools that are presently available. We propose a method for computing polarized cross sections that works by directly modifying Feynman rules instead of (squared) amplitudes. The method is applicable to loop-induced processes, and can capture the interference between arbitrary polarization configurations, interference with non-resonant diagrams, as well as off-shell/finite-width effects. By construction, previous results that work at the (squared) amplitude level are recoverable. As a demonstration, we report the prospect of observing and studying polarized <math><msub><mrow><mi>Z</mi></mrow><mrow><mi>λ</mi></mrow></msub><msub><mrow><mi>Z</mi></mrow><mrow><msup><mrow><mi>λ</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></msub></math> pairs when produced via gluon fusion and electroweak processes in final-states with four charged leptons at the LHC, using the new method to simulate the gluon fusion process. Our Feynman rules are publicly available as a set of Universal FeynRules Object libraries called SM_Loop_VPolar.

Slovakia

Rafael Coelho Lopes de Sá

Jay Sandesara

Polarized pairs in gluon fusion and vector boson fusion at the LHC

CERN

Carlotta Accettura

Dean Adams

Rohit Agarwal

Claudia Ahdida

Chiara Aimè

Nicola Amapane

David Amorim

Paolo Andreetto

Fabio Anulli

Robert Appleby

Artur Apresyan

Aram Apyan

Sergey Arsenyev

Pouya Asadi

Egypt

Mohammed Mahmoud

Aleksandr Azatov

John Back

Lorenzo Balconi

Laura Bandiera

Roger Barlow

Nazar Bartosik

Emanuela Barzi

Fabian Batsch

Matteo Bauce

J. Berg

Andrea Bersani

Alessandro Bertarelli

Alessandro Bertolin

Kevin Black

Fulvio Boattini

Alex Bogacz

Maurizio Bonesini

Bernardo Bordini

Salvatore Bottaro

Luca Bottura

Alessandro Braghieri

Marco Breschi

Natalie Bruhwiler

Xavier Buffat

Laura Buonincontri

Philip Burrows

Graeme Burt

Dario Buttazzo

Barbara Caiffi

Marco Calviani

Simone Calzaferri

Daniele Calzolari

Rodolfo Capdevilla

Christian Carli

Fausto Casaburo

Massimo Casarsa

Luca Castelli

Maria Catanesi

Lorenzo Cavallucci

Gianluca Cavoto

Spain

Francesco Celiberto

Luigi Celona

Alessandro Cerri

Gianmario Cesarini

Cari Cesarotti

Portugal

Grigorios Chachamis

Antoine Chance

Switzerland

Siyu Chen

Yang-Ting Chien

Mauro Chiesa

Anna Colaleo

Francesco Collamati

Gianmaria Collazuol

Marco Costa

Nathaniel Craig

Camilla Curatolo

Canada

David Curtin

Giacomo Molin

Magnus Dam

Heiko Damerau

Sridhara Dasu

Jorge Blas

Stefania Curtis

Ernesto Matteis

Stefania Rosa

Jean-Pierre Delahaye

Dmitri Denisov

Türkiye

Haluk Denizli

Christopher Densham

Radovan Dermisek

Luca Luzio

Elisa Meco

Biagio Micco

Keith Dienes

Eleonora Diociaiuti

Tommaso Dorigo

Alexey Dudarev

Robert Edgecock

Filippo Errico

Marco Fabbrichesi

Stefania Farinon

Anna Ferrari

Jose Somoza

Netherlands

Frank Filthaut

Davide Fiorina

Erratum: Towards a muon collider

A muon collider would enable the big jump ahead in energy reach that is needed for a fruitful exploration of fundamental interactions. The challenges of producing muon collisions at high luminosity and 10 TeV centre of mass energy are being investigated by the recently-formed International Muon Collider Collaboration. This Review summarises the status and the recent advances on muon colliders design, physics and detector studies. The aim is to provide a global perspective of the field and to outline directions for future work.

Towards a muon collider

The type II seesaw model remains a popular and viable explanation of neutrino masses and mixing angles. By hypothesizing the existence of a scalar that is a triplet under the weak gauge interaction, the model predicts strong correlations among neutrino oscillation parameters, signals at lepton flavor experiments, and collider observables at high energies. We investigate reports that the type II seesaw can naturally accommodate recent measurements by the CDF collaboration, which finds the mass of the <math><mi>W</mi></math> boson to be significantly larger than allowed by electroweak precision data, while simultaneously evading constraints from direct searches. Experimental scrutiny of this parameter space in the type II seesaw has long been evaded since it is not characterized by “golden channels” at colliders but instead by cascade decays, moderate mass splittings, and many soft final states. In this work, we test this parameter space against publicly released measurements made at the Large Hadron Collider. By employing a newly developed tool chain combining madgraph5_amc@nlo and contur, we find that most of the favored space for this discrepancy is already excluded by measurements of Standard Model final states. We give suggestions for further exploration at run III of the LHC, which is now under way.

