The ITk is a new silicon tracker for the ATLAS experiment designed to increase detector resolution, readout capacity, and radiation hardness, in preparation for the larger number of simultaneous proton–proton interactions at the High Luminosity LHC. This paper presents the first direct measurement of the material budget of an ATLAS ITk pixel module, performed at a testbeam at the CERN Proton Synchrotron via the multiple scattering of low energy positrons within the module volume. Using a four plane telescope of thin monolithic pixel detectors from the MALTA Collaboration, scattering datasets were recorded at a beam energy of $$1.2\,\text {GeV}$$ . Kink angle distributions were extracted from tracks derived with and without information from the ITk pixel module, and were fit to extract the RMS scattering angle, which was converted to a fractional radiation length $$x/X_0$$ . The average $$x/X_0$$ across the module was measured as $$[0.89 \pm 0.01 \text { (resolution)} \pm 0.01 \text { (subtraction)} \,\,\pm \,\, 0.08 \text {~(beam momentum band)}]\%$$ , which agrees within uncertainties with an estimate of $$0.88\%$$ derived from material component expectations.

United Kingdom

Simon Koch

Switzerland

Brian Moser

Antonín Lindner

United States

Valerio Dao

Ignacio Asensi

Daniela Bortoletto

Marianne Brekkum

Florian Dachs

Germany

Hans Joos

Norway

Milou Rijnbach

Abhishek Sharma

Ismet Siral

Carlos Solans

Yingjie Wei

Measuring the ATLAS ITk pixel detector material via multiple scattering of positrons at the CERN PS

We here report on the progress of the HHH Workshop, that took place in Dubrovnik in July 2023. After the discovery of a particle that complies with the properties of the Higgs boson of the Standard Model, all Standard Model (SM) parameters are in principle determined. However, in order to verify or falsify the model, the full form of the potential has to be determined. This includes the measurement of the triple and quartic scalar couplings.

Morocco

Hamza Abouabid

Abdesslam Arhrib

Hannah Arnold

Duarte Azevedo

Croatia

Vuko Brigljevic

Maggie Chen

Daniel Diaz

Javier Duarte

Netherlands

Tristan Pree

Jaouad Falaki

Dinko Ferencek

Portugal

Pedro. Ferreira

France

Benjamin Fuks

India

Japan

Sanmay Ganguly

Osama Karkout

Marina Kolosova

Jacobo Konigsberg

Greg Landsberg

Canada

China

Bingxuan Liu

CERN

Margarete Mühlleitner

Andreas Papaefstathiou

Sweden

Roman Pasechnik

Tania Robens

Rui Santos

Brian Sheldon

Gregory Soyez

Marko Stamenkovic

Panagiotis Stylianou

Tatjana Susa

Gilberto Tetlalmatzi-Xolocotzi

Georg Weiglein

Giulia Zanderighi

Rui Zhang

HHH whitepaper

We study the integrability and the Bethe/Gauge correspondence of the Generalized Calogero-Moser system proposed by Berntson, Langmann and Lenells [1] which we call the elliptic quadruple Calogero-Moser system (eqCM). We write down the Dunkl operators which give commuting Hamiltonians of the quantum integrable system. We identify the gauge theory in correspondence is a supergroup version of the gauge origami, from which we construct the transfer matrix of the eqCM system.

Taro Kimura

South Korea

Norton Lee

Generalized Calogero-Moser system and supergroup gauge origami

Poland

Wojciech Bizoń

Ulrich Haisch

Italy

Luca Rottoli

Zach Gillis

Philipp Windischhofer

Addendum to: Constraints on the quartic Higgs self-coupling from double-Higgs production at future hadron colliders

We analyze the integrability of the <math><mi>N</mi></math>-extended supersymmetric Calogero–Moser model. We explicitly construct the Lax pair <math><mo>{</mo><mi>L</mi><mo>,</mo><mi>A</mi><mo>}</mo></math> for this system, which properly reproduces all equations of motion. After adding a supersymmetric oscillator potential we reduce the latter to solving <math><mover><mrow><mi>U</mi></mrow><mrow><mo>˙</mo></mrow></mover><mo>=</mo><mi>A</mi><mspace width="0.2em"></mspace><mi>U</mi></math> for the time evolution operator <math><mi>U</mi><mo>(</mo><mi>t</mi><mo>)</mo></math>. The bosonic variables, however, evolve independently of U on closed trajectories, as is required for superintegrability. To visualize the structure of the conserved currents we derive the complete set of Liouville charges up to the fifth power in the momenta, for the <math><mi>N</mi><mo>=</mo><mn>2</mn></math> supersymmetric model. The additional, non-involutive, conserved charges needed for a maximal superintegrability of this model are also found.

JINR

Sergey Krivonos

Olaf Lechtenfeld

Anton Sutulin

Integrability of supersymmetric Calogero–Moser models

We systematically study the interesting relations between the quantum elliptic Calogero-Moser system (eCM) and its generalization, and their corresponding supersymmetric gauge theories. In particular, we construct the suitable characteristic polynomial for the eCM system by considering certain orbifolded instanton partition function of the corresponding gauge theory. This is equivalent to the introduction of certain co-dimension two defects. We next generalize our construction to the folded instanton partition function obtained through the so-called “gauge origami” construction and precisely obtain the corresponding characteristic polynomial for the doubled version, named the elliptic double Calogero-Moser (edCM) system.

Taiwan

Heng-Yu Chen

Quantum elliptic Calogero-Moser systems from gauge origami

We explicitly construct a supersymmetric <math><mi>s</mi><mi>o</mi><mo>(</mo><mi>n</mi><mo>)</mo></math> spin-Calogero model with an arbitrary even number <math><mi>N</mi></math> of supersymmetries. It features <math><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mi>N</mi><mi>n</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></math> rather than <math><mi>N</mi><mi>n</mi></math> fermionic coordinates and a very simple structure of the supercharges and the Hamiltonian. The latter, together with additional conserved currents, form an <math><mi>o</mi><mi>s</mi><mi>p</mi><mo>(</mo><mi>N</mi><mo>|</mo><mn>2</mn><mo>)</mo></math> superalgebra. We provide a superspace description for the simplest case, namely <math><mi>N</mi><mo>=</mo><mn>2</mn></math> supersymmetry. The reduction to an <math><mi>N</mi></math>-extended supersymmetric goldfish model is also discussed.

Russia

Supersymmetric many-body Euler–Calogero–Moser model

SU(2|1) supersymmetric multi-particle quantum mechanics with additional semi-dynamical spin degrees of freedom is considered. In particular, we provide an  <math><mi>N</mi><mo>=</mo><mn>4</mn></math> $$ \mathcal{N}=4 $$ supersymmetrization of the quantum U(2) spin Calogero-Moser model, with an intrinsic mass parameter coming from the centrally-extended superalgebra  <math><mover><mrow><mi>s</mi><mi>u</mi></mrow><mo>^</mo></mover><mfenced><mrow><mn>2</mn><mo>|</mo><mn>1</mn></mrow></mfenced></math> $$ \widehat{su}\left(2\Big|1\right) $$. The full system admits an SU(2|1) covariant separation into the center-of-mass sector and the quotient. We derive explicit expressions for the classical and quantum SU(2|1) generators in both sectors as well as for the total system, and we determine the relevant energy spectra, degeneracies, and the sets of physical states.

Sergey Fedoruk

Evgeny Ivanov

Stepan Sidorov

Quantum SU(2|1) supersymmetric Calogero-Moser spinning systems