A first determination of the strong-phase difference between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mover accent="true"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mo stretchy="false">→</mo><msup><mrow><mi>K</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><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> is performed using <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>ψ</mi><mo stretchy="false">(</mo><mn>3770</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> data collected by the BESIII detector corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>20.3</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. The measurements are made in four pairs of bins in phase space, which are chosen to provide optimal sensitivity to the angle <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math> of the unitarity triangle in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>±</mo></msup><mo stretchy="false">→</mo><mi>D</mi><msup><mi>K</mi><mo>±</mo></msup></math> decays. From these measurements, it follows that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-even fraction of the decay is <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mo>+</mo></msub><mo>=</mo><mn>0.754</mn><mo>±</mo><mn>0.01</mn><msub><mn>0</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mspace linebreak="goodbreak"></mspace><mn>0.00</mn><msub><mn>8</mn><mrow><mi>syst</mi></mrow></msub></math>. In addition, 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><msup><mi>K</mi><mo>−</mo></msup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> is measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>2.863</mn><mo>±</mo><mspace linebreak="goodbreak"></mspace><mn>0.02</mn><msub><mn>8</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.04</mn><msub><mn>5</mn><mrow><mi>syst</mi></mrow></msub><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math>, which is twice as precise as previous results obtained at other experiments.

China

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

Germany

O. Afedulidis

X.C. Ai

R. Aliberti

Italy

A. Amoroso

Q. An

Y. Bai

JINR

O. Bakina

I. Balossino

Y. Ban

H.R. Bao

Poland

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M. Bertani

D. Bettoni

F. Bianchi

E. Bianco

A. Bortone

I. Boyko

United States

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

B. Ding

X.X. Ding

Y. Ding

J. Dong

L.Y. Dong

M.Y. Dong

X. Dong

M.C. Du

S.X. Du

Y.Y. Duan

Z.H. Duan

P. Egorov

Y.H. Fan

J. Fang

S.S. Fang

W.X. Fang

Y. Fang

Y.Q. Fang

R. Farinelli

L. Fava

F. Feldbauer

G. Felici

C.Q. Feng

J.H. Feng

Y.T. Feng

M. Fritsch

C.D. Fu

J.L. Fu

Y.W. Fu

H. Gao

Measurement of the strong-phase difference between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mover accent="true"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mo stretchy="false">→</mo><msup><mrow><mi>K</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><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> in bins of phase space

The discovery of numerous new hadrons over the past two decades has provided unprecedented opportunities to understand the nonperturbative QCD and hadron structure. The hadronic molecule picture plays an important role in explaining these new hadrons and enriching the configurations of exotic hadronic states. In this Letter, using the model-independent <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>K</mi></math> potential extracted from the relevant experimental data, a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mn>0</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mi>s</mi></msub><mi>D</mi><mi>K</mi></math> three-body hadronic molecule is predicted with a mass of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mn>4310</mn></mrow><mrow><mo>−</mo><mn>24</mn></mrow><mrow><mo>+</mo><mn>14</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>. This state shows decoupling to conventional <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover></math> charmonia or the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mi>s</mi></msub><msubsup><mi>D</mi><mrow><mi>s</mi><mn>0</mn></mrow><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>2317</mn><mo stretchy="false">)</mo></math> two-body molecular state. It can be regarded as a compelling three-body hadronic molecular candidate. We further demonstrate that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>D</mi><mrow><mo>*</mo><mo>±</mo></mrow></msup><msup><mi>D</mi><mo>∓</mo></msup><msup><mi>K</mi><mo>+</mo></msup></math> decays could be promising channels for searching for the predicted state in future high-luminosity LHCb runs.

Tian-Wei Wu

Ming-Zhu Liu

Li-Sheng Geng

Implication of the Existence of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mo>−</mo></mrow></msup><mtext> </mtext><msub><mrow><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>s</mi></mrow></msub><mi>D</mi><mi>K</mi></mrow></math> Bound State on the Nature of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi><mn>0</mn></mrow><mrow><mo>*</mo></mrow></msubsup><mo stretchy="false">(</mo><mn>2317</mn><mo stretchy="false">)</mo></mrow></math>, and a New Configuration of Exotic State

We report a precise measurement of the ratio of branching fractions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>p</mi><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msup><mi>π</mi><mn>0</mn></msup><mo stretchy="false">)</mo><mo>/</mo><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>p</mi><msup><mi>K</mi><mo>−</mo></msup><msup><mi>π</mi><mo>+</mo></msup><mo stretchy="false">)</mo></math> using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>980</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> of <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> data from the Belle experiment. We obtain a value of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>p</mi><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msup><mi>π</mi><mn>0</mn></msup><mo stretchy="false">)</mo><mo>/</mo><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>p</mi><msup><mi>K</mi><mo>−</mo></msup><msup><mi>π</mi><mo>+</mo></msup><mo stretchy="false">)</mo><mo>=</mo><mn>0.339</mn><mo>±</mo><mn>0.002</mn><mo>±</mo><mn>0.009</mn></math>, where the first and second uncertainties are statistical and systematic, respectively. This Belle result is consistent with the previous measurement from the CLEO experiment but has a fivefold improvement in precision. By combining our result with the world average <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>p</mi><msup><mi>K</mi><mo>−</mo></msup><msup><mi>π</mi><mo>+</mo></msup><mo stretchy="false">)</mo></math>, we obtain the absolute branching fraction <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>p</mi><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msup><mi>π</mi><mn>0</mn></msup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>2.12</mn><mo>±</mo><mspace linebreak="goodbreak"></mspace><mn>0.01</mn><mo>±</mo><mn>0.05</mn><mo>±</mo><mn>0.10</mn><mo stretchy="false">)</mo><mo>%</mo></math>, where the uncertainties are statistical, systematic, and the uncertainty in the absolute branching fraction scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>p</mi><msup><mi>K</mi><mo>−</mo></msup><msup><mi>π</mi><mo>+</mo></msup><mo stretchy="false">)</mo></math>, respectively. This measurement can shed light on hadronic decay mechanisms in charmed baryon decays.

I. Adachi

L. Aggarwal

H. Ahmed

J.K. Ahn

H. Aihara

N. Akopov

M. Alhakami

A. Aloisio

N. Althubiti

M. Angelsmark

N. Anh Ky

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

V. Bhardwaj

B. Bhuyan

T. Bilka

D. Biswas

A. Bobrov

D. Bodrov

A. Bolz

A. Bondar

J. Borah

A. Boschetti

A. Bozek

M. Bračko

P. Branchini

T.E. Browder

A. Budano

S. Bussino

Q. Campagna

M. Campajola

L. Cao

G. Casarosa

C. Cecchi

J. Cerasoli

M.C. Chang

P. Chang

P. Cheema

B.G. Cheon

K. Chilikin

K. Chirapatpimol

H.E. Cho

K. Cho

S.J. Cho

S. Choudhury

J. Cochran

L. Corona

J.X. Cui

E. De La Cruz-Burelo

S.A. De La Motte

G. De Nardo

G. De Pietro

R. de Sangro

S. Dey

R. Dhamija

A. Di Canto

F. Di Capua

J. Dingfelder

Z. Doležal

I. Domínguez Jiménez

Measurement of the branching fraction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Λ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>p</mi><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msup><mi>π</mi><mn>0</mn></msup></math> at Belle