Recent discoveries of exotic hadrons, which cannot be classified within the conventional quark model of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math> mesons and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mi>q</mi><mi>q</mi></math> baryons, strongly imply the existence of dynamically generated hadronic molecules. Some of these hadron-hadron interactions are accompanied by coupled-channel effects, which remain challenging to quantitatively determine. In this work, we demonstrate that femtoscopy provides a sensitive probe of such coupled-channel dynamics. We calculate correlation functions for the double-strangeness pentaquark candidates <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mrow><mi>c</mi><mi>s</mi><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4493</mn><mo stretchy="false">)</mo></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math>) and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mrow><mi>c</mi><mi>s</mi><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4633</mn><mo stretchy="false">)</mo></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math>), revealing clear signatures of the attractive interactions that can form bound states. The results are markedly different from those obtained in scenarios that neglect off-diagonal transitions, highlighting the importance of coupled-channel effects for understanding the structure of these hadrons.

China

Zheng-Ting Lai

Jun-Xu Lu

Zhi-Wei Liu

Brazil

A. Martínez Torres

K.P. Khemchandani

Li-Sheng Geng

Revealing the nature of double-strangeness pentaquark states via femtoscopic correlation functions

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.

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

We apply the generalized effective-range expansion of Du et al. [<a href="http://dx.doi.org/10.1103/cwdt-dj6z">Phys. Rev. Lett. 135, 011903 (2025)</a>], which incorporates the left-hand cut from one-pion exchange to low-energy neutron–proton scattering in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><msub><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow><mprescripts></mprescripts><none></none><mrow><mn>1</mn></mrow></mmultiscripts></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><msub><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></mrow></math> channels. The amplitude zero for the center-of-mass momentum near 0.35 GeV in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><msub><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow><mprescripts></mprescripts><none></none><mrow><mn>1</mn></mrow></mmultiscripts></mrow></math> channel is naturally accommodated within this framework. We extract the pole position, scattering length, effective range, shape parameter, and the pseudoscalar pion–nucleon coupling constant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>g</mi><mrow><mi>π</mi><mi>N</mi></mrow><mn>2</mn></msubsup><mo>/</mo><mo stretchy="false">(</mo><mn>4</mn><mi>π</mi><mo stretchy="false">)</mo></math> at different expansion orders. The low-energy parameters are stable and consistent with established values, while <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>g</mi><mrow><mi>π</mi><mi>N</mi></mrow><mn>2</mn></msubsup><mo>/</mo><mo stretchy="false">(</mo><mn>4</mn><mi>π</mi><mo stretchy="false">)</mo></math> exhibits larger uncertainties. The extraction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>g</mi><mrow><mi>π</mi><mi>N</mi></mrow><mn>2</mn></msubsup><mo>/</mo><mo stretchy="false">(</mo><mn>4</mn><mi>π</mi><mo stretchy="false">)</mo></math> is data driven, relying on the analytic constraints from the left-hand cut and phase-shift data within the one-pion-exchange approximation. Despite larger uncertainties compared to high-precision extractions, the consistency with established values demonstrates that this framework can probe the left-hand-cut singularity.

Bo-Yang Liu

Bing Wu

Ji-Wei Fu

Meng-Lin Du

Feng-Kun Guo

Germany

Ulf-G. Meißner

Extraction of the pion-nucleon coupling constant using the effective-range expansion with the left-hand cut

We establish the multipole structure of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">→</mo><mi mathvariant="normal">Δ</mi></math> transition at the level of the generalized parton distributions (GPDs). We decompose the four transition GPDs into one monopole, two dipole, and one quadrupole components in the transverse plane by a multipole expansion of the covariant transition matrix element in terms of the three-dimensional spin-transition tensors and the transverse momentum transfer. These multipole components are in one-to-one correspondence with the light-front helicity amplitudes. In the zero-skewness limit, the multipole GPDs define impact-parameter transition densities, which generalize the transverse transition charge densities to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>-dependent level. These transition densities arise from nondiagonal matrix elements between two distinct hadronic states and must therefore be distinguished from the diagonal densities of the nucleon and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi></math>. The multipole transition densities visualize the monopole, dipole, and quadrupole structures of the partonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">→</mo><mi mathvariant="normal">Δ</mi></math> transition in the transverse plane.

