We investigate the bound-state equations (BSEs) in two-dimensional QCD in the $ N_{\rm{c}}\to \infty$ limit, viewed from both the infinite momentum frame (IMF) and the finite momentum frame (FMF). The BSE of a meson in the original 't Hooft model, $\textit{viz.}$, spinor QCD$_{2}$ containing only fermionc quarks, has been extensively studied in literature. In this work, we focus on the BSEs pertaining to two types of ''exotic'' hadrons, a ''tetraquark'' which is composed of a bosonic quark and bosonic antiquark, and a ''baryon'' which is composed of a bosonic antiquark and a fermionic quark. Utilizing the Hamiltonian approach, we derive the corresponding BSEs for both types of ''exotic'' hadrons, from the perspectives of the light-front and equal-time quantization, and confirm the known results. The recently available BSEs for ''tetraquark'' in FMF has also been recovered with the aid of the diagrammatic approach. For the first time we also present the BSEs of a ''baryon'' in FMF in the extended 't Hooft model. By solving various BSEs numerically, we obtain the mass spectra pertaining to ''tetraquark'' and ''baryon'' and the corresponding bound-state wave functions of the lowest-lying states. It is numerically demonstrated that, when a ''tetraquark'' or ''baryon'' is continuously boosted, the forward-moving component of the bound-state wave function approaches the corresponding light-cone wave function, while the backward-moving component fades away.

China

Xiaolin Li

Yu Jia

Ying Li

Zhewen Mo

Solving bound-state equations in QCD$_{2}$ with bosonic and fermionic quarks * Supported in part by the National Science Foundation of China (12475090, 11925506, 12435004) and the Natural Science Foundation of Shandong province (ZR2022ZD26). The work of Zhewen Mo is also supported in part by the National Natural Science Foundation of China (12347145, 12347105)

In this study, we investigate the possibility of enhancing the di-jet resonance searches by tagging the final state radiation (FSR) jet using an event-level deep neural network. It is found that solely relying on the 4-momenta of the leading three jets allows the algorithm to achieve good discriminating power that can identify the hardest FSR jet in the signal while rejecting other soft jets. Once the invariant mass is corrected with the tagged FSR jet, the mass resolution of the signal is greatly enhanced, and the sensitivity of the search is also improved by more than 10%. By crafting the input variables carefully, the algorithm introduces minimal mass sculpting for the background, and its applicability extends to a broad mass range. This work proves that FSR jet tagging can potentially enhance di-jet resonance searches, suiting various stages of the physics programmes at the Large Hadron Collider (LHC) and High-Luminosity LHC (HL-LHC).

Bingxuan Liu

Yuxuan Shen

Yuanshunzi Sui

Enhancing di-jet resonance searches via a final-state radiation jet tagging algorithm * Bingxuan Liu is supported by Shenzhen Campus of the Sun Yat-sen University under project 74140-12255011, and by the Young Scientists Fund (C Class) of the National Natural Science Foundation of China (12405122). Both Yuxuan Shen and Yuanshunzi Sui are supported by College Students’ Innovative Entrepreneurial Training Plan Program

We investigate the collider signatures of a maximally flavor-violating $ U(1)_{L_\mu-L_\tau} $ model, where a new gauge boson $ Z^\prime $ and scalar triplets induce lepton flavor-changing interactions in the $\textit{μ}$-$\textit{τ}$ sector. Focusing on four-lepton final states at multi-TeV lepton colliders, we conduct a detailed analysis of cross sections, asymmetries, and polarization effects. We show that the signal cross section is highly sensitive to $ m_{Z^\prime} $ and the effective parameters $ \tilde{g}/m_{Z^\prime} $ , whereas it remains largely insensitive to the triplet Yukawa couplings within the phenomenologically allowed region. The forward-backward asymmetry exhibits a characteristic monotonic dependence on $ m_{Z^\prime} $ , and beam polarization can significantly suppress the Standard Model backgrounds while enhancing new physics contributions. We find that, in the phenomenologically allowed parameter space, the predicted observables remain highly sensitive to the underlying model parameters. These results show that multi-lepton final states are powerful probes of the $ U(1)_{L\mu - L_\tau} $ framework and can offer valuable guidance for future searches at muon and electron-positron colliders.

Jianing Qin

Fei Huang

Honglei Li

Zhi-Long Han

Jin Sun

Collider probes of four-lepton final states in maximally flavor-violating ${U(1)_{L_\mu-L_\tau}} $ model * Supported by National Natural Science Foundation of China (12505112, 11805081), Shandong Province Natural Science Foundation (ZR2024QA138, ZR2022MA056) and State Key Laboratory of Dark Matter Physics, University of Jinan Disciplinary Cross-Convergence Construction Project 2024 (XKJC- 202404) and Jin Sun is supported by IBS under the project code, (IBS-R018-D1)

<p>We present a theoretical analysis of the process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>p</mi><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math> within the chiral unitary approach, with particular emphasis on the dynamically generated <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">(</mo><mn>1535</mn><mo stretchy="false">)</mo></math> resonance. In addition to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">(</mo><mn>1535</mn><mo stretchy="false">)</mo></math>, our model incorporates contributions from other intermediate resonances including <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">(</mo><mn>1650</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup><mo stretchy="false">(</mo><mn>892</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>1430</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">(</mo><mn>1440</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Σ</mi><mo stretchy="false">(</mo><mn>1750</mn><mo stretchy="false">)</mo></math>. The calculated invariant mass distributions and Dalitz plot are in good agreement with the recent Belle measurements. Our analysis highlights the crucial role of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">(</mo><mn>1535</mn><mo stretchy="false">)</mo></math> state in this decay channel and supports its interpretation as a dynamically generated state arising from coupled-channel meson-baryon interactions.</p>

