We present a computation of the one-loop QCD corrections to top-quark pair production in association with a $\textit{W}$ boson, including terms up to order $\textit{ε}$ in dimensional regularization. Providing a first glimpse into the complexity of the corresponding two-loop amplitude, this result is a first step towards a description of this process at next-to-next-to-leading order (NNLO) in QCD. We perform a tensor decomposition and express the corresponding form factors in terms of a basis of independent special functions with compact rational coefficients, providing a structured framework for future developments. In addition, we derive an explicit analytic representation of the form factors, valid up to order $\textit{ε}$ , expressed in terms of logarithms and dilogarithms. For the complete set of special functions required, we obtain a semi-numerical solution based on generalized power series expansion.

Italy

Matteo Becchetti

Switzerland

Germany

Maximilian Delto

Sara Ditsch

Philipp Kreer

Mattia Pozzoli

Lorenzo Tancredi

One-loop QCD corrections to $\textit{ūd}$ → $$ t\overline{t}W $$ at $$ \mathcal{O}\left({\varepsilon}^2\right) $$

Fundamental principles of quantum field theory (QFT) such as Lorentz invariance, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi><mi>T</mi></math> symmetry, and locality may be tested to extremely high precision in atomic and molecular spectroscopy. The narrow natural linewidth of rovibrational states in the hydrogen molecular ion <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">H</mi><mn>2</mn><mrow><mo>+</mo></mrow></msubsup></math> and its antimatter counterpart <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mover accent="true"><mi mathvariant="normal">H</mi><mo stretchy="false">¯</mo></mover><mn>2</mn><mrow><mo>−</mo></mrow></msubsup></math> make these ideal candidates, and give <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo stretchy="false">(</mo><msub><mi>m</mi><mi>p</mi></msub><mo>/</mo><msub><mi>m</mi><mi>e</mi></msub><mo stretchy="false">)</mo></math> increased sensitivity to Lorentz and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi><mi>T</mi></math> violation in the proton sector compared to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">H</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi mathvariant="normal">H</mi><mo stretchy="false">¯</mo></mover></math> atoms. In a previous paper, we presented a detailed analysis of the rovibrational spectrum of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">H</mi><mn>2</mn><mrow><mo>+</mo></mrow></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mover accent="true"><mi mathvariant="normal">H</mi><mo stretchy="false">¯</mo></mover><mn>2</mn><mrow><mo>−</mo></mrow></msubsup></math> in an effective QFT encoding Lorentz and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi><mi>T</mi></math> violation, focusing on spin-independent effects. Here, we extend this analysis to include the full hyperfine-Zeeman spectrum and include spin-dependent Lorentz and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi><mi>T</mi></math> violating operators in the effective theory. The results demonstrate how constraints on these symmetry-violating couplings may be extracted from specific rovibrational transitions between hyperfine-Zeeman states in the presence of an applied magnetic field.

United Kingdom

Graham M. Shore

Lorentz and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi><mi>T</mi></math> violation and the hydrogen and antihydrogen molecular ions. II. Hyperfine-Zeeman spectrum

This report, summarising work achieved in the context of the LHC Dark Matter Working Group, investigates the phenomenology of $\textit{t}$-channel dark matter models, spanning minimal setups with a single dark matter candidate and mediator to more complex constructions closer to UV-complete models. For each considered class of models, we examine collider, cosmological and astrophysical implications. In addition, we explore scenarios with either promptly decaying or long-lived particles, as well as featuring diverse dark matter production mechanisms in the early universe. By providing a unified analysis framework, numerical tools and guidelines, this work aims to support future experimental and theoretical efforts in exploring $\textit{t}$-channel dark matter models at colliders and in cosmology.

