In this work, we investigate possible bound states in the $ D_s\bar{D}_s $ system using the Bethe-Salpeter (BS) formalism within both the ladder and instantaneous approximations. By numerically solving the Bethe-Salpeter equation with a kernel that incorporates contributions from $\textit{ϕ}$ and $ J/\psi $ meson exchanges, we confirm the existence of a loosely bound state. Furthermore, we explore the partial decay widths of the $ D_s\bar{D}_s $ bound state into the $ D\bar{D} $ , $ \eta_c\eta $ , and $ J/\psi\omega $ channels, and observe that these widths are sensitive to the model parameter $\textit{α}$. Notably, we find the dominant decay channel for the $ D_s\bar{D}_s $ bound state to be $ D\bar{D} $ .

China

Jing-Juan Qi

Zhen-Yang Wang

Zhu-Feng Zhang

Xin-Heng Guo

The properties of the $\textit{S}$-wave D$_{s}$ D $_{s}$ bound state * Supported by the National Natural Science Foundation of China (12405115, 12275024, 12105149)

Recently, the BESIII Collaboration observed the three-body decays $ D_s^+\to \eta \omega\pi^+ $ , $ D^+\to K^0_S\pi^+\omega $ , and $ D^0\to K^-\pi^+\omega $ . In this study, we investigate the contributions of the subprocesses $ \rho^+\to \omega\pi^+ $ in these Cabibbo-favored decays $ D \to h\omega\pi $ , with $ \rho^+= \{\rho(770)^+, \rho(1450)^+, \rho(770)^+\&amp;\rho(1450)^+\} $ and $ h=\{ \eta, K^0_S, K^-\} $ , by introducing these subprocesses into the decay amplitudes of the relevant decay processes via the vector form factor $ F_{\omega\pi} $ , which has been measured in the related $\textit{τ}$ and $ e^+e^- $ processes. We provide the first theoretical predictions for the branching fractions of the quasi-two-body decays $ D_s^+\to\eta[\rho^+\to]\omega\pi^+ $ , $ D^+\to K^0_S[\rho^+\to]\omega\pi^+ $ , and $ D^0\to K^-[\rho^+\to]\omega\pi^+ $ . Our findings reveal that the contributions from the subprocess $ \rho(770)^+\to\omega\pi^+ $ are significant in these observed three-body decays $ D_s^+\to\eta \omega\pi^+ $ , $ D^+\to K^0_S \omega\pi^+ $ , and $ D^0\to K^- \omega\pi^+ $ , notwithstanding the contributions originating from the Breit-Wigner tail effect of $ \rho(770)^+ $ . The numerical results of this study suggest that the dominant resonance contributions for the three-body decays $ D_s^+\to\eta \omega\pi^+ $ and $ D^+\to K^0_S \omega\pi^+ $ originate from the $\textit{P}$-wave intermediate states $ \rho(770)^+ $ , $ \rho(1450)^+ $ and their interference effects.

Wen-Fei Wang

Jiao-Yuan Xu

Si-Hong Zhou

Spain

Pan-Pan Shi

Contributions of $\textit{ρ}$(770,1450)→$\textit{ωπ}$ to Cabibbo-favored $\textit{D}$→$\textit{hωπ}$ decays * Supported in part by the National Natural Science Foundation of China (12465017) and the Foundation of Shanxi '1331 Project' Key Subjects Construction

