We calculate the dimension-six <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">Δ</mi><mi>Q</mi><mo>=</mo><mn>0</mn></mrow></math> four-quark matrix elements describing heavy-meson lifetime ratios using the gradient flow with its short flow-time expansion (SFTX) as a renormalization procedure. On six RBC/UKQCD <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>-flavor domain-wall fermion ensembles, we determine flowed bag parameters for physical charm and strange quarks and match to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>MS</mi><mo stretchy="true">¯</mo></mover></math> scheme with perturbative SFTX coefficients through next-to-next-to-leading order (NNLO). A multiscale matching procedure using renormalization-group running improves the extrapolation to zero flow time. For the operators relevant to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi><mo stretchy="false">(</mo><msub><mi>D</mi><mi>s</mi></msub><mo stretchy="false">)</mo><mo>/</mo><mi>τ</mi><mo stretchy="false">(</mo><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">)</mo></math> at the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>SU</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></mrow><mi mathvariant="normal">F</mi></msub></mrow></math> symmetric point, we obtain <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow><mrow><mover accent="true"><mrow><mi>MS</mi></mrow><mrow><mo stretchy="true">¯</mo></mrow></mover></mrow></msubsup><mo stretchy="false">(</mo><mn>3</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo stretchy="false">)</mo><mo>=</mo><mn>1.0524</mn><mo stretchy="false">(</mo><mn>97</mn><mo stretchy="false">)</mo></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mn>2</mn></mrow><mrow><mover accent="true"><mrow><mi>MS</mi></mrow><mrow><mo stretchy="true">¯</mo></mrow></mover></mrow></msubsup><mo stretchy="false">(</mo><mn>3</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0.9621</mn><mo stretchy="false">(</mo><mn>70</mn><mo stretchy="false">)</mo></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>ε</mi></mrow><mrow><mn>1</mn></mrow><mrow><mover accent="true"><mrow><mi>MS</mi></mrow><mrow><mo stretchy="true">¯</mo></mrow></mover></mrow></msubsup><mo stretchy="false">(</mo><mn>3</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo stretchy="false">)</mo><mo>=</mo><mo>−</mo><mn>0.2275</mn><mo stretchy="false">(</mo><mn>76</mn><mo stretchy="false">)</mo></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>ε</mi></mrow><mrow><mn>2</mn></mrow><mrow><mover accent="true"><mrow><mi>MS</mi></mrow><mrow><mo stretchy="true">¯</mo></mrow></mover></mrow></msubsup><mo stretchy="false">(</mo><mn>3</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo stretchy="false">)</mo><mo>=</mo><mo>−</mo><mn>0.0005</mn><mo stretchy="false">(</mo><mn>8</mn><mo stretchy="false">)</mo></mrow></math> using a specific choice of evanescent operators. This is the first lattice-QCD determination of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mi>Q</mi><mo>=</mo><mn>0</mn></math> four-quark operators with a full error budget. It opens the path toward higher-precision predictions of heavy-meson lifetimes and similar quantities exhibiting operator mixing under renormalization.

United Kingdom

Germany

Matthew Black

Robert V. Harlander

Jonas T. Kohnen

Switzerland

Fabian Lange

Denmark

Antonio Rago

United States

Andrea Shindler

Oliver Witzel

Bag Parameters for Heavy Meson Lifetimes from a Lattice QCD Calculation at the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SU</mi><mo stretchy="false">(</mo><mn>3</mn><msub><mrow><mo stretchy="false">)</mo></mrow><mrow><mi mathvariant="normal">F</mi></mrow></msub></mrow></math>-symmetric Point

We find that heavy quark transport beyond leading logarithm at weak coupling is intrinsically non-Gaussian: the longitudinal momentum transfer distribution has asymmetric exponential tails that are crucial for equilibration dynamics. We show this by computing the leading-order momentum transfer kernel for relativistic heavy quarks in weakly coupled non-Abelian plasmas, matching perturbative momentum transfer on the thermal scale to hard-thermal-loop-resummed soft physics. This is the same structure previously found in strongly coupled holographic plasmas, showing that it is not peculiar to weak or strong coupling, conformality, or supersymmetry. We therefore expect that this is a robust feature that physical quark-gluon plasma should also exhibit.

