We consider a movable conducting plate of finite mass, between two fixed ones, whose mechanical degrees of freedom are treated quantum-mechanically and bound to its equilibrium position by a harmonic potential. The movable wall is thus subjected to quantum fluctuations of its position. This creates a system of two subcavities separated by the movable fluctuating plate, and two massless one-dimensional scalar fields, one in each subcavity. This system is described by an appropriate generalization of the Law Hamiltonian. The presence of the movable wall yields an effective plate-fields interaction, as well as an effective interaction between the field modes. We obtain, at the second order in perturbation theory, the ground state of the interacting system and the reduced density operator of the fields in each subcavity by tracing out the wall’s degrees of freedom. We calculate the entanglement between two field modes, one in each cavity, by evaluating analytically the negativity; we then also evaluate numerically the total multimode negativity. Our results show that in both cases the fields in the two subcavities are entangled, in contrast to the case in which the wall is fixed in space. We discuss the amount of the field entanglement present as a function of relevant physical parameters of the system such as the mass and oscillation frequency of the movable wall, its distance from the fixed walls and the frequencies of the field modes considered.

Italy

Luca Giovanni Cammarata

Tommaso Fazio

Roberto Passante

Lucia Rizzuto

Entanglement generation between field modes mediated by a fluctuating conducting wall

We investigate the lineshape of the <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><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> cross section in the vicinity of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>+</mo><mi mathvariant="italic">c</mi><mo>.</mo><mi mathvariant="italic">c</mi><mo fontstyle="italic">.</mo></math> threshold, where the “so-called” <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math> is observed in the <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><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> channel. To take into account the possible <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>+</mo><mi mathvariant="italic">c</mi><mo>.</mo><mi mathvariant="italic">c</mi><mo fontstyle="italic">.</mo></math> open channel effects or possible contributions from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math>, we include the intermediate meson loop transitions in <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><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math>. As a consequence, a triangle singularity (TS) is fulfilled which can produce nontrivial structures in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>π</mi></math> invariant-mass spectrum. Moreover, the TS transition also allows access to exotic quantum number of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mi>I</mi><mo>,</mo><msup><mi>J</mi><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>C</mi><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>1</mn><mo>,</mo><msup><mn>1</mn><mrow><mo>−</mo><mo stretchy="false">(</mo><mo>−</mo><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo></math> in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>π</mi></math> invariant-mass spectrum. We present predictions for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>π</mi></math> invariant-mass spectrum and our results clarify the different manifestations of the kinematic effects and genuine resonances. In particular, we show that resonance structures arising from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> scatterings or hidden charm tetraquark state with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mi>I</mi><mo>,</mo><msup><mi>J</mi><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>C</mi><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>1</mn><mo>,</mo><msup><mn>1</mn><mrow><mo>−</mo><mo stretchy="false">(</mo><mo>−</mo><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo></math> can be identified by the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>π</mi></math> invariant mass spectrum. It can provide a theoretical guidance for future experimental searches for these exotic candidates.

China

Jun Wang

Qiang Zhao

Study of the <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><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> lineshape near the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mo>+</mo><mi fontstyle="italic" mathvariant="italic">c</mi><mo>.</mo><mi mathvariant="italic">c</mi><mo fontstyle="italic">.</mo></mrow></math> threshold and possible signals for exotic hidden charm states

Solving the classical equations of motion in general relativity recursively, we consider the metric of a spatially localized and stationary source of matter. Having in mind a star of general composition, we characterize it by means of its infinite set of mass and current multipoles. Specializing to de Donder gauge we set up the recursive equations that produce the metric outside the star to any desired order in perturbation theory, expanded both in Newton’s constant and in the order of multipoles. Up to second post-Minkowskian order we express the result to any order in the multipole expansion in terms of generalized (tensor) bubble integrals in momentum space and a corresponding simple expansion in inverse distances. In a special corner of the space of multipoles we recover the Kerr black hole solution to the given order. By tweaking just slightly the multipoles away from the Kerr limit the metric will describe stars that are Kerr-like and yet are not black holes. A subtlety with respect to the gauge ambiguity of de Donder gauge is also pointed out.

