In double charmonium production, a long-standing challenge is that the theoretical predictions are not consistent with the measurements at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> factories. Within the Non-Relativistic Quantum Chromodynamics (NRQCD) framework, the next-to-leading order calculation has proved its power to cut down the discrepancy between theory and experiments. To further clarify this puzzle, we have performed the next-to-next-to-leading order calculation. The amplitude is obtained as an analytical asymptotic expansion in the ratio of the squared charm-quark mass over the squared center-of-mass energy, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>m</mi><mi>c</mi><mn>2</mn></msubsup><mo>/</mo><mi>s</mi></math>. We investigate the origin of the leading logarithms by performing a region analysis, revealing the intricate factorization structure in this process. We provide numerical predictions on the total cross sections of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>+</mo><msub><mi>η</mi><mi>c</mi></msub></math> production, which agree with the experimental results. Extension of our computation to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo>+</mo><msub><mi>η</mi><mi>b</mi></msub></math> production is also discussed.

Xiang Chen

Xin Guan

Chuan-Qi He

Yan-Qing Ma

Jian Wang

Da-Jiang Zhang

Analytical two-loop amplitudes 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><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>+</mo><msub><mi>η</mi><mi>c</mi></msub></math> at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> factories

We propose a mechanism for relaxing a gauge theory <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violating phase in discrete steps to very small values. The idea is that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violating phase includes the magnetic dual of a 4-form flux that can discharge by the nucleation of membranes. Inside the bubbles surrounded by the membranes, the total <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violating phase is reduced. When the bubbles are produced rapidly during radiation domination in the early Universe, near the chiral symmetry breaking scale, they will collide and percolate, melting away into gauge theory radiation and dramatically relaxing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation.

Nemanja Kaloper

Quantal theory of restoration of strong <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> symmetry

We employed the chiral unitarity approach to investigate the decay process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Σ</mi><mo>+</mo></msup><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math>, by considering that the low lying nucleon resonance <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">(</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math> and the low lying scalar meson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math> that could be dynamically generated through the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave pseudoscalar meson-octet baryon and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave pseudoscalar-meson–pseudoscalar-meson interactions, respectively. In the invariant mass distributions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">Σ</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math>, we observe a distinct peak structure associated with the resonant state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">(</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math> and a bit enhancement near the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> threshold that is corresponding to the mesons <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math>, respectively. Consequently, we recommend more precise experimental measurements of this process in the future.

Ruitian Li

Xuan Luo

Hao Sun

Theoretical study of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">(</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo stretchy="false">)</mo></math> in the process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Σ</mi><mo>+</mo></msup><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math>

We firstly carry out a systematic analysis on the spin <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>+</mo></msup></math> weak transition process in the framework of three-point QCD sum rules, where the initial and final states are doubly and singly charmed baryons. On the phenomenological side, all possible couplings of interpolating current to hadronic states are considered. In doing operator production expansion on the QCD side, the contributions of the perturbative part and vacuum condensate terms of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">⟨</mo><mrow><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mi>q</mi></mrow><mo stretchy="false">⟩</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">⟨</mo><msubsup><mi>g</mi><mi>s</mi><mn>2</mn></msubsup><mi>G</mi><mi>G</mi><mo stretchy="false">⟩</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">⟨</mo><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><msub><mi>g</mi><mi>s</mi></msub><mi>σ</mi><mi>G</mi><mi>q</mi><mo stretchy="false">⟩</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>g</mi><mi>s</mi><mn>2</mn></msubsup><mo stretchy="false">⟨</mo><mrow><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mi>q</mi></mrow><msup><mo stretchy="false">⟩</mo><mn>2</mn></msup></math> are all considered. After the form factors in the spacelike region (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Q</mi><mn>2</mn></msup><mo>&gt;</mo><mn>0</mn></math>) are obtained, the numerical results are extrapolated into the timelike region (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Q</mi><mn>2</mn></msup><mo>&lt;</mo><mn>0</mn></math>) by a fitting function. Using the predicted form factors, we finally analyze the semileptonic decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Σ</mi><mi>c</mi><mrow><mo>*</mo><mo>+</mo></mrow></msubsup><msup><mi>l</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>l</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mrow><mo>′</mo><mo>*</mo><mo>+</mo></mrow></msubsup><msup><mi>l</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>l</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ω</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mrow><mo>′</mo><mo>*</mo><mn>0</mn></mrow></msubsup><msup><mi>l</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>l</mi></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ω</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup><mo stretchy="false">→</mo><msubsup><mi mathvariant="normal">Ω</mi><mi>c</mi><mrow><mo>*</mo><mn>0</mn></mrow></msubsup><msup><mi>l</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>l</mi></msub></math> with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>l</mi><mo>=</mo><mi>e</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>μ</mi></mrow></math>. The predictions in this work can deepen our understanding of the dynamics in the decay processes of doubly heavy baryons and provide useful information to explore the possibility of new physics in heavy baryonic decay channels.

