We present a determination of the Cabibbo-Kobayashi-Maskawa matrix element <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>V</mi><mrow><mi>c</mi><mi>b</mi></mrow></msub><mo stretchy="false">|</mo></math> from the decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>D</mi><mo>ℓ</mo><msub><mi>ν</mi><mo>ℓ</mo></msub></math> using a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>365</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> <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 mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>4</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>B</mi><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover></math> data sample recorded by the Belle II experiment at the SuperKEKB collider. The semileptonic decay of one <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> meson is reconstructed in the modes <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>D</mi><mo>−</mo></msup><mo stretchy="false">(</mo><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo stretchy="false">)</mo><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><mo stretchy="false">(</mo><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo stretchy="false">)</mo><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>ℓ</mo></math> denotes either an electron or a muon. Charge conjugation is implied. The second <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> meson in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>4</mn><mi>S</mi><mo stretchy="false">)</mo></math> event is not reconstructed explicitly. Using an inclusive reconstruction of the unobserved neutrino momentum, we determine the recoil variable <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>w</mi><mo>=</mo><msub><mi>v</mi><mi>B</mi></msub><mo>·</mo><msub><mi>v</mi><mi>D</mi></msub></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>v</mi><mi>B</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>v</mi><mi>D</mi></msub></math> are the four-velocities of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math> mesons. We measure the total decay branching fractions to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><mrow><mo stretchy="false">(</mo><mn>2.06</mn><mo>±</mo><mn>0.05</mn><mo stretchy="false">(</mo><mrow><mi>stat</mi></mrow><mo stretchy="false">)</mo><mo>±</mo><mn>0.10</mn><mo stretchy="false">(</mo><mrow><mi>sys</mi></mrow><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>%</mo></mrow></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub><mo stretchy="false">)</mo><mo>=</mo><mrow><mo stretchy="false">(</mo><mn>2.31</mn><mo>±</mo><mn>0.04</mn><mo stretchy="false">(</mo><mrow><mi>stat</mi></mrow><mo stretchy="false">)</mo><mo>±</mo><mn>0.09</mn><mo stretchy="false">(</mo><mrow><mi>sys</mi></mrow><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>%</mo></mrow></math>. We probe lepton flavor universality by measuring <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">→</mo><mi>D</mi><mi>e</mi><msub><mi>ν</mi><mi>e</mi></msub><mo stretchy="false">)</mo><mo>/</mo><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">→</mo><mi>D</mi><mi>μ</mi><msub><mi>ν</mi><mi>μ</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mrow><mn>1.020</mn><mo>±</mo><mn>0.020</mn><mo stretchy="false">(</mo><mrow><mi>stat</mi></mrow><mo stretchy="false">)</mo><mo>±</mo><mn>0.022</mn><mo stretchy="false">(</mo><mrow><mi>sys</mi></mrow><mo stretchy="false">)</mo></mrow></math>. Fitting the partial decay branching fraction as a function of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>w</mi></math> and using the average of lattice QCD calculations of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>D</mi></math> form factor, we obtain <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>V</mi><mrow><mi>c</mi><mi>b</mi></mrow></msub><mo stretchy="false">|</mo><mo>=</mo><mrow><mo stretchy="false">(</mo><mn>39.2</mn><mo>±</mo><mn>0.4</mn><mo stretchy="false">(</mo><mrow><mi>stat</mi></mrow><mo stretchy="false">)</mo><mo>±</mo><mn>0.6</mn><mo stretchy="false">(</mo><mrow><mi>sys</mi></mrow><mo stretchy="false">)</mo><mo>±</mo><mn>0.5</mn><mo stretchy="false">(</mo><mrow><mi>th</mi></mrow><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math>.