Belgium

Chiara Arina

France

Benjamin Fuks

Luca Panizzi

United States

Michael Baker

South Africa

Alan Cornell

Jan Heisig

Benedikt Maier

Portugal

Rute Pedro

Dominique Trischuk

Diyar Agin

Alexandre Arbey

Giorgio Arcadi

Emanuele Bagnaschi

Kehang Bai

Brazil

Disha Bhatia

Mathias Becker

Alexander Belyaev

Ferdinand Benoit

Monika Blanke

Canada

Jackson Burzynski

Jonathan Butterworth

Antimo Cagnotta

China

Lorenzo Calibbi

Linda Carpenter

Spain

Xabier Cid Vidal

Emanuele Copello

Louie Corpe

Francesco D’Amico

Aldo Deandrea

Australia

Aman Desai

Caterina Doglioni

South Korea

Sunil Dogra

Mathias Garny

Mark Goodsell

Norway

Sohaib Hassan

Philip Harris

Julia Harz

Alejandro Ibarra

Alberto Iorio

Felix Kahlhoefer

Deepak Kar

Egypt

Shaaban Khalil

Valery Khoze

Pyungwon Ko

Sabine Kraml

Greg Landsberg

Andre Lessa

Laura Lopez-Honorez

Alberto Mariotti

Vasiliki Mitsou

Kirtimaan Mohan

Chang-Seong Moon

Colombia

Alexander Moreno Briceno

Maria Moreno Llacer

Leandre Munoz-Aillaud

Taylor Murphy

Anele Ncube

Wandile Nzuza

Clarisse Prat

Lena Rathmann

Thobani Sangweni

Dipan Sengupta

William Shepherd

Sukanya Sinha

Tim Tait

Andrea Thamm

Michel Tytgat

Zirui Wang

David Yu

Shin-Shan Yu

$\textit{t}$-channel dark matter models – a whitepaper

An <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math>-jet tagging approach to determine the Cabibbo-Kobayashi-Maskawa matrix component <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>V</mi><mrow><mi>t</mi><mi>s</mi></mrow></msub><mo stretchy="false">|</mo></math> directly in the dileptonic final state events of the top pair production in proton-proton collisions has been previously studied by measuring the branching fraction of the decay of one of the top quarks by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>t</mi><mo stretchy="false">→</mo><mi>s</mi><mi>W</mi></mrow></math>. The main challenge is improving the discrimination performance between strange jets from top decays and other jets. This study proposes novel jet discriminators, called disaja, using a Transformer-based deep learning method. The first model, disaja-h, utilizes multidomain inputs (jets, leptons, and missing transverse momentum). An additional model, disaja-l, further improves the setup by using lower-level jet constituent information, rather than the high-level clustered information. disaja-l is a novel model that combines low-level jet constituent analysis with event classification using multidomain inputs. The model performance is evaluated via a CMS-like LHC Run 2 fast simulation by comparing various statistical test results to those from a Transformer-based jet classifier which considers only the individual jets. This study shows that the disaja models have significant performance gains over the individual jet classifier, and we show the potential of the measurement during Run 3 of the LHC and the High-Luminosity LHC.

Jeewon Heo

Woojin Jang

Jason S.H. Lee

Youn Jung Roh

Ian James Watson

Seungjin Yang

Improving the direct determination of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>V</mi><mrow><mi>t</mi><mi>s</mi></mrow></msub><mo stretchy="false">|</mo></math> using deep learning

We demonstrate that the necessary condition for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>O</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo><mo>×</mo><mi>S</mi><mi>O</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></math> duality invariance manifests as a partial differential equation in two-dimensional scalar theories. This condition, expressed as a partial differential equation, corresponds precisely to the integrability condition. We derive a general perturbation solution to this partial differential equation, which includes both a root <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> flow equation and an irrelevant <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>-like flow equation. Additionally, we identify a general form for these flow equations that commute with each other. Our results establish a general integrable theory characterized by theory-dependent coefficients at each order in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math> expansion. This unified framework systematically classifies all integrable theories possessing two Lorentz-invariant variables (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mn>1</mn></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mn>2</mn></msub></math>) while accommodating arbitrary orders of the coupling constants (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math>). The theory provides a comprehensive classification scheme that encompasses both known and novel integrable systems within this class.

H. Babaei-Aghbolagh

Song He

Hao Ouyang

Generalized <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>-like flows for scalar theories in two dimensions

