We measure the time- and phase-space-integrated <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetry <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">A</mi><mrow><mi>C</mi><mi>P</mi></mrow></msub></math> in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math> decays reconstructed in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></mrow><mo stretchy="false">→</mo><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover></mrow></math> events collected by the Belle II experiment from 2019 to 2022. This sample corresponds to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>428</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. We require <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup></math> mesons to be produced in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><mo stretchy="false">→</mo><msup><mi>D</mi><mn>0</mn></msup><msup><mi>π</mi><mo>+</mo></msup></math> decays to determine their flavor at production. Control samples of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>−</mo></msup><msup><mi>π</mi><mo>+</mo></msup></math> decays are used to correct for reconstruction-induced asymmetries. The result, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="script">A</mi></mrow><mrow><mi>C</mi><mi>P</mi></mrow></msub><mo stretchy="false">(</mo><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow><mo stretchy="false">)</mo><mo>=</mo><mspace linebreak="goodbreak"></mspace><mo stretchy="false">(</mo><mn>0.29</mn><mo>±</mo><mn>0.27</mn><mo>±</mo><mn>0.13</mn><mo stretchy="false">)</mo><mo>%</mo></mrow></math>, where the first uncertainty is statistical and the second systematic, is the most precise result to date and is consistent with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> conservation.

M. Abumusabh

I. Adachi

L. Aggarwal

H. Ahmed

Y. Ahn

H. Aihara

N. Akopov

S. Alghamdi

M. Alhakami

A. Aloisio

N. Althubiti

K. Amos

N. Anh Ky

D.M. Asner

H. Atmacan

T. Aushev

R. Ayad

V. Babu

H. Bae

N.K. Baghel

S. Bahinipati

P. Bambade

Sw. Banerjee

M. Barrett

M. Bartl

J. Baudot

A. Beaubien

F. Becherer

J. Becker

J.V. Bennett

F.U. Bernlochner

V. Bertacchi

M. Bertemes

E. Bertholet

M. Bessner

S. Bettarini

V. Bhardwaj

B. Bhuyan

F. Bianchi

T. Bilka

D. Biswas

A. Bobrov

D. Bodrov

G. Bonvicini

J. Borah

A. Boschetti

A. Bozek

M. Bračko

P. Branchini

R.A. Briere

T.E. Browder

A. Budano

S. Bussino

Q. Campagna

M. Campajola

G. Casarosa

C. Cecchi

P. Chang

P. Cheema

L. Chen

B.G. Cheon

C. Cheshta

H. Chetri

K. Chilikin

J. Chin

K. Chirapatpimol

H.E. Cho

K. Cho

S.J. Cho

S.K. Choi

S. Choudhury

J.A. Colorado-Caicedo

I. Consigny

L. Corona

J.X. Cui

S. Das

E. De La Cruz-Burelo

S.A. De La Motte

G. De Nardo

G. De Pietro

R. de Sangro

M. Destefanis

A. Di Canto

Z. Doležal

I. Domínguez Jiménez

T.V. Dong

X. Dong

M. Dorigo

G. Dujany

P. Ecker

D. Epifanov

J. Eppelt

R. Farkas

P. Feichtinger

T. Ferber

T. Fillinger

C. Finck

G. Finocchiaro

F. Forti

B.G. Fulsom

Measurement of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetry in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math> decays at Belle II

We investigate the velocity-dependent one-scale model to the case of one cosmic F-string and two D-strings as color flux tubes in pure Spin(<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>4</mn><mi>N</mi></math>) gauge theory. We analytically calculate the scaling string density as a function of the reconnection probabilities, and confirm our results with numerical calculations. We also determine the timescale at which the string density reaches the scaling regime, and find that for certain values of the reconnection probability, the scaling time can become extremely large, by many orders of magnitude. This leads to a characteristic suppression signature of the gravitational-wave signal at high frequencies, which may become observable in the frequency range of future interferometric gravitational-wave observations.