<p>Searches are presented for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>D</mi><msup><mi>h</mi><mo>+</mo></msup><msup><mi>h</mi><mo>−</mo></msup></math> decays, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math> is a charmed meson and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>h</mi><mo>±</mo></msup></math> is a charged pion or kaon, using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math> collision data collected by the LHCb experiment corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>9</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. The decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msup><mi>D</mi><mo>+</mo></msup><msup><mi>K</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msup><mi>D</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><msup><mi>K</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>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> are observed for the first time. Their branching fractions, expressed as ratios relative to that of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msubsup><mi>B</mi><mi>s</mi><mn>0</mn></msubsup><msup><mi>π</mi><mo>+</mo></msup></math> decay, are determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">R</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>1.96</mn><mo>±</mo><mn>0.23</mn><mo>±</mo><mn>0.08</mn><mo>±</mo><mn>0.10</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">R</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo><mo>+</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mspace linebreak="goodbreak"></mspace><mo stretchy="false">(</mo><mn>3.67</mn><mo>±</mo><mn>0.55</mn><mo>±</mo><mn>0.24</mn><mo>±</mo><mn>0.20</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">R</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>+</mo></mrow></msubsup><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>1.61</mn><mo>±</mo><mn>0.35</mn><mo>±</mo><mn>0.13</mn><mo>±</mo><mn>0.07</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math>, where the first uncertainty is statistical, the second is systematic, and the third is due to the limited precision on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math>-meson branching fractions. The decay channels proceed primarily through excited <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mn>0</mn></msup></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup></math> resonances or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math> mesons, and open a new avenue for studies of charge-parity violation in beauty mesons.</p>

Netherlands

R. Aaij

United Kingdom

A.S.W. Abdelmotteleb

Switzerland

C. Abellan Beteta

F. Abudinén

T. Ackernley

United States

A.A. Adefisoye

B. Adeva

M. Adinolfi

P. Adlarson

France

C. Agapopoulou

C.A. Aidala

Z. Ajaltouni

S. Akar

K. Akiba

Italy

P. Albicocco

Germany

J. Albrecht

R. Aleksiejunas

CERN

F. Alessio

P. Alvarez Cartelle

R. Amalric

Brazil

S. Amato

J.L. Amey

Y. Amhis

L. An

L. Anderlini

M. Andersson

P. Andreola

M. Andreotti

S. Andres Estrada

A. Anelli

D. Ao

C. Arata

F. Archilli

Z. Areg

M. Argenton

Costa Rica

S. Arguedas Cuendis

L. Arnone

A. Artamonov

M. Artuso

E. Aslanides

R. Ataíde Da Silva

M. Atzeni

B. Audurier

J.A. Authier

D. Bacher

I. Bachiller Perea

S. Bachmann

M. Bachmayer

J.J. Back

P. Baladron Rodriguez

V. Balagura

A. Balboni

W. Baldini

Z. Baldwin

L. Balzani

H. Bao

J. Baptista de Souza Leite

C. Barbero Pretel

M. Barbetti

I.R. Barbosa

R.J. Barlow

M. Barnyakov

S. Barsuk

W. Barter

J. Bartz

Poland

S. Bashir

B. Batsukh

P.B. Battista

A. Bay

A. Beck

M. Becker

F. Bedeschi

I.B. Bediaga

N.A. Behling

S. Belin

A. Bellavista

K. Belous

I. Belov

I. Belyaev

G. Benane

G. Bencivenni

E. Ben-Haim

A. Berezhnoy

R. Bernet

S. Bernet Andres

A. Bertolin

C. Betancourt

F. Betti

J. Bex

Ia. Bezshyiko

O. Bezshyyko

J. Bhom

M.S. Bieker

N.V. Biesuz

P. Billoir

A. Biolchini

M. Birch

F.C.R. Bishop

A. Bitadze

A. Bizzeti

Observation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>D</mi><msup><mi>h</mi><mo>+</mo></msup><msup><mi>h</mi><mo>−</mo></msup></math> Decays

