Understanding flux string dynamics can provide insight into quark confinement and hadronization. First-principles quantum and numerical simulations have mostly focused on toy-model Abelian lattice gauge theories (LGTs). With the advent of state-of-the-art quantum simulation experiments, it is timely to study string dynamics in non-Abelian LGTs beyond one spatial dimension. Using tensor network methods, we simulate the real-time string dynamics of a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn><mi mathvariant="normal">D</mi></mrow></math> SU(2) Yang-Mills LGT with dynamical matter. In the strong-coupling regime and at resonance, string breaking occurs via a sharp Casimir reduction, along with meson and baryon-antibaryon formation, a distinctively non-Abelian feature. At finite baryon density, we discover a baryon blockade mechanism that delays string breaking. Away from resonance, the magnetic term drives purely non-Abelian fluctuations: glueball-like excitations and self-crossed strings that resolve two SU(2) intertwiners with distinct dynamics. For higher-energy strings, we uncover representation-dependent tension-reduction resonances. Our findings serve as a guide for upcoming quantum simulators of non-Abelian LGTs.

Germany

Giovanni Cataldi

Italy

Simone Orlando

South Korea

Jad C. Halimeh

Real-Time String Dynamics in a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn><mi mathvariant="normal">D</mi></mrow></math> Non-Abelian Lattice Gauge Theory: String Breaking, Glueball Formation, Baryon Blockade, and Tension Reduction

Poland

Trambak Bhattacharyya

Maciej Rybczyński

Grzegorz Wilk

Zbigniew Włodarczyk

Addendum to “A harmonic oscillator in nonadditive statistics and a novel transverse momentum spectrum in high-energy collisions” [Phys. Lett. B 867 (2025) 139588]

Within the QCD sum-rule framework, we investigate hidden-heavy tetraquark channels with the exotic quantum number <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>J</mi></mrow><mrow><mi>PC</mi></mrow></msup><mo>=</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mo>−</mo></mrow></msup></mrow></math> using four representative local color-octet–octet interpolating currents. The currents include both vector-axialvector and scalar-pseudoscalar Dirac structures. The operator product expansion is carried out up to dimension-eight condensates. The four diagonal sum rules yield mutually consistent mass estimates in the range 10.8–11.1 GeV for the hidden-bottom sector and around 4.3–4.6 GeV for the corresponding hidden-charm sector, with the bottom sector exhibiting the clearest Borel stability. Since local tetraquark currents with the same quantum numbers are related by Fierz rearrangements, the current-dependent results do not by themselves imply four distinct states or uniquely defined internal color structures. We also discuss quantum-number-allowed decay channels and emphasize the absence of the lowest pseudoscalar-pseudoscalar heavy-meson modes for a neutral <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>0</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup></math> state. The results provide theoretical guidance for future experimental searches at Belle II, LHCb, and BESIII.

China

Bing-Dong Wan

Jun-Hao Zhang

Yan Zhang

Ming-Yang Yuan

Spectroscopy of hidden-heavy tetraquark states with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>J</mi></mrow><mrow><mi>PC</mi></mrow></msup><mo>=</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mo>−</mo></mrow></msup></mrow></math> in a color-octet configuration

The work was motivated by the numerical result that, in a pure SU(2) gauge theory, the ratio <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math> of the effective noncompact and compact lattice spacing is larger than 1 and increases with decreasing gauge coupling, with the expectation that it should further increase extending the parameter space. This means that with a noncompact regularization, at a given number of lattice sites and comparable scaling, one can obtain a larger physical volume whose importance for the control of size effects has long been known. We confirm qualitatively results and expectation by a perturbative evaluation of the effective lattice spacing in an expansion in the Plank constant of noncompact pure SU(2) and Abelian gauge theories, but we find in addition that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math> reaches the maximum value of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mn>2</mn></msqrt></math>. Including matter fields, we find that R increases (still up to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mn>2</mn></msqrt></math>) or decreases depending on the difference between the number of scalar and spinor degrees of freedom, and there are bounds on such a difference.

F. Palumbo

Larger physical volume and bounds on the number of matter fields in noncompact gauge theories on a lattice

It is well known that nonrelativistic or semirelativistic constituent quark models can describe a large number of the meson and baryon properties with surprising accuracy. In this work, we study the Killingbeck potential using the WKB approximation in the constituent quark model. The implicit approximate solutions for the energy eigenvalues, together with analytical expressions for the root-mean-square radii and the probability densities at the origin, of the Schrödinger equation are obtained by using appropriate quantization conditions. Finally, we discuss applications to double-heavy-meson spectroscopy within the Killingbeck potential.