I. Adachi

K. Adamczyk

L. Aggarwal

H. Ahmed

Y. Ahn

H. Aihara

N. Akopov

S. Alghamdi

M. Alhakami

A. Aloisio

K. Amos

M. Angelsmark

N. Anh Ky

C. Antonioli

D.M. Asner

H. Atmacan

T. Aushev

V. Aushev

M. Aversano

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

J.V. Bennett

F.U. Bernlochner

V. Bertacchi

M. Bertemes

E. Bertholet

M. Bessner

S. Bettarini

B. Bhuyan

F. Bianchi

T. Bilka

D. Biswas

A. Bobrov

D. Bodrov

A. Bondar

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

L. Cao

G. Casarosa

C. Cecchi

M.C. Chang

P. Cheema

L. Chen

B.G. Cheon

K. Chilikin

J. Chin

K. Chirapatpimol

H.E. Cho

K. Cho

S.J. Cho

S.K. Choi

S. Choudhury

I. Consigny

L. Corona

J.X. Cui

E. De La Cruz-Burelo

S.A. De La Motte

G. De Pietro

R. de Sangro

M. Destefanis

A. Di Canto

J. Dingfelder

Z. Doležal

I. Domínguez Jiménez

T.V. Dong

X. Dong

K. Dugic

G. Dujany

P. Ecker

J. Eppelt

R. Farkas

P. Feichtinger

T. Ferber

T. Fillinger

C. Finck

G. Finocchiaro

F. Forti

A. Frey

Determination of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>V</mi><mrow><mi>c</mi><mi>b</mi></mrow></msub><mo stretchy="false">|</mo></math> using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>D</mi><mo>ℓ</mo><msub><mi>ν</mi><mi>l</mi></msub></math> decays at Belle II

We explicitly construct a class of multivariate generalized hypergeometric series which is conjectured in our previous paper [1] to calculate multipoint one-loop parametric conformal integrals in $\textit{D}$ dimensions. Our approach is based on a simple diagrammatic algorithm which systematically builds both arguments and series coefficients in terms of a convex polygon which is part of the Baxter lattice. The examples of the box, pentagon, and hexagon integrals are considered in detail.

Russia

Konstantin Alkalaev

Semyon Mandrygin

Multipoint conformal integrals in $\textit{D}$ dimensions. Part II. Polygons and basis functions

Duality symmetries have been extensively investigated in various contexts, playing a crucial role in understanding quantum field theory and condensed matter theory. In this paper, we extend this framework by studying $\textit{N}$ -ality symmetries, which are a generalization of duality symmetries and are mathematically described by ℤ -graded fusion categories. In particular, we focus on an $\textit{N}$ -ality symmetry obtained by gauging a non-anomalous subgroup of ℤ × ℤ × ℤ symmetry with a type III anomaly. We determine the corresponding fusion rules via two complementary approaches: a direct calculation and a representation-theoretic method. As an application, we study the symmetry-protected topological (SPT) phases associated with the $\textit{N}$ -ality symmetry. We classify all such SPT phases using the SymTFT framework and explicitly construct lattice Hamiltonians for some of them.

Japan

Jun Maeda

Tsubasa Oishi

$\textit{N}$-ality symmetry and SPT phases in (1+1)d

Following the discovery of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>3000</mn><mo stretchy="false">)</mo></math>, its mass and full width have been extensively studied. Yet its nature remains undetermined to date. Since it was discovered through nonleptonic decay of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> mesons and the corresponding cascade process, we therefore in this paper investigate the nonleptonic and semileptonic decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> meson to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>2</mn><mo>+</mo></msup></math> charmed mesons using the Bethe-Salpeter equation approach. Our calculations on nonleptonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> decays reveal that the unconfirmed resonance <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>3000</mn><mo stretchy="false">)</mo></math> aligns well with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><msup><mn>2</mn><mn>3</mn></msup><msub><mi>P</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math> predictions. Other candidates, including <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><msup><mn>1</mn><mn>3</mn></msup><msub><mi>F</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><msup><mn>3</mn><mn>3</mn></msup><msub><mi>P</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><msup><mn>2</mn><mn>3</mn></msup><msub><mi>F</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math>, are excluded due to their very small branching ratios in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> decays. Considering that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>1</mn><mi>F</mi><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>3</mn><mi>P</mi><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>2</mn><mi>F</mi><mo stretchy="false">)</mo></math> have not yet been experimentally observed, we investigate the feasibility of their detection in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math>-meson decays.

China

Shi-Hang Zhang

Wen-Yuan Ke

Su-Yan Pei

Wei Li

Germany

Xiao-Ze Tan

Lili Zhu

Guo-Li Wang

Identification of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>3000</mn><mo stretchy="false">)</mo></math> as the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><msup><mn>2</mn><mn>3</mn></msup><msub><mi>P</mi><mn>2</mn></msub><mo stretchy="false">)</mo></math> and exploring potential of undiscovered <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>2</mn><mo>+</mo></msup></math> mesons via <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> decays