Jean F. Du Plessis

Bruno Scheihing-Hitschfeld

Heavy Quark Transport Is Non-Gaussian beyond Leading Logarithm

Quantum simulation offers a powerful approach to studying quantum field theories, particularly <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mi mathvariant="normal">D</mi></mrow></math> quantum electrodynamics (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>QED</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math>) with Wilson fermions, which hosts a rich landscape of physical phenomena. A key challenge in lattice formulations is the proper realization of topological phases and the Chern-Simons terms, where fermion discretization plays a crucial role. In this Letter, we highlight the differences between staggered and Wilson fermions coupled to U(1) gauge fields in the Hamiltonian formulation. We analyze why staggered fermions fail to induce <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mi mathvariant="normal">D</mi></mrow></math> topological phases, while Wilson fermions admit a variety of topological phases including Chern insulator and quantum spin Hall phases. Additionally, we uncover a rich phase diagram for the two-flavor Wilson fermion model in the presence of a chemical potential. Our findings resolve existing ambiguities in Hamiltonian formulations and provide a theoretical foundation for future quantum simulations of lattice field theories with topological phases. We further outline connections to experimental platforms, offering guidance for implementations on near-term quantum computing architectures. A complementary presentation of the analytical calculations, the identification of robust topological structure and response, and extensive numerical results is contained in a joint submission [S. Bharadwaj et al., Phys. Rev. D 114, 094502 (2026)].

Sriram Bharadwaj

Emil Rosanowski

Simran Singh

Alice Di Tucci

Changnan Peng

Cyprus

Karl Jansen

Lena Funcke

China

Di Luo

Path to Quantum Simulations of Topological Phases: <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow><mo stretchy="false">)</mo><mi mathvariant="normal">D</mi></mrow></math> Quantum Electrodynamics with Wilson Fermions

We analyze the two-dimensional Palatini Gauss-Bonnet theory on an infinite strip (product of a finite interval with the infinite line, corresponding to “time”). The theory has only boundary degrees of freedom. Its phase space is the cotangent bundle to the group manifold of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>L</mi><mo stretchy="false">(</mo><mn>2</mn><mo>,</mo><mi mathvariant="bold">R</mi><mo stretchy="false">)</mo></math>, subject to a (first-class) constraint quadratic in the momenta. With the simplest choice of boundary Hamiltonian, namely <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>H</mi><mo>=</mo><mn>0</mn></math>, the theory is shown to describe geodesics on the group manifold of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>L</mi><mo stretchy="false">(</mo><mn>2</mn><mo>,</mo><mi mathvariant="bold">R</mi><mo stretchy="false">)</mo></math>, with a “mass” determined by the Palatini Gauss-Bonnet coupling constant. Other choices of boundary Hamiltonians compatible with gauge invariance are also possible. The symmetry group contains (left and right) group translations on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>L</mi><mo stretchy="false">(</mo><mn>2</mn><mo>,</mo><mi mathvariant="bold">R</mi><mo stretchy="false">)</mo></math>. These are “boundary symmetries” from the bulk point of view, with one copy acting on one end of the interval and the other copy acting on the other end. Comments on the quantum theory are also given.

Chile

Máximo Bañados

France

Marc Henneaux

Exact Solution of Two-Dimensional Palatini Gauss-Bonnet Theory on a Strip

Framing anomaly is a key property of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mi>d</mi></math> chiral topological orders, for it reveals that the chirality is an intrinsic bulk property of the system, rather than a property that requires a boundary between two systems. Understanding framing anomaly in lattice models is particularly interesting, as concrete, solvable lattice models of chiral topological orders are rare. In a previous work [Z.-A. Xu and J.-Y. Chen, <a href="http://dx.doi.org/10.1007/JHEP08(2025)062">J. High Energy Phys. 08 (2025) 062</a>.], we defined and solved the U(1) Chern-Simons-Maxwell theory on spacetime lattice, showing its chiral edge mode and the associated gravitational anomaly on boundary. In this Letter, we show its framing anomaly in the absence of boundary by computing the expectation of a lattice version of the modular <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math> operator in the ground subspace on a spatial torus, from which we extract that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">⟨</mo><mi>T</mi><mo stretchy="false">⟩</mo></math> has a universal phase of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>2</mn><mi>π</mi><mo>/</mo><mn>12</mn></math> as expected: <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>2</mn><mi>π</mi><mo>/</mo><mn>8</mn></math> from the Gauss-Milgram sum of the topological spins of the ground states, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>π</mi><mo>/</mo><mn>24</mn></math> from the framing anomaly. We can also extract the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>π</mi><mo>/</mo><mn>24</mn></math> framing anomaly phase alone from the full spectrum of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math> in the ground subspace by computing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">⟨</mo><msup><mi>T</mi><mi>m</mi></msup><mo stretchy="false">⟩</mo></math>. This pins down the last and most crucial property required for a valid lattice definition of U(1) Chern-Simons theory.