Cheng-Qun Pang

Lhamo Chosto

Ya-Rong Wang

Zhi-Bin Gao

Hao Chen

Yu-Long Kang

Wei Li

WKB approximation under a Killingbeck potential and its application to double-heavy-meson spectroscopy

A search for proton decay via <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mo stretchy="false">→</mo><msup><mi>l</mi><mo>+</mo></msup><mo>+</mo><mi>X</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>l</mi><mo>+</mo></msup></math> is a positively charged lepton and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi></math> is an invisible, massless, neutral particle, was performed using a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>401</mn><mtext> </mtext><mtext> </mtext><mi>kton</mi><mo>·</mo><mi>years</mi></mrow></math> exposure representing the entire pure water phase of Super-Kamiokande. No significant indication of a proton decay was observed beyond the expected atmospheric neutrino background. Lower limits on the partial lifetime of the proton were set to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1.72</mn><mo>×</mo><msup><mn>10</mn><mn>33</mn></msup><mtext> </mtext><mtext> </mtext><mi>years</mi></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mo stretchy="false">→</mo><msup><mi>e</mi><mo>+</mo></msup><mo>+</mo><mi>X</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0.61</mn><mo>×</mo><msup><mn>10</mn><mn>33</mn></msup><mtext> </mtext><mtext> </mtext><mi>years</mi></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mo stretchy="false">→</mo><msup><mi>μ</mi><mo>+</mo></msup><mo>+</mo><mi>X</mi></math> at the 90% confidence level. These results improve on previous limits by factors of 2 and 1.5, respectively.

Japan

Y.M. Liu

K. Terada

K. Abe

Y. Asaoka

M. Harada

Y. Hayato

K. Hiraide

T.H. Hung

K. Ieki

M. Ikeda

J. Kameda

Y. Kataoka

United States

S. Mine

M. Miura

S. Moriyama

K. Nakagiri

M. Nakahata

S. Nakayama

Y. Noguchi

G. Pronost

K. Sato

H. Sekiya

R. Shinoda

M. Shiozawa

Y. Suzuki

A. Takeda

Y. Takemoto

H. Tanaka

S. Chen

Y. Itow

T. Kajita

R. Nishijima

K. Okumura

T. Tashiro

T. Tomiya

X. Wang

Spain

F.J. de Garay Arcones

P. Fernandez

L. Labarga

D. Samudio

C. Yanagisawa

B. Jargowsky

E. Kearns

J. Mirabito

L. Wan

T. Wester

Canada

B.W. Pointon

J. Bian

B. Cortez

N.J. Griskevich

Y. Jiang

M.B. Smy

H.W. Sobel

V. Takhistov

J. Hill

B.D. Xu

D. Jung

D.H. Moon

R.G. Park

B.S. Yang

K. Scholberg

C.W. Walter

France

O. Drapier

A. Ershova

M. Ferey

Z. Hu

E. Le Blévec

T. Leplumey

Th. A. Mueller

P. Paganini

C. Quach

R. Rogly

T. Nakamura

J.S. Jang

United Kingdom

R.P. Litchfield

L.N. Machado

F.J.P. Soler

J.G. Learned

K. Choi

Vietnam

S. Cao

T.V. Ngoc

L.H.V. Anthony

N.W. Prouse

M. Scott

Y. Uchida

V. Berardi

N.F. Calabria

M.G. Catanesi

N. Ospina

E. Radicioni

A. Langella

G. De Rosa

G.T. Burton

G. Collazuol

M. Feltre

M. Mattiazzi

L. Ludovici

M. Gonin

L. Périssé

B. Quilain

Search for proton decay into a single charged antilepton and a massless invisible particle using the full pure water data set of Super-Kamiokande

The efficient preparation of correlated thermal states, such as the thermofield double state, is a fundamental prerequisite for simulating quantum gravity models and many-body thermodynamics on quantum processors. In this work, we investigate the ground-state preparation of the two coupled Sachdev-Ye-Kitaev model, known as the Maldacena-Qi model, which is dual to a traversable wormhole in anti–de Sitter space in two dimensions, utilizing feedback-based quantum algorithms. We demonstrate that the standard feedback-based quantum algorithm (FALQON) and its time-rescaled variant (TR-FALQON) face severe kinetic limitations in this system, failing to converge to the highly entangled ground state when initialized in trivial product states. To overcome these barriers, we propose the hybrid ITE-TR-FALQON protocol, which integrates the imaginary-time evolution present in imaginary-time-enhanced FALQON with the time-rescaling mechanism. Our ideal state-vector simulations show that imaginary-time filtering overcomes the stagnation observed for the unitary protocols with the chosen driver and initial state, while time rescaling reduces the number of algorithmic layers. The hybrid protocol achieves fidelities close to unity with the exact-diagonalization ground state and reproduces its von Neumann and Rényi entropies with high precision. These results constitute a numerical proof of principle: implementing the nonunitary updates, repeated feedback measurements, and the resulting compiled circuits remains a substantial obstacle, and the protocol in its present form is not a practical state-preparation method for current noisy intermediate-scale quantum devices.