We have carried out an evaluation of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><msup><mi>π</mi><mo>+</mo></msup></math> mass distributions in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>2536</mn><mo stretchy="false">)</mo></math> decay to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math>, from the perspective that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>2536</mn><mo stretchy="false">)</mo></math> is a molecular state, mostly made from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup><mi>D</mi></math> in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>0</mn></math>. We are able to obtain not only the mass distributions, but also the branching ratio of this decay. The shape of the mass distributions differs appreciably from those of the analogous reaction <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>2460</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math>, which has been measured by the LHCb Collaboration and analyzed theoretically from the perspective that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>2460</mn><mo stretchy="false">)</mo></math> is a molecular state of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><mi>K</mi></math>, showing good agreement with the data. In spite of the analogy with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>2460</mn><mo stretchy="false">)</mo></math> decay, the dynamical differences in the decay mechanism are important, since now 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>500</mn><mo stretchy="false">)</mo></math> resonance is not generated, while it was the dominant mechanism in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>2460</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> decay. Nonetheless, we find striking differences in the mass distributions compared with phase space as a consequence of the decay mechanism. The branching ratio obtained is an order of magnitude bigger than the one of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>2460</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> reaction, mostly due to the larger available phase space. We also show that the shape of the distributions obtained from the molecular picture is quite different from those obtained based on a <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> picture. We conclude that measuring the shape of the mass distributions and the total strength of the decay mode should be very valuable to learn about the structure of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>2536</mn><mo stretchy="false">)</mo></math>.

Brazil

Jorgivan Morais Dias

Spain

Yi-Yao Li

Eulogio Oset

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><msup><mi>π</mi><mo>±</mo></msup></math> mass spectra in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>2536</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> decays

We perform a theoretical study of the decay process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">→</mo><msup><mi>D</mi><mo>−</mo></msup><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math> in search of the doubly heavy tetraquark states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> with quark content <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>d</mi><mo stretchy="false">¯</mo></mover></math>. These <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> states are assumed to be dynamically generated molecular states from the S-wave interactions between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mi>s</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mn>0</mn></mrow></msubsup><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>+</mo></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mn>0</mn></mrow></msup><msubsup><mi>D</mi><mi>s</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>+</mo></mrow></msubsup></math> meson pairs. Based on the total angular momentum and the type of the constituent mesons (pseudoscalars <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math> or vectors <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi></math>), they are labeled as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>P</mi><mi>P</mi></mrow></msubsup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>2</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math>, respectively. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math> invariant mass distribution for this decay is calculated using current algebra, incorporating contributions from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> states arising from final-state interactions. Our results reveal a clear peak structure in the 7415–7425 MeV region, which is attributed to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>2</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math> state. Additionally, a distinct dip structure appears near the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mrow><mo>*</mo><mn>0</mn></mrow></msup><msubsup><mi>D</mi><mi>s</mi><mrow><mo>*</mo><mo>+</mo></mrow></msubsup></math> threshold, characteristic of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>2</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math> as a hadronic molecular state. A near-threshold enhancement associated with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>P</mi><mi>P</mi></mrow></msubsup></math> state and a dip arising from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math> state are also identified, though the manifestation of these features depends sensitively on model parameter fine-tuning. Therefore, with increased experimental statistics, the decay channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">→</mo><msup><mi>D</mi><mo>−</mo></msup><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math> offers a promising avenue for discovering and characterizing the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> states.

Wen-Ying Liu

Hua-Xing Chen

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> states in the process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">→</mo><msup><mi>D</mi><mo>−</mo></msup><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math>

We investigate the electromagnetic properties of the axial-vector molecular states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><mi>K</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>K</mi><mo>*</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>*</mo></msup><mi>K</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><msup><mi>K</mi><mo>*</mo></msup></math>, which are used to model the charmed states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow><mo>+</mo></msubsup><mo stretchy="false">(</mo><mn>2460</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow><mo>+</mo></msubsup><mo stretchy="false">(</mo><mn>2536</mn><mo stretchy="false">)</mo></math>, and their bottom partners with quantum numbers <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>. To our knowledge, this presents the first comprehensive calculation of the magnetic and quadrupole moments for these specific molecular configurations. Employing the QCD light-cone sum rule method with molecular-type interpolating currents, we compute these moments and perform a detailed flavor decomposition to reveal the internal distribution of the electromagnetic charge and spin. Our results demonstrate that the light up and down quarks dominate the electromagnetic response, with negligible contributions from the heavy quarks. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><mi>K</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>*</mo></msup><mi>K</mi></math> states exhibit negative quadrupole moments and slightly oblate charge distributions, whereas the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>K</mi><mo>*</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><msup><mi>K</mi><mo>*</mo></msup></math> states possess positive quadrupole moments and prolate distributions, with significant contributions from the strange quark. The predicted moments provide benchmarks for lattice QCD calculations and are testable through their influence on radiative transitions and photo- and electroproduction observables at high-luminosity facilities, offering crucial insights into the internal structure and nature of these axial-vector states.