Japan

Kazuto Nakamura

Masaki Yamada

Delayed scaling of multitype cosmic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>F</mi></math>- and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math>-strings in velocity-dependent one-scale models

In the present work, we propose to investigate the production of $$d_{N \Omega }$$ in the $$\Omega ^{-} d \rightarrow p d_{N \Omega }^-$$ process by utilizing an effective Lagrangian approach, where $$d_{N \Omega }$$ is identified as $$N\Omega $$ bound state with the binding energy $$E_{b}=2.46$$ MeV. Experimentally, the J-PARC hadron facility proposed to investigate the $$K^{-}p \rightarrow \Omega ^{-} \bar{K}^{(*)0} K^{+}$$ process, which is expected to yield an $$\Omega $$ beam with the momentum of approximately 3 GeV. Additionally, theoretical studies of the $$\psi (2S) \rightarrow \Omega ^{-} \bar{\Omega }^{+}$$ process at BESIII provided an $$\Omega $$ beam with the momentum of 774 MeV. Considering these two potential $$\Omega $$ beam sources, our estimations show that for the $$\Omega ^{-} d \rightarrow p d_{N \Omega }^-$$ process, the cross sections are $$\Big (329.7^{+26.9}_{-49.6}\Big )$$ $$\mu $$ b, $$\Big (174.0^{+26.5}_{-38.2}\Big )$$ $$\mu $$ b, $$\Big (16.9^{+7.4}_{-7.7}\Big )$$ $$\mu $$ b, and $$\Big (2.0^{+1.8}_{-1.4}\Big )$$ $$\mu $$ b at $$P_{\Omega } =$$ 0.7, 0.9, 2.0, and 4.0 GeV, respectively, where the central values are estimated with $$\Lambda _{r}=1.0$$ GeV, and the errors come from the variation of $$\Lambda _{r}$$ from 0.8 to 1.2 GeV. We also estimate the differential cross sections, which reach the maximum at the forward angle limit. In addition, since the $$d_{N \Omega }$$ dibaryon predominantly decays into $$\Xi \Lambda $$ . Therefore, we further investigate the $$\Omega ^{-} d \rightarrow p \Xi ^- \Lambda $$ process and estimate the relevant cross sections. It is expected that the present estimations can be tested by further experimental measurements at J-PARC and STCF in the future.

China

Quan-Yun Guo

Jing Liu

Dian-Yong Chen

$$d_{N \Omega }$$ production in $$\Omega d$$ scattering process

Holographic D-brane constructions, governed by the Dirac-Born-Infeld (DBI) action, play a central role in the AdS/CFT correspondence, particularly in applications to quantum chromodynamics and condensed matter systems. In this work, we demonstrate how to equip these bottom-up holographic models with dynamical boundary gauge fields, thereby introducing electromagnetic interactions into their dual field theory descriptions. As a direct application of this formalism, we compute the dispersion relations of the lowest quasinormal modes around both equilibrium and nonequilibrium steady states, and show that their behavior matches the predictions from hydrodynamics with dynamical U(1) symmetry.

Yong Ahn

Matteo Baggioli

Spain

Hyun-Sik Jeong

Masataka Matsumoto

Holographic D-brane constructions with dynamical gauge fields

The Belle Collaboration recently reported a potential candidate for the spin-2 $$D^*\bar{D}^*$$ partner of the $\textit{X}$(3872), denoted as $$X_2$$ , with a mass of $$(4014.3\pm 4.0\pm 1.5)$$ MeV and a width of $$(4\pm 11\pm 6)$$ MeV. Assuming the $$X_2$$ as a $$D^*\bar{D}^*$$ molecular state, we calculate its hidden charm decay $$X_2 \rightarrow \pi ^+ \pi ^- \eta _{c}$$ via box loop diagram using an effective Lagrangian approach. To investigate the dependence of the decay width on the molecular structure, we consider four different phase angles: $$\theta =0$$ , $$\pi /6$$ , $$\pi /4$$ , and $$\pi /2$$ . The decay width is found to be sensitive to the mass of the $$X_2$$ . The decay partial widths are predicted to be on the order of 1 keV. We expect that the present calculations, performed in the molecular framework, would provide useful guidance for future experimental studies.