Jon Butterworth

Julian Heeck

South Korea

Si Hyun Jeon

Testing the scalar triplet solution to CDF’s heavy <math><mi>W</mi></math> problem at the LHC

Motivated by searches for so-called leptonic scalars at the LHC and the recent measurement of the W boson’s mass at the Tevatron, we revisit the phenomenology of the Zee-Babu model for neutrino masses and the ability to differentiate it from the Type II Seesaw model at the LHC. We conclude that this task is much more difficult than previously believed. All inputs equal in the two scenarios, we find that total and differential rates for producing pairs of doubly and singly charged scalars are identical in shape and only differ in normalization. The normalization is given by the ratio of hadronic cross sections and can be unity. Differences in cross sections are small and can be hidden by unknown branching rates. This holds for Drell-Yan, γγ fusion, and gg fusion, as well as observables at LO and NLO in QCD. This likeness allows us to reinterpret Run II limits on the Type II Seesaw and estimate projections for the HL-LHC. Using updated neutrino oscillation data, we also find that some collider observables, e.g., lepton flavor-violating branching ratios, are now sufficiently precise to provide a path forward. Other means of discrimination are also discussed. As a byproduct of this work, we report the availability of new Universal FeynRules Object libraries, the SM_ZeeBabu UFO, that enable fully differential simulations up to NLO+LL(PS) with tool chains employing MadGraph5_aMC@NLO.

Doubly charged Higgs boson production at hadron colliders II: a Zee-Babu case study

Due to the inclination for forward gauge radiation, lepton colliders beyond a few TeV are effectively electroweak (EW) boson colliders, suggesting the treatment of EW bosons as constituents of high-energy leptons. In the context of a muon collider, we revisit the validity of W and Z parton distribution functions (PDFs) at leading order in 2 → n process. We systematically investigate universal and quasi-universal power-law and logarithmic corrections that arise when deriving (polarized) weak boson PDFs in the collinear limit. We go on to survey a multitude of 2 → n processes at   <math> <msqrt> <mi>s</mi> </msqrt> </math>  $$ \sqrt{s} $$  = 2–30 TeV via polarized and unpolarized EW boson fusion/scattering. To conduct this study, we report a public implementation of the Effective W/Z and Weizsäcker-Williams Approximations, which we collectively call the Effective Vector Boson Approximation, into the Monte Carlo event generator MadGraph5_aMC@NLO. This implementation lays the groundwork for developing matrix-element matching prescriptions involving EW parton showers and renormalized EW PDFs. To further with this agenda, we give recommendations on using W/Z PDFs.

Antonio Costantini

Fabio Maltoni

The Effective Vector Boson Approximation in high-energy muon collisions

We investigate contributions to the anomalous magnetic moments of charged leptons in the neutrino-extended Standard Model Effective Field Theory (νSMEFT). We discuss how νSMEFT operators can contribute to a lepton’s magnetic moment at one- and two-loop order. We show that only one operator can account for existing electronic and muonic discrepancies, assuming new physics appears above 1 TeV. In particular, we find that a right-handed charged current in combination with minimal sterile-active mixing can explain the discrepancy for sterile neutrino masses of   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (100) GeV while avoiding direct and indirect constraints. We discuss how searches for sterile neutrino production at the (HL-)LHC, measurements of h → μ + μ  −  and searches for h → e + e  − , neutrinoless double beta decay experiments, and improved unitarity tests of the CKM matrix can further probe the relevant parameter space.

Vincenzo Cirigliano

Wouter Dekens

Jordy Vries

Kaori Fuyuto

Emanuele Mereghetti

Leptonic anomalous magnetic moments in ν SMEFT

Motivated by searches for <math><mn>0</mn><mi>ν</mi><mi>β</mi><mi>β</mi></math> decay in nuclear experiments and collider probes of lepton number violation at dimension <math><mi>d</mi><mo>≥</mo><mn>7</mn></math>, we investigate the sensitivity to the <math><mi>d</mi><mo>=</mo><mn>5</mn></math> Weinberg operator using the nonresonant signature <math><mi>p</mi><mi>p</mi><mo>→</mo><msup><mo>ℓ</mo><mo>±</mo></msup><msup><msup><mo>ℓ</mo><mo>′</mo></msup><mo>±</mo></msup><mi>j</mi><mi>j</mi></math> at the LHC. We develop a prescription for the operator that is applicable in collisions and decays, and focus on the <math><mo>ℓ</mo><msup><mo>ℓ</mo><mo>′</mo></msup><mo>=</mo><mi>μ</mi><mi>μ</mi></math> channel, which is beyond the reach of nuclear decays. For a Wilson coefficient <math><msubsup><mi>C</mi><mn>5</mn><mrow><mi>μ</mi><mi>μ</mi></mrow></msubsup><mo>=</mo><mn>1</mn></math>, scales as heavy as <math><mi>Λ</mi><mo>∼</mo><mn>8.3</mn><mo>(</mo><mn>11</mn><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math> can be probed with <math><mrow><mi>L</mi><mo>=</mo><mn>300</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>fb</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>(</mo><mn>3</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>ab</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></math>. This translates to an effective <math><mi>μ</mi><mi>μ</mi></math> Majorana mass of <math><mo>|</mo><msub><mi>m</mi><mrow><mi>μ</mi><mi>μ</mi></mrow></msub><mo>|</mo><mo>∼</mo><mn>7.3</mn><mo>(</mo><mn>5.4</mn><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> and establishes a road map for testing the Weinberg operator at accelerators.

Jonas Neundorf

Krisztian Peters

Matthias Saimpert

Probing the Weinberg operator at colliders