We study fermion zero-mode wave functions with various chiralities in the magnetized <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>T</mi><mrow><mn>2</mn><mi>g</mi></mrow></msup></math>, (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><mi>g</mi><mo>=</mo><mn>2</mn></mrow><mo>,</mo><mn>3</mn></mrow></math>), torus. First, we consider the wave functions satisfying the Dirac equation and the boundary conditions on the magnetized torus. Second, we introduce the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>O</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></math> (or parity) transformations and derive the wave functions under the modular transformation. Additionally, we calculate the Yukawa couplings taking chirality into account. Lastly, we briefly review how to construct the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>T</mi><mn>4</mn></msup><mo>/</mo><msub><mi mathvariant="double-struck">Z</mi><mi>N</mi></msub></math>, (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn></mrow></math>), and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>T</mi><mn>6</mn></msup><mo>/</mo><msub><mi mathvariant="double-struck">Z</mi><mn>12</mn></msub></math> twisted orbifold. Also, we explicitly analyze the number of the wave functions in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="double-struck">Z</mi><mi>N</mi></msub></math> sectors.

Japan

Tim Jeric

Tatsuo Kobayashi

Kaito Nasu

Shohei Takada

Generation structures and Yukawa couplings in magnetized <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>T</mi></mrow><mrow><mn>2</mn><mi>g</mi></mrow></msup><mo>/</mo><msub><mrow><mi mathvariant="double-struck">Z</mi></mrow><mrow><mi>N</mi></mrow></msub></mrow></math> models

We study SU($\textit{N}$) super Yang-Mills theory with a small gaugino mass $\textit{m}$ and vacuum angle $\textit{θ}$ on the four-torus $$ {\mathbbm{T}}^4 $$ with ’t Hooft twisted boundary conditions. Introducing a detuning parameter ∆, which measures the deviation from an exactly self-dual $$ {\mathbbm{T}}^4 $$ , and working in the limits $\textit{mLN}$ ≪ Λ$\textit{LN}$ ≪ 1 and $$ \frac{\left(N-1\right){m}^2{L}^2}{4\pi}\ll \Delta \ll 1 $$ , where $\textit{L}$ is the torus size and Λ the strong-coupling scale, we compute the scalar and pseudo-scalar condensates to leading order in $\textit{m}$ $\textit{L}$ /∆. The twists generate fractional-charge instantons, and we show that summing over all such contributions is crucial for reproducing the correct physical observables in the decompactified strong-coupling regime. From a Hamiltonian perspective, the sum over twisted sectors, already at small torus size, projects in the $\textit{m}$ = 0 limit onto a definite superselection sector of the $\textit{ℝ}$ theory. In the massless limit, we recover the exact value of the gaugino condensate |〈$\textit{λλ}$〉| = 16$\textit{π}$ Λ , and demonstrate how a spurious U(1) symmetry eliminates all $$ \mathcal{CP} $$ -violating effects. Our results are directly testable in lattice simulations, and our method extends naturally to non-supersymmetric gauge theories.

United Kingdom

Mohamed Anber

Canada

Erich Poppitz

Mass-deformed super Yang-Mills theory on $$ {\mathbbm{T}}^4 $$ : sum over twisted sectors, $\textit{θ}$-angle, and CP violation

Modern collider phenomenology requires unprecedented precision for the theoretical predictions, for which slicing techniques provide an essential tool at next-to-next-to-leading order (NNLO) in the strong coupling. The most popular slicing variable is based on the transverse momentum <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>q</mi><mi>T</mi></msub></math> of a color-singlet final state, but its generalization to final states with jets is known to be very difficult. Here we propose two generalizations of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>q</mi><mi>T</mi></msub></math> that can be used for jet processes, providing proof of concept with an NLO slicing for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi><mo stretchy="false">→</mo><mn>2</mn></math> jets. We present factorization formulas that enable our approach to NNLO, calculate the NNLO collinear-soft function, and demonstrate slicing at this order for <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><mo stretchy="false">→</mo><mn>2</mn></math> jets. One of these generalizations of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>q</mi><mi>T</mi></msub></math> only applies to planar Born processes, such as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi><mo stretchy="false">→</mo><mn>2</mn></math> jets, but offers a dramatic simplification of the soft function. We also discuss how our approach can directly be extended to obtain predictions for the fragmentation of hadrons. This presents a promising path for high-precision QCD calculations with multijet final states.

China

Rong-Jun Fu

Austria

Rudi Rahn

Ding Yu Shao

Netherlands

Wouter J. Waalewijn

Spain

Bin Wu

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>q</mi><mi>T</mi></msub></math> Slicing with Multiple Jets

The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi></math>-channel singularity is a divergence in the scattering amplitude which occurs when a stable particle propagating in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi></math>-channel scattering process becomes an on-shell state. Such situations appear either in the system of collider experiments or in the context of the cosmological particle production. No scheme which is generally applicable is known. In this work, we propose a new formulation to identify and remove the source of the divergence. The scheme is fully analytical and various applications can be expected. This work provides a valuable tool in this research field.

Kento Asai

Nagisa Hiroshima

Joe Sato

Ryusei Sato

Masaki J.S. Yang

Analytic prescription for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi></math>-channel singularities

In this work we consider the QCD predictions for spin correlations in $$ t\overline{t} $$ production in hadronic collisions. In view of recent tensions between experimental data and theoretical calculations, it has been argued that one should include in the predictions also the effects of the production of the $\textit{η}$ , i.e. the pseudoscalar $$ t\overline{t} $$ bound state, or alternatively the full effects of the non-relativistic dynamics of the $$ t\overline{t} $$ pair near threshold. This implies the resummation of all corrections that scale like powers of $\textit{α}$ /$\textit{v}$ (where $\textit{v}$ is the velocity of the top quark in the $$ t\overline{t} $$ rest frame) which are dominated by values of $\textit{v}$ of order $\textit{α}$ . In this work, we show that, since the observables that are usually considered for these studies are integrated cross sections up to a $$ t\overline{t} $$ mass cut that is not small, it is possible to perform the calculation using perturbation theory, considering only the contributions that scale as the first few powers of $\textit{α}$ /$\textit{v}$. We examine the implications of our approach by computing corrections to nominal Monte Carlo results for correlation-sensitive observables, and compare them with available data, showing that the tension with data is no longer present.