South Korea

June-Young Kim

Hyun-Chul Kim

Multipole structure of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo stretchy="false">→</mo><mi mathvariant="normal">Δ</mi></math> transition generalized parton distributions

We study the origin of the nonmonotonic magnetic field dependence of the lowest charged pion excitation observed in lattice QCD. In a magnetic field, the charged pion mixes with the longitudinally polarized charged rho meson, which shares the same quantum numbers. Within the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>SU</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></mrow><mi>f</mi></msub></mrow></math> Nambu–Jona-Lasinio model supplemented by a gauge invariant tree-level <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>π</mi><mtext>−</mtext><mi>ρ</mi></mrow></math> mixing operator constrained by the experimental <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>ρ</mi><mo>±</mo></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>±</mo></msup><mi>γ</mi></math> decay width, we compare four mass extraction schemes: rest mass reconstruction, local bosonization, direct determinant solving with Landau projection, and near-pole expansion. The rest mass scheme cannot reproduce the lattice type turnover, while in the local derivative expansion scheme the turnover presence but is weak which occurs at large magnetic field. By contrast, the direct determinant and near-pole schemes both retain a robust nonmonotonic lowest mode. The former is most faithful to the Landau level kinematics of the charged excitation, while the latter most clearly shows that residue suppression enhances the effective mixing after canonical normalization. Our results indicate that the lattice behavior is a genuine quasiparticle mixing effect, but one whose robustness depends crucially on how the charged meson pole structure is extracted in a magnetic field.

Ziyue Wang

Comparative study of mass extraction schemes and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>π</mi></mrow><mrow><mo>±</mo></mrow></msup><mtext>−</mtext><msup><mrow><mi>ρ</mi></mrow><mrow><mo>±</mo></mrow></msup></mrow></math> mixing

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.

Italy

F. Palumbo

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

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 masses of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup></math> P-wave charmoniumlike and bottomoniumlike tetraquark states are calculated in a constituent quark model where the Cornell-like potential and Breit-Fermi interaction are employed. All model parameters were imported from previous work, and predetermined by studying the low-lying conventional S- and P-wave light, charmed, bottom, charmonium, and bottomonium meson mass spectra. The lowest <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup></math> tetraquark mass is predicted to be around 4.15 GeV. The decay widths of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup></math> P-wave tetraquark states are calculated for possible two-body strong decay channels within the rearrangement mechanism, including <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mi>J</mi><mo>/</mo><mi>ψ</mi></math> for charmoniumlike tetraquarks, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi><msub><mi>χ</mi><mrow><mi>b</mi><mi>J</mi></mrow></msub></math> for bottomoniumlike tetraquarks. The theoretical results are compared with the selected exotic states, also known as Y states, and tentative assignments are suggested. This study suggests that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>4230</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>4360</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>4660</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>10753</mn><mo stretchy="false">)</mo></math> may be P-wave tetraquark states and that multiple states might exist around 4.36 GeV.

Thailand

Zheng Zhao

Attaphon Kaewsnod

Kai Xu

Nattapat Tagsinsit

Xuyang Liu

Ayut Limphirat

Yupeng Yan

Study of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup><mtext> </mtext><mtext> </mtext><mi>P</mi></math>-wave charmoniumlike and bottomoniumlike tetraquark spectroscopy

Evaluating quantum loop corrections to curvature perturbations in non-attractor inflation presents theoretical ambiguities. A crucial aspect of this challenge arises from unconstrained finite contributions to renormalization counterterms and from regularization-scheme dependence. In this work, we derive Ward identities via the path integral formalism based on the large gauge symmetry of the background-perturbation split. These identities are shown to impose nontrivial, model-independent constraints on the renormalization procedure. Provided the ultraviolet completion respects this symmetry, the Ward identities constrain the infrared evolution of the power spectrum and fix the residual finite ambiguity. This symmetry-based framework offers a systematic criterion for addressing recent theoretical discrepancies concerning one-loop corrections in ultra-slow-roll inflation.

Cheng-Jun Fang

Zong-Kuan Guo

Fixing the renormalization of inflationary loops via Ward identities

In this paper, we discuss the entanglement phase transition of pseudo entropy in CFTs. We focus on the case where the in-state and the out-state are different boundary states related by boundary condition changing operators. We compute the pseudo entropy with BCFT methods and find a phase transition with respect to the conformal weight of the boundary condition changing operators. For holographic CFTs, we confirm that the CFT results match that evaluated in AdS.

Hiroki Kanda

Tadashi Takayanagi

Zixia Wei

CFT derivation of entanglement phase transition in pseudo entropy