Vector Boson Scattering Processes: Status and Prospects Diogo Buarque Franzosi (ed.)g,d, Michele Gallinaro (ed.)h, Richard Ruiz (ed.)i, Thea K. Aarrestadc, Mauro Chiesao, Antonio Costantinik, Ansgar Dennert, Stefan Dittmaierf, Flavia Cetorellil, Robert Frankent, Pietro Govonil, Tao Hanp, Ashutosh V. Kotwala, Jinmian Lir, Kristin Lohwasserq, Kenneth Longc, Yang Map, Luca Mantanik, Matteo Marchegianie, Mathieu Pellenf, Giovanni Pellicciolit, Karolos Potamianosn,Jurgen¨ Reuterb, Timo Schmidtt, Christopher Schwanm, Michał Szlepers, Rob Verheyenj, Keping Xiep, Rao Zhangr aDepartment of Physics, Duke University, Durham, NC 27708, USA bDeutsches Elektronen-Synchrotron (DESY) Theory Group, Notkestr. 85, D-22607 Hamburg, Germany cEuropean Organization for Nuclear Research (CERN) CH-1211 Geneva 23, Switzerland dDepartment of Physics, Chalmers University of Technology, Fysikgården 1, 41296 G¨oteborg, Sweden eSwiss Federal Institute of Technology (ETH) Z¨urich, Otto-Stern-Weg 5, 8093 Z¨urich, Switzerland fUniversit¨atFreiburg, Physikalisches Institut, Hermann-Herder-Straße 3, 79104 Freiburg, Germany gPhysics Department, University of Gothenburg, 41296 G¨oteborg, Sweden hLaborat´oriode Instrumenta¸c˜aoe F´ısicaExperimental de Part´ıculas(LIP), Lisbon, Av. Prof. Gama Pinto, 2 - 1649-003, Lisboa, Portugal iInstitute of Nuclear Physics, Polish Academy of Sciences, ul. Radzikowskiego, Cracow 31-342, Poland jUniversity College London, Gower St, Bloomsbury, London WC1E 6BT, United Kingdom kCentre for Cosmology, Particle Physics and Phenomenology (CP3), Universit´eCatholique de Louvain, Chemin du Cyclotron, B-1348 Louvain la Neuve, Belgium lMilano - Bicocca University and INFN, Piazza della Scienza 3, Milano, Italy mTif Lab, Dipartimento di Fisica, Universit`adi Milano and INFN, Sezione di Milano, Via Celoria 16, 20133 Milano, Italy nDepartment of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK oDipartimento di Fisica, Universit`adi Pavia, Via A. Bassi 6, 27100 Pavia, Italy pPittsburgh Particle Physics, Astrophysics, and Cosmology Center, Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA qDepartment of Physics, Sheffield University, UK rCollege of Physics, Sichuan University, Chengdu 610065, China sNational Center for Nuclear Research, ul. Pasteura 7, 02-093 Warszawa, Poland tUniversit¨atW¨urzburg, Institut f¨urTheoretische Physik und Astrophysik, Emil-Hilb-Weg 22, 97074 W¨urzburg, Germany Abstract Insight into the electroweak (EW) and Higgs sectors can be achieved through measurements of vector boson scattering (VBS) processes. The scattering of EW bosons are rare processes that are precisely predicted in the Standard Model (SM) and are closely related to the Higgs mechanism. Modifications to VBS processes are also predicted in models of physics beyond the SM (BSM), for example through changes to the Higgs boson couplings to gauge bosons and the resonant production of new particles. In this review, experimental results and theoretical developments of VBS at the Large Hadron Collider, its high luminosity upgrade, and future colliders are presented. Keywords: Standard Model, Beyond Standard Model, Vector Boson Scattering, Vector Boson Fusion, Colliders Contents III VBS prospects for the HL-LHC 9 4 Experimental projections for the HL-LHC 9 arXiv:2106.01393v1 [hep-ph] 2 Jun 2021 I Introduction 2 5 SMEFT in VBS at the HL-LHC 14 II VBS at the LHC 2 6 Neutrino BSM with VBS signatures 15 1 Current results on vector boson scattering 2 7 Anomaly detection with machine learning 18 2 Polarization and τ lepton studies in VBS 4 8 Machine learning for VBS 22 3 Precise theoretical predictions for VBS 7 9 Detector and performance upgrades for the HL-LHC 25 Editor email addresses: [email protected], [email protected], IV VBS at future colliders 28 [email protected] Preprint numbers: CP3-21-14, DESY-21-064, IFJPAN-IV-2021-8, PITT-PACC-2106, VBSCAN-PUB-04-21 June 4, 2021 10 EW parton distribution functions 28 Part I 11 EW parton showers 32 Introduction 12 SMEFT with VBS at µ+µ− colliders 35 The importance of the vector boson scattering (VBS) and vector 13 BSM with VBS at µ+µ− colliders 38 boson fusion (VBF) processes in understanding the electroweak (EW) sector is well-established in high energy physics. At scat- 14 VBS at e+e− colliders 40 tering energies far above the EW scale, the longitudinal modes of the weak bosons are manifestations of the Nambu-Goldstone 15 HH production from new resonances 43 bosons originating from the spontaneous breaking of EW sym- metry. Probing their interactions therefore helps unveil the dy- namics behind the Higgs mechanism [1, 2, 3, 4]. Moreover, V Conclusions 45 VBS is relevant to testing the gauge structure of EW interac- tions due to the contribution of quartic interactions and their in- terplay with trilinear couplings, which leads to potentially large gauge cancellations. These