En Wang

Li-Sheng Geng

Ju-Jun Xie

Dynamically generated <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">(</mo><mn>1535</mn><mo stretchy="false">)</mo></math> state in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>p</mi><msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math> decay

We construct static, spherically symmetric wormhole solutions with a nontrivial redshift function, inspired by noncommutative geometry, in which point sources are replaced by Gaussian smearing of minimal length, yielding a regular shape function. Within this framework, we derive model-independent relations that isolate the role of the redshift function in controlling the stress-energy components and the violation of the null energy condition (NEC). Negative or suitably tuned redshifts confine the exotic matter to a thin neighbourhood of the throat. We then reformulate this redshift engineering in matter terms through a quasi-de Sitter equation of state (EOS) with localised Gaussian or Lorentzian perturbations, obtaining minimally exotic wormholes that are regular, horizon-free, and asymptotically flat. Finally, we extend the analysis to a Chaplygin-like EOS, introducing a nonlinear coupling between pressure and density that yields redshift wells with possible local blueshift regions and tunable anisotropies governed by a certain nonlinearity parameter. Together, these results provide a unified and physically transparent framework for constructing traversable noncommutative-geometry-inspired wormholes with controlled, spatially localised exotic matter content.

United Arab Emirates

Davide Batic

Denys Dutykh

Mark Essa Sukaiti

Noncommutative geometry-inspired wormholes supported by quasi-de Sitter and Chaplygin-like equations of state

We consider Einstein gravity with positive cosmological constant coupled to matter in an asymptotically de Sitter universe with sphere boundary at timelike infinity. In this setting we show that, to one-loop order and at late time, the norm of the no-boundary state vanishes, going as $$ {e}^{S_0}\frac{Z{S}_0^{-d\left(d+1\right)/4}}{\textrm{vol}\left(\textrm{SO}\left(d,1\right)\right)} $$ with $\textit{S}$ the tree-level entropy of the static patch, $\textit{d}$ the spacetime dimension, and $\textit{Z}$ non-negative. We show that the presence of an observer stabilizes the norm to a large, positive value.

United States

Jordan Cotler

Canada

Kristan Jensen

Norm of the no-boundary state

We consider spherically symmetric static black hole configurations that obey the vacuum equation of state: <math altimg='si1.svg'><mrow><msub><mi>p</mi><mi>r</mi></msub><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mi>&#961;</mi></mrow></math>, where <italic>p<inf>r</inf></italic> is the radial pressure, <italic>&#961;</italic> being energy density. We find in a closed form the metric for an arbitrary equation of state for tangential pressure <italic>p<inf>&#952;</inf></italic>( <italic>&#961;</italic>). The corresponding formulas enable us to embrace compact Schwarzschild-like configurations and dispersed systems. They include metrics with a regular center and singular ones. In a particular case, the metric of the Kiselev black hole is reproduced.

Ukraine

O.B. Zaslavskii

Inverted equation of state and general approach to vacuum-like configurations

A correction to this paper has been published: https://doi.org/10.1007/JHEP05(2023)020

United Kingdom

Rachel Ashby-Pickering

Alan Barr

Agnieszka Wierzchucka

Erratum to: Quantum state tomography, entanglement detection and Bell violation prospects in weak decays of massive particles

We introduce a method called resolution refinement that allows one to bootstrap eigenstate preparation on a quantum computer. We first prepare an eigenstate of a low-resolution Hamiltonian using any method of choice. The eigenstate is then lifted to higher resolution and adiabatically evolved to produce the corresponding eigenstate of a higher-fidelity Hamiltonian. We give examples of resolution refinement applied to both single-particle basis states as well as a spatial lattice grid. For basis refinement, we compute few-body ground states of the Busch model for interacting particles in a harmonic trap in one dimension. For lattice refinement, we compute Hartree-Fock nuclear states for a central Woods-Saxon potential in three dimensions, and we compute bound states and continuum states in a multi-species Hubbard model of fermions in one dimension. In all cases, the method is efficient and requires an adiabatic evolution time that scales with the inverse of the energy gap times the square root of the system size. We show that this very favorable scaling arises from the fact that resolution refinement does not make large changes to the structure or energies of the low-energy eigenstates.

Scott Bogner

Heiko Hergert

Norway

Morten Hjorth-Jensen

Ryan LaRose

Dean Lee

Matthew Patkowski

Quantum state preparation with resolution refinement

The Hilbert-Schmidt measure is a useful geometric tool used to investigate the properties on the manifold of mixed Gaussian states in multimode continuous variable quantum systems. In this work, we study the relationship between the scalar curvature and quantum entanglement across causally disconnected regions (open charts) in de Sitter spacetime. We first consider a two-mode squeezed state shared between Alice and Bob, where the Gaussian channel models the effects of spacetime curvature. We employ logarithmic negativity as a witness for quantum entanglement. We study the impact of the mass, parameter <italic>p</italic> and squeezing parameter on the scalar curvature and entanglement. We find an interesting interplay between scalar curvature and entanglement for certain values of the mass and parameter <italic>p</italic>. By varying <italic>p</italic>, we thus explore how information geometry and entanglement are influenced by both ultraviolet and infrared modes. Moreover, the relationship between scalar curvature and entanglement is discussed under the influence of various parameters characterizing the geometric system under consideration.

Morocco

Mohamed Amazioug

Mohammed Daoud

Scalar curvature and entanglement of the Gaussian state manifold in de Sitter spacetime