Ze-An Xu

Jing-Yuan Chen

Framing Anomaly in Lattice Chern-Simons-Maxwell Theory

We study the processes <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><msub><mi mathvariant="normal">ϒ</mi><mi>J</mi></msub><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo><mi>η</mi></math> and <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><msub><mi mathvariant="normal">ϒ</mi><mi>J</mi></msub><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> at center-of-mass energies <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msqrt><mrow><mi>s</mi></mrow></msqrt><mo>=</mo><mo stretchy="false">(</mo><mn>10.73</mn><mo>−</mo><mn>11.02</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math> using a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>142.5</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> data sample, including <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>122</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> near the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>10860</mn><mo stretchy="false">)</mo></math> peak (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>10.866</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>), collected with the Belle detector at the KEKB asymmetric-energy <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></math> collider. From the peak sample, the products of Born cross section times branching fraction are obtained for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>σ</mi><mtext>Born</mtext></msub><mo stretchy="false">(</mo><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><msub><mi mathvariant="normal">ϒ</mi><mi>J</mi></msub><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo><mi>η</mi><mo stretchy="false">)</mo></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>σ</mi><mtext>Born</mtext></msub><mo stretchy="false">(</mo><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><msub><mi mathvariant="normal">ϒ</mi><mi>J</mi></msub><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mi mathvariant="normal">ϒ</mi><mi>J</mi></msub><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>b</mi><mn>1</mn></mrow></msub><mi>γ</mi><mo stretchy="false">)</mo></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mi mathvariant="normal">ϒ</mi><mi>J</mi></msub><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>b</mi><mn>2</mn></mrow></msub><mi>γ</mi><mo stretchy="false">)</mo></math> for each <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">ϒ</mi><mi>J</mi></msub><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo></math> state. The corresponding branching fractions for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>10860</mn><mo stretchy="false">)</mo></math> decays are also obtained. The significances of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">ϒ</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">ϒ</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">ϒ</mi><mn>3</mn></msub><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo></math> signals are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>4.8</mn><mi>σ</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>&gt;</mo><mn>10</mn><mi>σ</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>3.0</mn><mi>σ</mi></mrow></math>, respectively, including systematic uncertainties. The mass for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">ϒ</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo></math> is measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>10167.0</mn><mo>±</mo><mn>1.0</mn><mo>±</mo><mn>0.2</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><msup><mi>c</mi><mn>2</mn></msup></math>, where the first and second uncertainties are statistical and systematic. The mass splittings <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>m</mi><mn>12</mn></msub><mo>=</mo><mi>m</mi><mo stretchy="false">(</mo><msub><mi mathvariant="normal">ϒ</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>−</mo><mi>m</mi><mo stretchy="false">(</mo><msub><mi mathvariant="normal">ϒ</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>m</mi><mn>23</mn></msub><mo>=</mo><mi>m</mi><mo stretchy="false">(</mo><msub><mi mathvariant="normal">ϒ</mi><mn>3</mn></msub><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>−</mo><mi>m</mi><mo stretchy="false">(</mo><msub><mi mathvariant="normal">ϒ</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math> are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>11.8</mn><mo>±</mo><mn>1.5</mn><mo>±</mo><mn>0.4</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><msup><mi>c</mi><mn>2</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>7.6</mn><mo>±</mo><mn>2.4</mn><mo>±</mo><mn>0.6</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><msup><mi>c</mi><mn>2</mn></msup></math>, respectively. We determine the energy dependence of the cross sections for <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><msub><mi mathvariant="normal">ϒ</mi><mi>J</mi></msub><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo><mi>η</mi></math> and <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><msub><mi mathvariant="normal">ϒ</mi><mi>J</mi></msub><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">ϒ</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">ϒ</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">ϒ</mi><mn>3</mn></msub><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo></math> states, combined.