are unique features of VBS pro- cesses. It is thus extremely important to achieve precise pre- dictions in the Standard Model (SM) of particle physics as well extensively investigate beyond-the-Standard Model (BSM) sce- narios, both in the context of specific models and effective field theory (EFT) frameworks. The importance of VBS physics has also been well-documented in the literature as reviewed by Refs. [5, 6, 7, 8, 9, 10]. Measurement of VBS processes are at last possible at the Large Hadron Collider (LHC), where the unprecedented ener- gies and integrated luminosities of data sets allowed for the first observations of such rare interactions [11, 12, 13, 14, 15]. The Run 3 of the LHC’s data taking is scheduled to start in 2022. And with the High-Luminosity extension (HL-LHC), the avail- able data will enable the community to move beyond first obser- vations and into the domain of precision measurements, aiming at the ambitious goal of isolating the transverse and longitudi- nal components of VBS. Future colliders can likewise improve this picture in several aspects, including direct exploration of when EW symmetry is approximately restored. In light of the experimental, phenomenological, and theo- retical advancements surrounding VBS, as well as the mandates of the 2020 European Strategy Update [16, 17], it is timely to produce a picture of the current state-of-the art in the field with focus on the instruments and concepts that will be needed for future developments. We start in Part II, where current mea- surements and analysis techniques of VBS are summarized. In Part III, projections for the HL-LHC are reviewed for both the SM and BSM scenarios. In Part IV, the nature of VBS itself and prospects for measurements at future colliders are discussed. Finally, we conclude with an outlook in Part V. Part II VBS at the LHC 1 Current results on VBS from the LHC At the LHC, the ATLAS and CMS collaborations first stud- ied diboson production via VBS in the W±W±, Wγ, and Zγ fi- 2 p nal states at s = 8 TeV in the LHC Run 1 [18, 19, 20, 21, 22, 23, 24] using the leptonic decay modes of weak bosons. These states were further investigated during the first full year of data taking at 13 TeV, when the W±W±, WZ, and ZZ channels were first observed [11, 12, 13, 14, 15], also using the leptonic decay modes. The first study of VBS using semi-leptonic decays was also made with this data set, targeting WZ=WW events where one of the boson decays to a boosted hadronic jet. A summary of these results can be found in Ref. [25] and references therein. With the nearly L = 140 fb−1 of data collected by each of the ATLAS and CMS collaborations during the LHC’s sec- ond run of data-taking (Run 2), the experimental outlook for searches and measurements of VBS processes is very bright. The initial searches have rapidly been extended, with several results reaching high-statistical significance for observation and becoming measurements in their own right. In particular, the WZ and W±W± processes have been observed and measured differentially [11, 15]. The search for the VBS ZZ production with leptonic decays was also updated with L = 35:9 fb−1 by CMS [26], exceeding the 3σ threshold for evidence but not yet reaching a 5σ observation. A 5σ observation of ZZ in the lep- tonic channels was achieved with L = 139 fb−1 by ATLAS [27]. Figure 1.1: The unfolded results for the WZjj process from In addition, the first experimental search for polarized VBS pro- Ref. [30]. The contribution of the EW production and the im- duction was performed in the W±W± channel [28], a measure- pact of NLO EW corrections are shown. ment widely considered a major priority for the HL-LHC. Ad- ditional results with L = 137 fb−1 have very recently been re- leased [29] and others are expected soon. cal predictions. In particular, the impact of the next-to-leading The following summary briefly discusses the current state (NLO) EW corrections, which are known to be large for VBS of the experimental studies of VBS processes. While focus is processes [31, 32, 33], are studied, as shown in Fig. 1.1. placed on results by the CMS collaboration, comparable find- This analysis was recently extended to perform the first study ings have been achieved by ATLAS. Further details can be found of a VBS process separated by the polarization of the vector in the relevant references. bosons [28]. Because the polarization is not a Lorentz-invariant quantity, its definition is reference frame dependent. Therefore, 1.1 Results on scattering of massive vector bosons the analysis independently measures the polarization fractions Due to its distinctive signature and relative lack of back- using the polarization defined in the parton-parton center-of- grounds, the W±W± process is the golden channel of VBS pro- mass frame and in the W boson pair center-of-mass frame.