Hao-Dong Cai

Gang Li

Shi-Dong Liu

Hidden charmed decays of spin-2 partner of $\textit{X}$(3872) within $$D^*\bar{D}^*$$ molecular framework

The energy-momentum tensor form factor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math> is finite and negative in hadronic models and lattice QCD when only strong forces are included. However, when electromagnetic forces are considered, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math> of charged hadrons undergoes a dramatic change: at small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi></math>, it changes sign and diverges like <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>/</mo><msqrt><mrow><mo>−</mo><mi>t</mi></mrow></msqrt></math> as shown for the proton in the classical model by Białynicki-Birula based on residual nuclear forces which can be understood as a mean field approach. We construct an analogous neutron model and show that this framework accurately explains the electromagnetic proton-neutron mass difference. We demonstrate that, after appropriately rescaling the residual nuclear forces, the model can reproduce lattice data on the nucleon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math> up to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mo>−</mo><mi>t</mi><mo stretchy="false">)</mo><mo>≲</mo><mn>1</mn><mtext> </mtext><mtext> </mtext><msup><mi>GeV</mi><mn>2</mn></msup></mrow></math> as well as QED effects. Based on this realistic model description, we show that the proton and neutron <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math> form factors are practically indistinguishable down to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mo>−</mo><mi>t</mi><mo stretchy="false">)</mo><mo>≈</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup><mtext> </mtext><mtext> </mtext><msup><mi>GeV</mi><mn>2</mn></msup></mrow></math>, far below what can currently be accessed experimentally. We conclude that in the foreseeable future the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math> form factors of the proton and neutron will practically look the same in experiments and phenomenology.

United States

Andrea Mejia

Peter Schweitzer

Energy-momentum tensor form factor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>D</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></math> of the proton and neutron

We present a neural network wave function framework for solving non-Abelian lattice gauge theories in a continuous group representation. Using a combination of SU(2) equivariant neural networks alongside an SU(2) invariant, physics-inspired ansatz, we learn a parametrization of the ground state wave function of SU(2) lattice gauge theory in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math> dimensions. Our method, performed in the Hamiltonian formulation, has a straightforward generalization to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SU</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></mrow></math>. We benchmark our approach against a solely invariant ansatz by computing the ground state energy, demonstrating the need for bespoke gauge equivariant transformations. We evaluate the Creutz ratio and average Wilson loop, and obtain results in strong agreement with perturbative expansions. Our method opens up an avenue for studying lattice gauge theories beyond one dimension, with efficient scaling to larger systems, and in a way that avoids both the sign problem and any discretization of the gauge group.

Netherlands

Thomas Spriggs

Eliska Greplova

Switzerland

Juan Carrasquilla

Jannes Nys

Accurate Ground States of SU(2) Lattice Gauge Theory in <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> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>3</mn><mo>+</mo><mn>1</mn><mi mathvariant="normal">D</mi></mrow></math>

In this work, we construct the <italic>D</italic>-wave isoscalar <math altimg='si1.svg'><mrow><mi>&#960;</mi><mi>&#960;</mi><mo linebreak='goodbreak'>/</mo><mi>K</mi><mover accent='true'><mi>K</mi><mo>&#175;</mo></mover></mrow></math> coupled-channel Omn&#232;s matrix, formulated to satisfy unitarity, analyticity, and the appropriate asymptotic behavior. We employ a two-channel <italic>K</italic>-matrix model containing poles associated with the <italic>f</italic> <inf>2</inf>(1270) and <math altimg='si7.svg'><mrow><msubsup><mi>f</mi><mrow><mn>2</mn></mrow><mo>&#8242;</mo></msubsup><mrow><mo>(</mo><mn>1525</mn><mo>)</mo></mrow></mrow></math> resonances. The resulting unitary scattering matrix, which reproduces the experimental <italic>&#960;&#960;</italic>&#8239;&#8594;&#8239; <italic>&#960;&#960;</italic> and <math altimg='si27.svg'><mrow><mi>&#960;</mi><mi>&#960;</mi><mo>&#8594;</mo><mi>K</mi><mover accent='true'><mi>K</mi><mo>&#175;</mo></mover></mrow></math> data and PDG information, serves as input to the homogeneous two-channel Muskhelishvili-Omn&#232;s equation. We compare our Omn&#232;s matrix with previous constructions based on <math altimg='si27.svg'><mrow><mi>&#960;</mi><mi>&#960;</mi><mo>&#8594;</mo><mi>K</mi><mover accent='true'><mi>K</mi><mo>&#175;</mo></mover></mrow></math> phases extracted from sums of Breit-Wigner amplitudes. The Omn&#232;s matrix developed here provides a reliable dispersive input for form-factor calculations and resonance studies in the tensor-meson sector. As an application, we show that it enables a simultaneous and accurate description of the BESIII <italic>J</italic>/ <italic>&#968;</italic>&#8239;&#8594;&#8239; <italic>&#960;</italic> 0 <italic>&#960;</italic> 0 <italic>&#947;</italic> and <italic>J</italic>/ <italic>&#968;</italic>&#8239;&#8594;&#8239; <italic>K<inf>S</inf>K<inf>S</inf>&#947;</italic> spectra in the <math altimg='si2.svg'><mrow><mi>J</mi><mo linebreak='goodbreak'>=</mo><mn>2</mn></mrow></math> electric-dipole (E1) partial wave.