Brazil

Guilherme E.L. Pexe

Lucas A.M. Rattighieri

Felipe F. Fanchini

Dario Rosa

Amilson R. Fritsch

Preparing a thermofield double state with feedback quantum algorithms

We study the dynamics of a heavy quark in a thermal plasma consisting of non-perturbatively interacting soft momentum gluons at high temperatures, described in terms of an effective theory of QCD. Discretizing this effective field theory on a three-dimensional lattice, we propose a numerical strategy that allows us to simulate the dynamics of a heavy quark for different values of initial momenta and for a wide temperature range, higher than 480 MeV. This allows us, for the first time, to extract the momentum dependence of the heavy quark drag and diffusion coefficients in a non-perturbatively interacting thermal, non-Abelian plasma.

India

Harshit Pandey

Sayantan Sharma

Momentum dependence of heavy quark diffusion in a thermal gluonic plasma on the lattice

Vector-like leptons (VLLs) are well-motivated candidates for physics beyond the standard model. We investigate the sensitivity of the 6 TeV muon collider to the neutral doublet VLL (denoted by $\textit{N}$) via its pair production in an SU(2) $$_L$$ doublet model with hypercharge $$Y=-\frac{1}{2}$$ . Assuming mixing with muons, we study the subsequent decay $$N\rightarrow W^+ \mu ^-$$ and analyze two representative signals, namely $$4j2\mu $$ and $$2\ell 2\mu E\hspace{-5.83328pt}/$$ , arising from the hadronic and leptonic decays of the $\textit{W}$ boson, respectively. The signal and background events are simulated within a Monte Carlo framework, and a cut-based analysis is performed at the 6 TeV muon collider with an integrated luminosity $$\mathcal {L}=4$$ ab $$^{-1}$$ for the unpolarized and polarized beam configurations, $$(P_{\mu ^+},P_{\mu ^-})=(0,0)$$ and $$(P_{\mu ^+},P_{\mu ^-})=(-1,1)$$ . We consider VLL masses in the range of $$1300{-}2980$$ GeV and evaluate the corresponding search sensitivity. Our results show that the 6 TeV muon collider could provide strong sensitivity to neutral doublet VLLs through the $$4j2\mu $$ and $$2\ell 2\mu E\hspace{-5.83328pt}/$$ signals, particularly for the idealized fully polarized beam configuration, under the detector, polarization, luminosity and background assumptions adopted in this analysis.

Chong-Xing Yue

Mei-Shu-Yu Wang

Xin-Yang Li

Si-Yu Zhang

Prospects for probing neutral vector-like leptons via pair production at a muon collider

According to the formulation of the charged large $\textit{D}$ membrane paradigm, an arbitrary dynamic black hole solution to a theory of gravity with a U(1) gauge field is dual to the dynamics of a membrane in a non-gravitational background. This membrane is endowed with a stress-energy tensor and a charge current, whose conservation equations govern its dynamics. In this work, we demonstrate that the dynamics of these membrane configurations (at the leading nontrivial order in 1/$\textit{D}$) can be mapped to a relativistic charged fluid, establishing a correspondence for asymptotically flat black holes with a particular class of fluid systems. Unlike the standard AdS/Hydrodynamics correspondence, this dual fluid does not reside on an asymptotic boundary, but is localised strictly on the non-gravitational membrane worldvolume. By evaluating the system in both the Eckart and Landau frames, we systematically extract the out-of-equilibrium transport coefficients. We find that the fluid is governed by a negative effective thermal conductivity and a negative heat capacity. This mechanism provides a hydrodynamic interpretation of thermodynamic stability, effectively translating the previously established quasinormal mode damping of the large-$\textit{D}$ Reissner-Nordström geometry into the language of fluid dynamics.

Supratim Halder

Manu Kurian

Mangesh Mandlik

A fluid dual to the charged large $\textit{D}$ membrane paradigm