M. Abumusabh

I. Adachi

K. Adamczyk

A. Aggarwal

H. Ahmed

Y. Ahn

M. Akdag

N. Akopov

S. Alghamdi

M. Alhakami

N. Althubiti

K. Amos

M. Angelsmark

N. Anh Ky

C. Antonioli

K. Arai

H. Atmacan

T. Aushev

V. Aushev

R. Ayad

V. Babu

H. Bae

N.K. Baghel

S. Bahinipati

P. Bambade

Sw. Banerjee

M. Barrett

M. Bartl

J. Baudot

A. Baur

A. Beaubien

F. Becherer

J. Becker

G.F. Benfratello

J.V. Bennett

F.U. Bernlochner

V. Bertacchi

M. Bertemes

E. Bertholet

M. Bessner

S. Bettarini

V. Bhardwaj

B. Bhuyan

F. Bianchi

T. Bilka

A. Biswas

D. Biswas

A. Bobrov

D. Bodrov

A. Bondar

G. Bonvicini

A. Boschetti

A. Bozek

M. Bračko

P. Branchini

R.A. Briere

T.E. Browder

A. Budano

Q. Campagna

M. Campajola

M. Carminati

G. Casarosa

C. Cecchi

M.C. Chang

P. Cheema

L. Chen

B.G. Cheon

C. Cheshta

H. Chetri

K. Chilikin

K. Chirapatpimol

H.E. Cho

K. Cho

S.J. Cho

S.K. Choi

S. Choudhury

S. Chutia

J.A. Colorado-Caicedo

I. Consigny

L. Corona

H. Crotte Ledesma

S. Cuccuini

J.X. Cui

E. De La Cruz-Burelo

S.A. De La Motte

G. De Nardo

G. De Pietro

R. de Sangro

M. Destefanis

S. Dey

R. Dhayal

A. Di Canto

J. Dingfelder

Z. Doležal

X. Dong

M. Dorigo

K. Dugic

G. Dujany

P. Ecker

D. Epifanov

First Measurement of the Masses of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">ϒ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">ϒ</mi><mn>3</mn></msub><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo></math> States and the Energy Dependence of the Cross Sections for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">→</mo><msub><mrow><mi mathvariant="normal">ϒ</mi></mrow><mrow><mi>J</mi></mrow></msub><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo><mi>η</mi></mrow></math> and <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><msub><mi mathvariant="normal">ϒ</mi><mi>J</mi></msub><mo stretchy="false">(</mo><mn>1</mn><mi>D</mi><mo stretchy="false">)</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math>