We examine inflationary models in the <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo stretchy='false'>)</mo></math> gravity framework where we have a conformal constant and an <italic>RT</italic>-mixing term apart from an R term. The RT-mixing term introduces non-minimal coupling between gravity and matter. We consider the exponential SUSY potential <math altimg='si2.svg'><mi>V</mi><mo stretchy='false'>(</mo><mi>&#981;</mi><mo stretchy='false'>)</mo><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><msup><mrow><mi>M</mi></mrow><mrow><mn>4</mn></mrow></msup><mrow><mo stretchy='true'>(</mo><mn>1</mn><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><msup><mrow><mi>e</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mi>&#955;</mi><mi>&#981;</mi><mo stretchy='false'>/</mo><msub><mrow><mi>M</mi></mrow><mrow><mi>p</mi><mi>l</mi></mrow></msub></mrow></msup><mo stretchy='true'>)</mo></mrow></math> and a novel potential <math altimg='si3.svg'><mi>V</mi><mo stretchy='false'>(</mo><mi>&#981;</mi><mo stretchy='false'>)</mo><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mi>&#955;</mi><msubsup><mrow><mi>M</mi></mrow><mrow><mi>p</mi><mi>l</mi></mrow><mrow><mn>4</mn><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mn>2</mn><mi>&#945;</mi></mrow></msubsup><msup><mrow><mi>&#981;</mi></mrow><mrow><mn>2</mn><mi>&#945;</mi></mrow></msup><msup><mrow><mi mathvariant='normal'>sin</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>&#8289;</mo><mrow><mo stretchy='true'>(</mo><mfrac><mrow><mi>&#946;</mi><msubsup><mrow><mi>M</mi></mrow><mrow><mi>p</mi><mi>l</mi></mrow><mrow><mi>&#945;</mi></mrow></msubsup></mrow><mrow><msup><mrow><mi>&#981;</mi></mrow><mrow><mi>&#945;</mi></mrow></msup></mrow></mfrac><mo stretchy='true'>)</mo></mrow></math>. With the help of COBE normalization, we constrain values of different parameters and extract the field value at the time of Hubble crossing. The end of inflation is marked by <math altimg='si4.svg'><msub><mrow><mover accent='true'><mrow><mi>&#1013;</mi></mrow><mrow><mo stretchy='false'>&#732;</mo></mrow></mover></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy='false'>(</mo><msub><mrow><mi>&#981;</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy='false'>)</mo><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>1</mn></math> where <math altimg='si5.svg'><msub><mrow><mi>&#981;</mi></mrow><mrow><mi>i</mi></mrow></msub></math> is the field value at the end of inflation. Equipped with these values, we then move on to calculate values of spectral index <math altimg='si6.svg'><msub><mrow><mi>n</mi></mrow><mrow><mi>s</mi></mrow></msub></math> and tensor-to-scalar ratio <italic>r</italic>. Our predicted values of <math altimg='si6.svg'><msub><mrow><mi>n</mi></mrow><mrow><mi>s</mi></mrow></msub></math> and <italic>r</italic> fall within their observed values from the Planck 2018 survey and BICEP/Keck array measurement for both potential, making them plausible candidates for the inflationary model. We also display the variation of the tensor-to-scalar ratio and spectral index with the coefficient of RT-mixing term for fixed values of e-fold number. There, we find the existence of two local maxima of <math altimg='si6.svg'><msub><mrow><mi>n</mi></mrow><mrow><mi>s</mi></mrow></msub></math>, which occur at a negative and a positive value of <italic>&#958;</italic>, the coefficient of <italic>RT</italic>-mixing term. Our analysis finds a significant impact of <italic>&#958;</italic> on values of observables.

India

Sohan Kumar Jha

Anisur Rahaman

Non-minimal <italic>RT</italic> coupling and its impact on inflationary evolution in <italic>f</italic>( <italic>R</italic>, <italic>T</italic>) gravity

We present a new equation of state for QCD in which the temperature <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math> and the three chemical potentials for baryon number <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>μ</mi><mi>B</mi></msub></math>, electric charge <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>μ</mi><mi>Q</mi></msub></math>, and strangeness <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>μ</mi><mi>S</mi></msub></math> can be varied independently. This result is based on a generalization of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>T</mi><mo>′</mo></msup></math> expansion scheme, thanks to which the diagonal <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>μ</mi><mi>B</mi></msub></math> extrapolation was pushed up to a baryo-chemical potential <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>μ</mi><mi>B</mi></msub><mo>/</mo><mi>T</mi><mo>∼</mo><mn>3.5</mn></math> for the first time. This considerably extended the coverage of the Taylor expansion, limited to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mi>B</mi></mrow></msub><mo>/</mo><mi>T</mi><mo>&lt;</mo><mn>2.5</mn><mi>–</mi><mn>3</mn></mrow></math>. As a consequence, we are able to offer a substantially larger coverage of the four-dimensional QCD phase diagram as well, compared to previously available Taylor expansion results. Our findings are based on new continuum estimated lattice data on the full set of second- and fourth-order fluctuations.