Guo-Liang Yu

Zhi-Gang Wang

Jie Lu

Bin Wu

Peng Yang

Ze Zhou

Analysis of the semileptonic decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ω</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> baryons in QCD sum rules

We present a systematic analysis of Bell nonlocality and entanglement in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">(</mo><mi>J</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></math> decays into a baryon pair (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover></math>), with particular emphasis on their production via the process <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>2</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>γ</mi><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math> at BESIII. From the baryon-antibaryon spin density matrix, we construct measurable Bell observables and concurrence, revealing a striking hierarchy of quantum correlations: <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> decays exhibit maximal violation and entanglement; <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> decays violate Bell inequalities for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>θ</mi><mn>1</mn></msub><mo>∈</mo><mo stretchy="false">(</mo><mn>0</mn><mo>,</mo><mi>π</mi><mo stretchy="false">)</mo></math> with angle-modulated strength; we find that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover></math> pair in <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> decays is in a separable state, and no indication of Bell inequality violation is observed. We provide complete analytical results for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>0</mn></math>, 1 and quantitative, uncertainty-aware estimations for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>2</mn></math> based on experimental inputs from BESIII. These results establish the <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> system produced via this radiative transition as a novel and promising platform for testing quantum entanglement and Bell nonlocality in high-energy collisions.

Peng-Cheng Hong

Rong-Gang Ping

Wei-Min Song

Bell nonlocality and entanglement in <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> decays into a baryon pair

The first four-dimensional amplitude analysis of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><msubsup><mi>K</mi><mi mathvariant="normal">S</mi><mn>0</mn></msubsup><msup><mi>π</mi><mo>+</mo></msup></math> decay is performed with proton-proton collision data collected by the LHCb experiment at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>13</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math>, corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>5.4</mn><mtext> </mtext><mtext> </mtext><mrow><mi mathvariant="normal">f</mi><msup><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></mrow></math>. The data cannot be fully explained by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><msup><mi>K</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup></math> contributions alone. A significantly better description of the data is obtained by adding a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover></mrow><mo>+</mo></msubsup></math> contribution decaying to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><msup><mi>π</mi><mo>+</mo></msup></math>. The properties of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover></mrow><mo>+</mo></msubsup></math> structure are consistent with the exotic state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>4430</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math> reported in the isospin-related <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><mo stretchy="false">→</mo><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><msup><mi>K</mi><mo>−</mo></msup><msup><mi>π</mi><mo>+</mo></msup></math> decay. Effects of a possible <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>4430</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup><mo stretchy="false">→</mo><msubsup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mn>1</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>2600</mn><msup><mo stretchy="false">)</mo><mn>0</mn></msup><msup><mi>D</mi><mo>+</mo></msup></math> decay mode on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>4430</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup><mo stretchy="false">→</mo><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><msup><mi>π</mi><mo>+</mo></msup></math> mass distribution are investigated through a Flatté parametrization, providing constraints on the relative decay strength. A description of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>4430</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math> structure using the triangle singularity mechanism is studied and also found to be consistent with the data.

R. Aaij

A.S.W. Abdelmotteleb

C. Abellan Beteta

F. Abudinén

T. Ackernley

A.A. Adefisoye

B. Adeva

M. Adinolfi

P. Adlarson

C. Agapopoulou

C.A. Aidala

Z. Ajaltouni

S. Akar

K. Akiba

M. Akthar

P. Albicocco

J. Albrecht

R. Aleksiejunas

F. Alessio

P. Alvarez Cartelle

R. Amalric

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

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

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

F. Betti

J. Bex

O. Bezshyyko

J. Bhom

M.S. Bieker

N.V. Biesuz

A. Biolchini

M. Birch

F.C.R. Bishop

A. Bitadze

A. Bizzeti

T. Blake

F. Blanc

Observation and investigation of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>4430</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math> structure in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><msubsup><mi>K</mi><mi mathvariant="normal">S</mi><mn>0</mn></msubsup><msup><mi>π</mi><mo>+</mo></msup></math> decays

Using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>10087</mn><mo>±</mo><mn>44</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup><mtext> </mtext><mtext> </mtext><mi>J</mi><mo>/</mo><mi>ψ</mi></math> events collected with the BESIII detector at the BEPCII collider, we report the first observation of the decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Ξ</mi><mn>0</mn></msup><msup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup></math>. The interference between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi>γ</mi><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">→</mo><mi>γ</mi><msup><mi mathvariant="normal">Ξ</mi><mn>0</mn></msup><msup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi>γ</mi><msup><mi mathvariant="normal">Ξ</mi><mn>0</mn></msup><msup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msub><mo stretchy="false">|</mo><mrow><mi>non</mi><mo>−</mo><mi>resonance</mi></mrow></msub></math> is considered in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">Ξ</mi><mn>0</mn></msup><msup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup></math> mass spectrum fits. The branching fractions are measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Ξ</mi><mn>0</mn></msup><msup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>1.33</mn><mo>±</mo><mn>0.03</mn><mo>±</mo><mn>0.18</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math> for the constructive interference and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Ξ</mi><mn>0</mn></msup><msup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>1.63</mn><mo>±</mo><mn>0.04</mn><mo>±</mo><mn>0.21</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math> for the destructive interference, where the first uncertainties are statistical and the second are systematic.

M. Ablikim

M.N. Achasov

X.C. Ai

C.S. Akondi

R. Aliberti

A. Amoroso

Q. An

Y.H. An

Y. Bai

O. Bakina

Y. Ban

H.R. Bao

X.L. Bao

V. Batozskaya

K. Begzsuren

N. Berger

M. Berlowski

M.B. 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

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

W. Chen

X.R. Chen

X.T. Chen

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z.K. Chen

J. Cheng

L.N. Cheng

S.K. Choi

X. Chu

G. Cibinetto

F. Cossio

J. Cottee-Meldrum

H.L. Dai

J.P. Dai

X.C. Dai

A. Dbeyssi

R.E. de Boer

D. Dedovich

C.Q. Deng

Z.Y. Deng

A. Denig

First observation of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>η</mi><mi>c</mi></msub><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Ξ</mi><mn>0</mn></msup><msup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup></math> decay