We present the first amplitude analysis of the semileptonic decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>e</mi></mrow></msub></mrow></math> by analyzing <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></math> annihilation data corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>20.3</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>fb</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math> collected at the center-of-mass energy of 3.773 GeV with the BESIII detector. A tiny <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">D</mi></math>-wave component of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>K</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>1430</mn><msup><mo stretchy="false">)</mo><mo>−</mo></msup></math> accounting for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>0.157</mn><mo>±</mo><mn>0.05</mn><msub><mrow><mn>6</mn></mrow><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.04</mn><msub><mrow><mn>2</mn></mrow><mrow><mi>syst</mi></mrow></msub><mo stretchy="false">)</mo><mo>%</mo></mrow></math> of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math> is observed for the first time with a significance of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>7.9</mn><mi>σ</mi></math> in addition to the dominant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">P</mi></math>-wave component of <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><msup><mo stretchy="false">)</mo><mo>−</mo></msup></math> and the subdominant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">S</mi></mrow></math>-wave. The hadronic form factors of the <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><mo stretchy="false">(</mo><mn>892</mn><msup><mo stretchy="false">)</mo><mo>−</mo></msup></math> transition are measured precisely as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>r</mi></mrow><mrow><mi>V</mi></mrow></msub><mo>=</mo><mi>V</mi><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo><mo>/</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo><mo>=</mo><mn>1.432</mn><mo>±</mo><mn>0.05</mn><msub><mrow><mn>0</mn></mrow><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.01</mn><msub><mrow><mn>7</mn></mrow><mrow><mi>syst</mi></mrow></msub></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>r</mi><mn>2</mn></msub><mo>=</mo><msub><mi>A</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo><mo>/</mo><msub><mi>A</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo><mo>=</mo><mn>0.786</mn><mo>±</mo><mn>0.03</mn><msub><mn>7</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.02</mn><msub><mn>7</mn><mrow><mi>syst</mi></mrow></msub></math>. The branching fraction 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><mo stretchy="false">(</mo><mn>892</mn><msup><mo stretchy="false">)</mo><mo>−</mo></msup><msup><mi>e</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>e</mi></msub></math> with <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><msup><mo stretchy="false">)</mo><mo>−</mo></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math> is measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>7.445</mn><mo>±</mo><mn>0.06</mn><msub><mrow><mn>1</mn></mrow><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.04</mn><msub><mrow><mn>8</mn></mrow><mrow><mi>syst</mi></mrow></msub><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math>. Combining the measurements of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo></mrow></msup><mo stretchy="false">(</mo><mn>892</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">(</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo></mrow></msup><mo stretchy="false">(</mo><mn>892</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">)</mo><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow></math>, lepton flavor universality is tested by the ratio <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="script">R</mi></mrow><mrow><mi>LFU</mi></mrow></msub><mo>=</mo><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo></mrow></msup><mo stretchy="false">(</mo><mn>892</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>μ</mi></mrow></msub><mo stretchy="false">)</mo><mo>/</mo><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo></mrow></msup><mo stretchy="false">(</mo><mn>892</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>e</mi></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><mn>0.928</mn><mo>±</mo><mn>0.02</mn><msub><mrow><mn>0</mn></mrow><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.01</mn><msub><mrow><mn>2</mn></mrow><mrow><mi>syst</mi></mrow></msub></mrow></math> with unprecedented precision; no violation is found. Furthermore, isospin symmetry in the <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><msup><mo stretchy="false">)</mo><mo>−</mo></msup></math> decay is tested by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="script">R</mi></mrow><mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo><mo>−</mo></mrow></msup></mrow></msub><mo>=</mo><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo></mrow></msup><mo stretchy="false">(</mo><mn>892</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">)</mo><mo>/</mo><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo></mrow></msup><mo stretchy="false">(</mo><mn>892</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">→</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mn>1.087</mn><mo>±</mo><mn>0.01</mn><msub><mrow><mn>3</mn></mrow><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.00</mn><msub><mrow><mn>9</mn></mrow><mrow><mi>syst</mi></mrow></msub></mrow></math> for the first time using the latest measurement 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><mo stretchy="false">(</mo><mn>892</mn><msup><mo stretchy="false">)</mo><mo>−</mo></msup><msup><mi>e</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>e</mi></msub></math> with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo></mrow></msup><mo stretchy="false">(</mo><mn>892</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">→</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math>. Finally, the phase shift of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>K</mi><mi>π</mi></mrow></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">S</mi></mrow></math>-wave is extracted in a model-independent way, which sheds light on the nature of the lightest strange scalar meson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow><mrow><mo>*</mo></mrow></msubsup><mo stretchy="false">(</mo><mn>700</mn><mo stretchy="false">)</mo></mrow></math>.

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

R. Aliberti

Italy

A. Amoroso

Q. An

Y. Bai

JINR

O. Bakina

Y. Ban

H.R. Bao

Poland

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M.B. Bertani

D. Bettoni

E. Bianco

A. Bortone

I. Boyko

A. Brueggemann

H. Cai

M.H. Cai

X. Cai

A. Calcaterra

G.F. Cao

N. Cao

Türkiye

S.A. Cetin

X.Y. Chai

J.F. Chang

T.T. Chang

G.R. Che

Y.Z. Che

C.H. Chen

Chao Chen

G. Chen

H.S. Chen

H.Y. Chen

M.L. Chen

S.J. Chen

S.M. Chen

T. Chen

X.R. Chen

X.T. Chen

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z.K. Chen

Haoyang Cheng

J.C. Cheng

L.N. Cheng

First Amplitude Analysis of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>e</mi></mrow></msub></mrow></math> and Observation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mn>2</mn></mrow><mrow><mo>*</mo></mrow></msubsup><mo stretchy="false">(</mo><mn>1430</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>e</mi></mrow></msub></mrow></math>