Ahmed Abuali

Szabolcs Borsányi

Hungary

Zoltán Fodor

Johannes Jahan

Micheal Kahangirwe

Paolo Parotto

Attila Pásztor

Claudia Ratti

Hitansh Shah

Seth A. Trabulsi

New 4D lattice QCD equation of state: Extended density coverage from a generalized <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>T</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></math> expansion

In this paper, we investigate the viability of an exponential <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>T</mi><mo stretchy='false'>)</mo></math> gravity for describing cosmic inflation with a canonical scalar field. In order to obtain concrete results, we use four well-known potentials such as general hilltop inflation potential, valley hybrid inflation potential, shaft potential and minimal inflation potential. For each considered potential, we evaluate the several inflationary parameters at background and perturbative levels. Then, we perform a Markov Chain Monte Carlo (MCMC) analysis to estimate the parameters of each potential model by exploring its parameter space. In addition, we plot the corresponding trajectories in the <math altimg='si2.svg'><mi>r</mi><mo linebreak='goodbreak' linebreakstyle='after'>&#8722;</mo><msub><mrow><mi>n</mi></mrow><mrow><mi>s</mi></mrow></msub></math> and <math altimg='si3.svg'><msub><mrow><mi>&#945;</mi></mrow><mrow><mi>s</mi></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>&#8722;</mo><msub><mrow><mi>n</mi></mrow><mrow><mi>s</mi></mrow></msub></math> planes. In this sense, we make the comparison with the two-marginalized joint confidence at 68% and 95% C.L. from the latest BICEP/Keck results. The results mostly show small values for the tensor -to-scalar ratio and acceptable values for the scalar spectral index, which are within the current observational bounds.

Pakistan

Abdul Jawad

Chile

Nelson Videla

Azerbaijan

Abdul Malik Sultan

Kazakhstan

N. Myrzakulov

Ayesha Aslam

Uzbekistan

Sanjar Shaymatov

Observational constraints on inflationary parameters in exponential <italic>f</italic>( <italic>T</italic>) gravity with well-known potentials

We perform a detailed comparison between three formalisms used in recent studies of $\textit{DD}$ scattering at heavier-than-physical pion masses, which aim to understand the properties of the doubly-charmed tetraquark, $$ {T}_{cc}^{+}(3875) $$ . These methods are the three-particle relativistic field theory (RFT) formalism, the two-body Lippmann-Schwinger (LS) equation with chiral effective field theory potentials, and the two-particle relativistic framework proposed by Baião Raposo and Hansen (BRH approach). In a simplified single-channel setting, we derive the conditions under which the infinite-volume integral equations from the RFT and BRH approaches reduce to the LS form. We present numerical examples showing that differences between these methods can be largely removed by adjusting short-range couplings. We also address a number of technical issues in the RFT approach.

Sebastian Dawid

Fernando Romero-López

Stephen Sharpe

Comparison of integral equations used to study $$ {T}_{cc}^{+} $$ for a stable $\textit{D}$

The photoproduction of doubly charmed tetraquark <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> is predicted through the resolved channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mo>+</mo><mi>g</mi><mo stretchy="false">→</mo><mo stretchy="false">⟨</mo><mi>c</mi><mi>c</mi><mo stretchy="false">⟩</mo><mo stretchy="false">[</mo><mi>n</mi><mo stretchy="false">]</mo><mo>+</mo><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mo>+</mo><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">→</mo><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo>+</mo><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mo>+</mo><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover></math> at ILC and CLIC. At <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> colliders, the initial photons <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math> can be produced from two primary sources, well-delineated within the Weizäcker Williams approximation (WWA) and the laser backscattering (LBS). And the initial gluon can be emitted from the photon. The spin and color quantum number [<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>n</mi></math>] of the intermediate diquark configuration can be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">⟨</mo><mi>c</mi><mi>c</mi><mo stretchy="false">⟩</mo><mo stretchy="false">[</mo><msub><mrow><mmultiscripts><mrow><mi>S</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mo stretchy="false">]</mo></mrow><mrow><mover accent="true"><mrow><mn>3</mn></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow></msub></mrow></math>. Then its nonperturbative hadronization to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> was discussed in the phenomenological potential models. Finally, the differential distributions and theoretical uncertainty of the doubly charmed tetraquark <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> were analyzed. As the collision energy increases, the contribution of the resolved photon channel will become increasingly significant, and it may even dominate the production of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> with the laser backscattering spectrum. The conclusion is that it is promising to observe <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> via the resolved channel of photoproduction both at the ILC and CLIC, and the results have a strong dependence on the mass of constituent charm quark <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>c</mi></msub></math> and the potential model.

Juan-Juan Niu

Hong-Hao Ma

Photoproduction of doubly charmed tetraquark <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow></msub></mrow></math> via photon-gluon fusion at ILC and CLIC