Türkiye

Ulaş Özdem

Electromagnetic properties of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow><mo>+</mo></msubsup><mo stretchy="false">(</mo><mn>2460</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow><mo>+</mo></msubsup><mo stretchy="false">(</mo><mn>2536</mn><mo stretchy="false">)</mo></math>, and their bottom partners in a molecular configuration

Under chiral effective field theory, we study the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> interactions up to second chiral order at one-loop level, which contain full contact, one-pion-exchange (OPE) and two-pion-exchange (TPE) contributions. Here, we adopt a new subtraction scheme of the two-particle-reducible contributions and attempt different regularization schemes uniquely for the TPE contributions since they are highly divergent on the momentum transfer. Under these schemes, we conclude that, in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>0</mn></math> channel, the TPE contribution is repulsive, then the competition between this powerful repulsing TPE and the other two (contact and OPE) results in a quite weak attraction. This explains why <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> has an extremely small binding energy if treated as the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>0</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> bound state. This feature resembles that of hidden charm <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math> as we investigated in previous work [<a href="http://dx.doi.org/10.1103/PhysRevD.105.034013">Phys. Rev. D 105, 034013 (2022)</a>], which also interpreted the extremely near-threshold phenomenon of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math>. In addition, we also solve the Bethe-Salpeter equation with the chiral interactions for a consistency check.

Hao Xu

Li-Xiang Ren

Investigating the two-pion exchange of the double charm <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> chiral interactions and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math>

Conformal field theory (CFT) can be placed on disparate space-time manifolds to facilitate investigations of their properties. For (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional [<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>] theories, one useful choice is the real projective space <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mi mathvariant="double-struck">RP</mi><mn>3</mn></msup></mrow></math> obtained by identifying antipodal points on the boundary sphere of a three-dimensional ball. One-point functions of scalar primary fields on this manifold generally do not vanish and encode the so-called crosscap coefficients. These coefficients also manifest on the sphere as the overlaps between certain crosscap states and CFT primary states. Taking the <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> Ising CFT as a concrete example, we demonstrate that crosscap coefficients can be extracted from microscopic models. We construct crosscap states in both lattice models defined on polyhedrons and continuum models in Landau levels, where the degrees of freedom at antipodal points are entangled in Bell-type states. By computing their overlaps with the eigenstates of many-body Hamiltonians, we obtain results consistent with those from conformal bootstrap. Importantly, our approach directly reveals the absolute values of crosscap overlaps, whereas bootstrap calculations typically yield only their ratios. Furthermore, we investigate the finite-size scaling of these overlaps and their evolution under perturbations away from criticality.

Jia-Ming Dong

Yueshui Zhang

Kai-Wen Huang

Hong-Hao Tu

Ying-Hai Wu

Numerical extraction of crosscap coefficients in microscopic models for <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> conformal field theory

Inspired by the abundant structure near the threshold of the $$D^{(*)}K^{(*)}/\bar{D}^{(*)}K^{(*)},$$ we estimate the strong decay properties of the $$T_{c\bar{s}1}^{f/a}$$ and $$T_{\bar{c}\bar{s}1}^{f/a}$$ with $$I(J^{P})=0/1(1^{+})$$ in $$DK^{*}$$ and $$\bar{D}K^{*}$$ molecular scenarios in the present paper. By employing the effective Lagrangian approach, the widths of the processes $$T_{c\bar{s}1}^{f}\rightarrow D^{*}K, D_{s}^{*}\eta , DK\pi ,$$ $$T_{c\bar{s}1}^{a}\rightarrow D^{*}K, D_{s}^{*}\pi , DK\pi ,$$ and $$T_{\bar{c}\bar{s}1}^{f/a}\rightarrow \bar{D}^{*}K, \bar{D}K\pi $$ are estimated. Considering the present estimations, we propose to search for $$T_{c\bar{s}1}^{f/a}$$ states in $$D^{*}K$$ and $$D_{s}^{*}\pi /D_{s}^{*}\eta $$ mass invariant spectra. Their ratios may serve as an important test of the molecular scenario.

Italy

Zi-Li Yue

Cheng-Jian Xiao

Mexico

H. García-Tecocoatzi

Dian-Yong Chen

Elena Santopinto

Strong decays of the $$DK^*$$ and $$\bar{D}K^{*}$$ molecular states