Italy

Paolo Nason

Emanuele Re

Luca Rottoli

Spin correlations in $$ t\overline{t} $$ production and decay at the LHC in QCD perturbation theory

We revisit the fermionic string theory on $$Ad{S}_{3}\times \mathcal{N}$$ with $\textit{k}$ = 1, and its single-trace $$T\overline{T }$$ deformation, with a focus on the (2, 2) superstring on (deformed) $$Ad{S}_{3}\times {\mathbb{T}}^{3}$$ . In a certain limit, it is dual to the symmetric product of the ( $$T\overline{T }$$ -deformed) SCFT on $${\mathbb{R}}\times {\mathbb{T}}^{3}$$ . We present the winding-one delta-function normalizable worldsheet operators which, in the $\textit{k}$ = 1 decoupling limit, correspond to those of $${\mathbb{R}}\times {\mathbb{T}}^{3}$$ in spacetime. We then demonstrate how their properties in string theory reproduce those of $${\mathbb{R}}\times {\mathbb{T}}^{3}$$ , or more generally, of a ( $$T\overline{T }$$ -deformed) $${\mathbb{R}}\times \mathcal{N}$$ seed of the boundary theory.

United States

Soumangsu Chakraborty

Israel

Amit Giveon

On string theory on (deformed) $$Ad{S}_{3}\times {\mathbb{T}}^{3}$$

We study the behaviour of SU(2) Yang-Mills fields on a $\textit{T}$ × $\textit{R}$ geometry where the two-torus is equipped with twisted boundary conditions. We monitor the evolution of the dynamics of the system as a function of the torus size $\textit{l}$ . For small sizes the behaviour of the system is well understood in terms of semiclassical predictions. In our case, the long distance structure is that of a two-dimensional gas of vortex-like fractional instantons with size and density growing with $\textit{l}$ . Our lattice Monte Carlo simulations confirm the semiclassical predictions and allow the determination of the relevant scale signalling the transition to the non-dilute situation. At low densities the string tension takes the standard value of a 2D center-vortex gas, growing with the density and approaching the value measured at infinite volume. Our work includes preliminary studies of the extension to SU(N) and to the region of large sizes in which boundary conditions are irrelevant, and all physical scales are determined by the Λ parameter.

Germany

Georg Bergner

Antonio González-Arroyo

Ivan Soler

A $\textit{T}$

We investigate the connection between simplified dark matter models featuring a $\textit{t}$-channel scalar mediator and the Standard Model Effective Field Theory (SMEFT). We focus on scenarios with fermionic dark matter interacting with leptons, under the assumption of Minimal Flavor Violation. The dimension-six SMEFT Wilson coefficients are computed in the Warsaw basis at one loop, with the aid of Matchete. Assuming a compressed mass spectrum for the dark matter and the mediator, we incorporate coannihilations, Sommerfeld enhancement, and bound-state effects in the relic density calculation. We then analyze the interplay between the dark matter energy density, global SMEFT fits, and direct detection constraints. Our results show that SMEFT bounds, though loop-suppressed, can meaningfully constrain the parameter space for $\textit{m}$ ≳ 200 GeV and $$ \mathcal{O}(1) $$ portal couplings.

S. Biondini

L. Tiberi

O. Panella

Connecting $\textit{t}$-channel dark matter models to the Standard Model Effective Field Theory

Belgium

Chiara Arina

France

Benjamin Fuks

Luca Panizzi

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

Jackson Burzynski

Jonathan Butterworth

Antimo Cagnotta

Lorenzo Calibbi

Linda Carpenter

Xabier Cid Vidal

Emanuele Copello

Louie Corpe

Francesco D’Eramo

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

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

$\textit{f}$($\textit{Q}$) and $\textit{f}$($\textit{T}$) gravity are based on fundamentally different geometric frameworks, yet they exhibit many similar properties. This article provides a comprehensive summary and comparative analysis of the various theoretical branches of torsional gravity and non-metric gravity, which arise from different choices of affine connection. We identify two types of background-dependent and classical correspondences between these two theories of gravity. The first correspondence is established through their equivalence within the Minkowski spacetime background. To achieve this, we develop the tetrad-spin formulation of $\textit{f}$($\textit{Q}$) gravity and derive the corresponding expression for the spin connection. The second correspondence is based on the equivalence of their equations of motion. Utilizing a metric-affine approach, we derive the general affine connection for static and spherically symmetric spacetime in $\textit{f}$($\textit{Q}$) gravity and compare its equations of motion with those of $\textit{f}$($\textit{T}$) gravity. Among others, our results reveal that, $\textit{f}$($\textit{T}$) solutions are not simply a subset of $\textit{f}$($\textit{Q}$) solutions; rather, they encompass a complex solution beyond $\textit{f}$($\textit{Q}$) gravity in black hole background.

Cheng Wu

Xin Ren

Yuhang Yang

Yu-Min Hu

Chile

Greece

Emmanuel Saridakis

Background-dependent and classical correspondences between $\textit{f}$($\textit{Q}$) and $\textit{f}$($\textit{T}$) gravity