Denmark

Poul H. Damgaard

South Korea

Hojin Lee

Kanghoon Lee

Tabasum Rahnuma

Gravitational metric of a star

Under the hypothesis that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1370</mn><mo stretchy="false">)</mo></math> is a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>κ</mi><mover accent="true"><mi>κ</mi><mo stretchy="false">¯</mo></mover></math> molecular state, we calculate the partial widths of its various decay channels, including the two-body decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mi>η</mi></math> and the four-body decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><mi>ρ</mi><mo>/</mo><mi>σ</mi><mi>σ</mi><mo stretchy="false">→</mo><mn>4</mn><mi>π</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mi>π</mi><mi>π</mi></math>. Treating the coupling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mrow><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1370</mn><mo stretchy="false">)</mo><mi>κ</mi><mover accent="true"><mi>κ</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> as a free parameter, we find that a value of 25–40 GeV brings the total width of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1370</mn><mo stretchy="false">)</mo></math> in line with the measured value 200–500 MeV. At the center-of-mass energy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>1.37</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, the channels that mainly contribute to the total width are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>4</mn><mi>π</mi></math> ranked as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Γ</mi><mo stretchy="false">(</mo><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">)</mo><mo>&gt;</mo><mi mathvariant="normal">Γ</mi><mo stretchy="false">(</mo><mn>4</mn><mi>π</mi><mo stretchy="false">)</mo><mo>&gt;</mo><mi mathvariant="normal">Γ</mi><mo stretchy="false">(</mo><mi>π</mi><mi>π</mi><mo stretchy="false">)</mo></math> with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mrow><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1370</mn><mo stretchy="false">)</mo><mi>κ</mi><mover accent="true"><mi>κ</mi><mo stretchy="false">¯</mo></mover></mrow></msub><mo>=</mo><mn>35</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. Around 1.37 GeV, the decay widths of the two-body channels <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mi>η</mi></math> remain stable with variation in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt></math>, whereas the decay widths of the four-body channels <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>4</mn><mi>π</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mi>π</mi><mi>π</mi></math> increase continuously with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt></math>. Most current data are model dependent and conflicting, particularly regarding the conclusion of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>4</mn><mi>π</mi></math> dominance and the ratio of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi></math> decay widths. The current data cannot rule out the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>κ</mi><mover accent="true"><mi>κ</mi><mo stretchy="false">¯</mo></mover></math> assignment for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1370</mn><mo stretchy="false">)</mo></math>. Further reliable theoretical and experimental analyses of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1370</mn><mo stretchy="false">)</mo></math> are required to reveal its nature.

Yin Cheng

Bing-Song Zou

Study of the decay pattern of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1370</mn><mo stretchy="false">)</mo></math> as a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>κ</mi><mover accent="true"><mi>κ</mi><mo stretchy="false">¯</mo></mover></math> molecular state

Neutrino rest mass enables left-handed states to “flip” to right-handed states and vice versa. In-medium effects can enhance the probability for such spin flip. We demonstrate that a full many-body calculation of this process in neutrino-dense environments can lead to spin-flip probabilities that exceed by orders of magnitude those calculated with mean-field treatments. We study simple configurations with a few neutrinos in well-defined momentum states, for which we show that the helicity conversion enhancement is connected to many-body momentum exchange. Such an effect would therefore be missed in a calculation that considers only forward processes. We speculate on the potential astrophysical implications of these results and the range of applicability of our calculation and its limitations.

United States

Yiheng Xu

Spain

Julien Froustey

George M. Fuller

Czechia

Lukáš Gráf

Amol V. Patwardhan

Neutrino helicity oscillations in astrophysical environments: A many-body approach

In our previous studies, we calculated the cross section for the production of free $\mu ^{+}\mu ^{-}$ pairs using a probability function dependent on the impact parameter, and also, we computed bound-free $e^{+}e^{-}$ pair production cross section. In this study, unlike the others, we obtained the cross section for the production of bound-free $e^{+}e^{-}$ pairs using the probability function dependent on the impact parameter. Here also, we simultaneously calculated the cross sections for producing free $\mu ^{+}\mu ^{-}$ with bound-free $e^{+}e^{-}$ pairs in relativistic Pb+Pb collisions at the LHC using Lorentz factors $\gamma =1500$ and $\gamma =3000$ reported in the literature. Our calculation is based on second-order perturbation theory, implemented by using Monte Carlo integration techniques. We present impact-parameter-dependent pair production probabilities for free $\mu ^{+}\mu ^{-}$ and bound-free $e^{+}e^{-}$ pair production processes. Notably, the bound-free $e^{+}e^{-}$ pair production was evaluated by using a formalism adapted from that of free $\mu ^{+}\mu ^{-}$ pair production. Our results obtained here for the free $\mu ^{+}\mu ^{-}$ with bound-free $e^{+}e^{-}$ pair production cross sections are compared with those from other theoretical methods available in the literature. This study aims to provide predictions that can be tested against future experimental data, thereby offering a valuable test of quantum electrodynamics (QED) in strong electromagnetic fields. Abstract Published by the Jagiellonian University 2026 authors

Türkiye

M. Yilmaz Şengül

Free $\mu ^{+}\mu ^{-}$ and Bound-free $e^{+}e^{-}$ Pair Production in Relativistic Heavy-ion Collisions