Germany

Igor Danilkin

Oleksandra Deineka

Emilie Passemar

Marc Vanderhaeghen

Coupled-channel Omnès matrix for the <italic>D</italic>-wave isoscalar <math altimg='si1.svg'><mrow><mi>&#960;</mi><mi>&#960;</mi><mo linebreak='goodbreak'>/</mo><mi>K</mi><mover accent='true'><mi>K</mi><mo>&#175;</mo></mover></mrow></math> system and its application to <italic>J</italic>/ <italic>&#968;</italic>&#8239;&#8594;&#8239; <italic>&#960;</italic> 0 <italic>&#960;</italic> 0 <italic>&#947;</italic>,&#8201; <italic>K<inf>S</inf>K<inf>S</inf>&#947;</italic>

We consider supersymmetric solutions of $\textit{D}$ = 5 Euclidean gauged supergravity coupled to an arbitrary number of vector multiplets. We consider solutions that admit both the R-symmetry Killing vector, $$ \mathcal{K} $$ , constructed as a bilinear in the Killing spinor, as well as an additional Killing vector $\textit{ℓ}$. Using $\textit{ℓ}$ to perform a dimensional reduction to $\textit{D}$ = 4, $$ \mathcal{N} $$ = 2 gauged supergravity, we show how the $\textit{D}$ = 5 on-shell action can be computed using equivariant localization. We illustrate the formalism with some examples, computing the supersymmetric Casimir energy and the supersymmetric index of the dual SCFT without using the explicit supergravity solutions.

Pietro Genolini

United Kingdom

Jerome Gauntlett

Yusheng Jiao

Jaeha Park

James Sparks

Equivariant localization for $\textit{D}$ = 5 gauged supergravity

An amplitude analysis of the decay $$ {D}^0\to {K}_S^0{\pi}^0{\pi}^0 $$ is performed to determine the relative magnitudes and phases of different intermediate processes. The analysis uses $\textit{e}$ $\textit{e}$ collision data collected at the center-of-mass energy of 3.773 GeV by the BESIII detector corresponding to an integrated luminosity of 20.3 fb . The absolute branching fraction of $$ {D}^0\to {K}_S^0{\pi}^0{\pi}^0 $$ is measured to be (1.026 $\textit{±}$ 0.008 $\textit{±}$ 0.009 )%. The dominant intermediate process is $$ {D}^0\to {\overline{K}}^{\ast }{(892)}^0\left(\to {K}_S^0{\pi}^0\right){\pi}^0 $$ , with a branching fraction of (4.10 $\textit{±}$ 0.10 $\textit{±}$ 0.07 ) $\textit{×}$ 10 .

M. Ablikim

Russia

M. Achasov

Sweden

P. Adlarson

X. Ai

R. Aliberti

Italy

A. Amoroso

Q. An

Y. Bai

O. Bakina

Y. Ban

H.R. Bao

Poland

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M. Bertani

D. Bettoni

E. Bianco

A. Bortone

I. Boyko

R. Briere

A. Brueggemann

H. Cai

M. Cai

X. Cai

A. Calcaterra

G. Cao

N. Cao

Türkiye

S. Cetin

X. Chai

J. Chang

G. Che

Y. Che

C. Chen

Chao Chen

G. Chen

H. Chen

M. Chen

S. Chen

T. Chen

X. Chen

Amplitude analysis and branching fraction measurement of the decay $$ {D}^0\to {K}_S^0{\pi}^0{\pi}^0 $$