<p>By analyzing a data sample of <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></mrow></math> collisions with center-of-mass energy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msqrt><mrow><mi>s</mi></mrow></msqrt><mo>=</mo><mn>3.773</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>, corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>7.9</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> collected with the BESIII detector operating at the BEPCII collider, we study semileptonic decays of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mrow><mn>0</mn><mo stretchy="false">(</mo><mo>+</mo><mo stretchy="false">)</mo></mrow></msup></math> mesons into the axial-vector meson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1235</mn><mo stretchy="false">)</mo></math> via the decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1235</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>ω</mi><mi>π</mi></mrow></math>. The 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><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1235</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> is observed with a significance of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>5.2</mn><mi>σ</mi></mrow></math> after considering systematic uncertainty, while evidence for the decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><mo stretchy="false">→</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1235</mn><msup><mrow><mo stretchy="false">)</mo></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> is obtained with a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>3.1</mn><mi>σ</mi></mrow></math> significance. The product branching fractions are determined 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>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1235</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><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1235</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">→</mo><mi>ω</mi><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">]</mo><mo>=</mo><mo stretchy="false">(</mo><mn>0.72</mn><mo>±</mo><mn>0.1</mn><msubsup><mrow><mn>8</mn></mrow><mrow><mo>−</mo><mn>0.08</mn></mrow><mrow><mo>+</mo><mn>0.06</mn></mrow></msubsup><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><mo stretchy="false">→</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1235</mn><msup><mrow><mo stretchy="false">)</mo></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><mo stretchy="false">]</mo><mo>×</mo><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1235</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><mi>ω</mi><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">]</mo><mo>=</mo><mspace linebreak="goodbreak"></mspace><mo stretchy="false">(</mo><mn>1.16</mn><mo>±</mo><mn>0.44</mn><mo>±</mo><mn>0.16</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup></mrow></math>, where the first uncertainties are statistical and the second systematic. The ratio of their partial decay widths is determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">{</mo><mi mathvariant="normal">Γ</mi><mo stretchy="false">[</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1235</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mo stretchy="false">−</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo stretchy="false">+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>e</mi></mrow></msub><mo stretchy="false">]</mo><mo>/</mo><mn>2</mn><mi mathvariant="normal">Γ</mi><mo stretchy="false">[</mo><msup><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">+</mo></mrow></msup><mo stretchy="false">→</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1235</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo stretchy="false">+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>e</mi></mrow></msub><mo stretchy="false">]</mo><mo stretchy="false">}</mo><mo>=</mo><mspace linebreak="goodbreak"></mspace><mn>0.78</mn><mo>±</mo><mn>0.1</mn><msubsup><mrow><mn>9</mn></mrow><mrow><mo>−</mo><mn>0.05</mn></mrow><mrow><mo>+</mo><mn>0.04</mn></mrow></msubsup></mrow></math>, which is consistent with unity, predicted by isospin invariance, within uncertainties.</p>

M. Ablikim

Russia

M.N. Achasov

Sweden

O. Afedulidis

X.C. Ai

R. Aliberti

A. Amoroso

Q. An

Y. Bai

JINR

O. Bakina

I. Balossino

Y. Ban

H.R. Bao

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M. Bertani

D. Bettoni

F. Bianchi

E. Bianco

A. Bortone

I. Boyko

R.A. Briere

A. Brueggemann

H. Cai

X. Cai

A. Calcaterra

G.F. Cao

N. Cao

Türkiye

S.A. Cetin

X.Y. Chai

J.F. Chang

G.R. Che

Y.Z. Che

G. Chelkov

C. Chen

C.H. Chen

Chao Chen

G. Chen

H.S. Chen

H.Y. Chen

M.L. Chen

S.J. Chen

S.L. Chen

S.M. Chen

T. Chen

X.R. Chen

X.T. Chen

Y.B. Chen

Y.Q. Chen

Z.J. Chen

Z.Y. Chen

South Korea

S.K. Choi

G. Cibinetto

F. Cossio

J.J. Cui

H.L. Dai

J.P. Dai

A. Dbeyssi

R.E. de Boer

D. Dedovich

C.Q. Deng

Z.Y. Deng

A. Denig

I. Denysenko

M. Destefanis

F. De Mori

Observation of the Singly Cabibbo Suppressed Decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msub><mi>b</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1235</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> and Evidence for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><mo stretchy="false">→</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1235</mn><msup><mrow><mo stretchy="false">)</mo></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>