The multiplicity-dependent suppression of $$\Upsilon (nS)$$ excited states in high-multiplicity $\textit{pp}$ and $\textit{p}$Pb collisions is analysed using publicly available CMS and LHCb data; preliminary CMS Physics Analysis Summary results in $\textit{p}$Pb and light-ion collisions are used only as supporting cross-system evidence. Six complementary differential constraints are considered: cone isolation, azimuthal-sector equivalence, transverse sphericity, transverse-momentum ordering, forward- $$E_T$$ long-range correlation, and the pPb/Pbp forward-backward asymmetry. Taken together, these constraints disfavour mechanisms controlled solely by local track density or by total multiplicity, and are consistent with an early, globally correlated, topology-sensitive suppression pattern. The characteristic multiplicity scale at which suppression sets in is independently consistent with the onset of a qualitative change in soft-sector behaviour identified by Campanini and Ferri [35] from inclusive charged-particle observables. The result is a data-driven constraint map consistent with an early, coloured pre-hadronic environment, possibly involving a deconfined stage.

Renato Campanini

A multi-differential constraint map for quarkonium suppression mechanisms in high-multiplicity $\textit{pp}$ and $\textit{p}$Pb collisions

We present a new formulation for the mean-field propagation part of relativistic quantum molecular dynamics, simulating an <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math>-body system of interacting Gaussian wave packets via Lorentz scalar and vector potentials. Covariant equations of motion are derived based on the principle of least action with a weak form of mass-shell conditions and time-fixation constraints defined with respect to a chosen foliation. However, as is common with traditional relativistic quantum molecular dynamics, the dynamics exhibits a residual dependence on the chosen foliation, which is unavoidable because a finite number of interacting degrees of freedom is not strictly compatible with relativity. Nevertheless, we show that this dependence remains small for physically reasonable choices of the foliation in practical applications. By introducing a new approximation method to the spatial integral in the equations of motion, these covariant equations of motion can be solved with a computational cost comparable to that of conventional noncovariant quantum molecular dynamics. Furthermore, the new equations of motion accurately estimate the density-dependent potential, as demonstrated through comparison of the forces with the numerical integration. We apply them to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math>-body systems interacting via the Skyrme-type potentials or the relativistic mean field to simulate heavy-ion collisions. Our results show that the derived equations of motion provide a robust approximation to the dynamics of the full numerical integrations.

Japan

Yasushi Nara

Asanosuke Jinno

Koichi Murase

Covariant formulation of relativistic quantum molecular dynamics for a system of interacting wave packets

The twist-3 transverse spin-dependent nucleon structure function <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mn>2</mn></msub></math> arises in high-energy processes involving a transversely polarized nucleon. Its connection to quark-gluon correlations allows for an interpretation in terms of the average transverse color Lorentz force acting on unpolarized quarks inside a transversely polarized nucleon. In this work, we investigate this force using light-front wave functions obtained by diagonalizing the light-front Hamiltonian with quantum chromodynamics inputs within the basis light-front quantization approach. We evolve our results to a common scale of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>5</mn><mtext> </mtext><mtext> </mtext><msup><mi>GeV</mi><mn>2</mn></msup></math> and present the corresponding form factors in momentum space as well as the transverse force components in impact-parameter space. These distributions provide a complementary perspective on the Sivers asymmetry in transversely polarized deep-inelastic scattering. In the forward limit, we extract the twist-3 reduced matrix element <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>d</mi><mn>2</mn></msub></math>, and our results are found to be comparable with those from other theoretical calculations and experimental determinations.

Ziqi Zhang

Chandan Mondal

Siqi Xu

Xingbo Zhao

James P. Vary

Transverse force tomography inside a proton from basis light-front quantization

This Letter presents a lattice quantum chromodynamics (QCD) determination of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi><mi>π</mi></math> scattering amplitudes for the isospin-2 channel with angular momentum and parity <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>1</mn><mo>+</mo></msup></math>. The calculation is performed using unphysically heavy light-quark masses, corresponding to a pion mass of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><mo>≈</mo><mn>400</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, for which the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math> meson manifests as a narrow resonance. The analysis employs a previously developed formalism that nonperturbatively relates the finite-volume spectra of two- and three-pion systems to their infinite-volume scattering amplitudes. We combine earlier lattice QCD results for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi></math> systems with isospins 1 and 2 with new determinations of the isospin-2 three-pion finite-volume spectrum, obtained for three cubic, periodic lattice volumes with box length ranging from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>≈</mo><mn>4</mn><mo>/</mo><msub><mi>m</mi><mi>π</mi></msub></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>6</mn><mo>/</mo><msub><mi>m</mi><mi>π</mi></msub></math>. These combined data constrain the low-lying partial waves of the infinite-volume three-pion <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>K</mi></mrow></math> matrix, from which we solve a set of coupled integral equations to extract the corresponding scattering amplitudes.

Raúl A. Briceño

United Kingdom

Maxwell T. Hansen

Andrew W. Jackura

Robert G. Edwards

Christopher E. Thomas

Isotensor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi><mi>π</mi></math> Scattering with a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math>-Resonant Subsystem from QCD