France

G. Aad

Norway

E. Aakvaag

United States

B. Abbott

United Arab Emirates

S. Abdelhameed

Germany

K. Abeling

N. Abicht

S. Abidi

M. Aboelela

Morocco

A. Aboulhorma

Israel

H. Abramowicz

H. Abreu

Y. Abulaiti

Italy

United Kingdom

B. Acharya

A. Ackermann

C. Bourdarios

Poland

L. Adamczyk

S. Addepalli

M. Addison

J. Adelman

Türkiye

A. Adiguzel

T. Adye

A. Affolder

Y. Afik

Spain

M. Agaras

J. Agarwala

A. Aggarwal

Romania

C. Agheorghiesei

Azerbaijan

F. Ahmadov

Canada

W. Ahmed

S. Ahuja

China

X. Ai

G. Aielli

A. Aikot

M. Tamlihat

B. Aitbenchikh

M. Akbiyik

Sweden

T. Åkesson

A. Akimov

Japan

D. Akiyama

N. Akolkar

S. Aktas

K. Khoury

G. Alberghi

J. Albert

P. Albicocco

G. Albouy

S. Alderweireldt

Z. Alegria

Switzerland

M. Aleksa

I. Aleksandrov

C. Alexa

Greece

T. Alexopoulos

F. Alfonsi

M. Algren

M. Alhroob

Czechia

B. Ali

H. Ali

S. Ali

S. Alibocus

South Africa

M. Aliev

G. Alimonti

W. Alkakhi

C. Allaire

B. Allbrooke

J. Allen

Chile

C. Flores

P. Allport

A. Aloisio

Argentina

F. Alonso

C. Alpigiani

Z. Alsolami

M. Estevez

A. Fernandez

M. Cardoso

M. Alviggi

M. Aly

Brazil

Y. Coutinho

A. Ambler

C. Amelung

M. Amerl

C. Ames

D. Amidei

B. Amini

K. Amirie

Portugal

S. Santos

K. Amos

D. Amperiadou

S. An

V. Ananiev

C. Anastopoulos

T. Andeen

J. Anders

A. Anderson

S. Andrean

A. Andreazza

S. Angelidakis

A. Angerami

A. Anisenkov

A. Annovi

C. Antel

Erratum: Precision measurement of the $$B^0$$ meson lifetime using $$B^0 \rightarrow J/\psi K^{*0}$$ decays with the ATLAS detector

<p>In this work, we investigate the dipion transition processes <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><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>=</mo><mn>0</mn></mrow></math>, 1, 2) within the framework of heavy hadron chiral perturbation theory, treating <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> as a molecular state composed of <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><mo>+</mo><mi mathvariant="normal">H</mi><mo>.</mo><mi mathvariant="normal">c</mi><mo>.</mo></math> components. By analyzing the box and triangle loop diagrams with the nonrelativistic effective field theory power-counting rule, we demonstrate that box diagrams dominate these dipion transition processes. Branching ratios are calculated as functions of the mixing angle <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>θ</mi></math>, which parametrizes the neutral and charged meson compositions of the <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>. Our results indicate that the branching fractions for <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><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub></math>, <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><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub></math>, and <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><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></math> are of the orders of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math>, respectively. We also predict the ratios <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn><mo>/</mo><mn>2</mn></mrow></msub><mo stretchy="false">]</mo></mrow><mo>/</mo><mrow><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo stretchy="false">]</mo></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">]</mo></mrow><mo>/</mo><mrow><mi mathvariant="script">B</mi><mo stretchy="false">[</mo><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">]</mo></mrow></math>. The latter deviates from isospin-symmetry expectations, revealing various degrees of isospin violation. By studying 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"><msup><mi>π</mi><mo>+</mo></msup><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math> invariant mass spectra, we find a double-bump structure in 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> invariant mass distributions of the process <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><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mo>+</mo></msup><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub></math> invariant mass distribution of the process <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><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub></math>, which could be tested by future experimental measurements.</p>

Qi Wu

Zhong-Quan Sun

Dian-Yong Chen

Shi-Dong Liu

Gang Li

Dipion transitions from <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> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>=</mo><mn>0</mn></mrow></math>, 1, 2)

<p>Utilizing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2712.4</mn><mo>±</mo><mn>14.3</mn><mtext> </mtext><mtext> </mtext><mi>million</mi></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo></math> events accumulated by the BESIII experiment, we perform a partial wave analysis of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>γ</mi><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">→</mo><mi>γ</mi><mi mathvariant="normal">Λ</mi><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover></math> decay (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>0</mn></math>, 1, 2). The ratio of the helicity amplitudes with same (++) and opposite (+-) helicity for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover></math> decay is determined for the first time to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></msub><mo>=</mo><mn>0.575</mn><mo>±</mo><mn>0.048</mn><mo>±</mo><mn>0.018</mn></math>, with a relative phase angle <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msub><mi mathvariant="normal">Φ</mi><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></msub><mo>=</mo><mn>0.37</mn><mo>±</mo><mn>0.15</mn><mo>±</mo><mn>0.05</mn><mtext> </mtext><mtext> </mtext><mi>rad</mi></math>. The parameters of the angular distribution of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></math> are determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></msub><mo>=</mo><mo>−</mo><mn>0.211</mn><mo>±</mo><mn>0.100</mn><mo>±</mo><mn>0.050</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>β</mi><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></msub><mo>=</mo><mo>−</mo><mn>0.039</mn><mo>±</mo><mn>0.089</mn><mo>±</mo><mn>0.033</mn></math>, based on the distribution <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><mi>N</mi><mo>/</mo><mi>d</mi><mi>cos</mi><mi>θ</mi><mo>=</mo><mn>1</mn><mo>+</mo><msub><mi>α</mi><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></msub><msup><mi>cos</mi><mn>2</mn></msup><mi>θ</mi><mo>+</mo><msub><mi>β</mi><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></msub><msup><mi>cos</mi><mn>4</mn></msup><mi>θ</mi></math>. The width of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub></math> is determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>12.31</mn><mo>±</mo><mn>0.26</mn><mo>±</mo><mn>0.12</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. Additionally, the branching fractions for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover></math> are measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>3.662</mn><mo>±</mo><mn>0.048</mn><mo>±</mo><mn>0.111</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>1.182</mn><mo>±</mo><mn>0.026</mn><mo>±</mo><mn>0.042</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>1.704</mn><mo>±</mo><mn>0.035</mn><mo>±</mo><mn>0.057</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></math>, respectively, where the first uncertainty is statistical and the second systematic.</p>

M. Ablikim

Russia

M.N. Achasov

P. Adlarson

X.C. Ai

R. Aliberti

A. Amoroso

Q. An

Y. Bai

JINR

O. Bakina

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

M.H. Cai

X. Cai

A. Calcaterra

G.F. Cao

N. Cao

S.A. Cetin

X.Y. Chai

J.F. 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.L. Chen

S.M. Chen

T. Chen

X.R. Chen

X.T. Chen

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z. Chen

Z.J. Chen

Z.K. Chen

South Korea

S.K. Choi

X. Chu

G. Cibinetto

F. Cossio

J. Cottee-Meldrum

J.J. Cui

H.L. Dai

J.P. Dai

A. Dbeyssi

R.E. de Boer

Helicity amplitude and branching fraction measurement of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">→</mo><mi mathvariant="normal">Λ</mi><mover accent="true"><mi mathvariant="normal">Λ</mi><mo stretchy="false">¯</mo></mover></math>