<p>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.</p>

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

<p>Based on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>2712.4</mn><mo>±</mo><mn>14.4</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>6</mn></mrow></msup><mtext> </mtext><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo></mrow></math> events collected with the BESIII detector, we present a high-precision study 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> mass spectrum in <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><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mi>J</mi><mo>/</mo><mi>ψ</mi></math> decays. A clear resonancelike structure is observed near 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> mass threshold for the first time. A fit with a Breit-Wigner function yields a mass of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>285.6</mn><mo>±</mo><mn>2.5</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math> and a width of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>16.3</mn><mo>±</mo><mn>0.9</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> with a statistical significance exceeding <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>10</mn><mi>σ</mi></mrow></math>. To interpret the data, we incorporate final-state interactions (FSI) within two theoretical frameworks: chiral perturbation theory (ChPT) and QCD multipole expansion (QCDME). ChPT describes the spectrum above <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0.3</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>/</mo><msup><mi>c</mi><mn>2</mn></msup></math> but fails to reproduce the threshold enhancement. In contrast, the QCDME model—assuming the <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> is an admixture of S- and D-wave charmonium—reproduces the data well. The pronounced dip near <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0.3</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>/</mo><msup><mi>c</mi><mn>2</mn></msup></math> offers new insight into the interplay between chiral dynamics and low-energy QCD.</p>

M. Ablikim

M.N. Achasov

P. Adlarson

X.C. Ai

R. Aliberti

A. Amoroso

Q. An

Y. Bai

O. Bakina

Y. Ban

H.R. 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

X.R. Chen

X.T. Chen

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z.K. Chen

J.C. 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

I. Denisenko

M. Destefanis

F. De Mori

X.X. Ding

Y. Ding

Y.X. Ding

J. Dong

L.Y. Dong

M.Y. Dong

X. Dong

M.C. Du

S.X. Du

X.L. Du

Y.Y. Duan

Z.H. Duan

P. Egorov

G.F. Fan

J.J. Fan

Y.H. Fan

J. Fang

S.S. Fang

W.X. Fang

Y.Q. Fang

L. Fava

F. Feldbauer

G. Felici

C.Q. Feng

J.H. Feng

L. Feng

Q.X. Feng

Y.T. Feng

M. Fritsch

Observation of a Threshold Enhancement 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> Spectrum in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>ψ</mi><mo stretchy="false">(</mo><mn>3686</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> Decays

Constraints on Wilson coefficients (WCs) corresponding to dimension-6 operators of the standard model effective field theory (SMEFT) are determined from a simultaneous fit to seven sets of CMS measurements probing Higgs boson, electroweak vector boson, top quark, and multijet production. Measurements of electroweak precision observables are also included and provide complementary constraints to those from the CMS experiment. The CMS measurements, using LHC proton-proton collision data at $$\sqrt{s}=13\,\text {Te}\text {V} $$ , corresponding to integrated luminosities of 36.3 or 138 $$\,\text {fb}^{-1}$$ , are chosen to provide sensitivity to a broad set of operators, for which consistent SMEFT predictions can be derived. These are primarily measurements of differential cross sections which are parameterized as functions of the WCs. In measurements targeting $${\text {t}} (\bar{\textrm{t}})\text {X} $$ production, SMEFT effects are modelled at the detector level. Individual constraints on 64 WCs, and constraints on 43 linear combinations of WCs, are obtained.

Armenia

V. Chekhovsky

A. Hayrapetyan

V. Makarenko

A. Tumasyan

Austria

W. Adam

J. Andrejkovic

L. Benato

T. Bergauer

K. Damanakis

M. Dragicevic

C. Giordano

P. Hussain

Belgium

M. Jeitler

N. Krammer

A. Li

D. Liko

I. Mikulec

J. Schieck

R. Schöfbeck

D. Schwarz

M. Sonawane

W. Waltenberger

C.E. Wulz

T. Janssen

H. Kwon

T. Laer

P. Mechelen

J. Bierkens

N. Breugelmans

J. D’Hondt

S. Dansana

A. Moor

M. Delcourt

F. Heyen

Y. Hong

S. Lowette

I. Makarenko

D. Müller

S. Tavernier

M. Tytgat

G. Onsem

S. Putte

D. Vannerom

B. Bilin

B. Clerbaux

A. Das

I. Bruyn

G. Lentdecker

H. Evard

L. Favart

P. Gianneios

A. Khalilzadeh

F. Khan

A. Malara

M. Shahzad

L. Thomas

M. Vanden Bemden

C. Vander Velde

P. Vanlaer

F. Zhang

M. Coen

D. Dobur

G. Gokbulut

J. Knolle

L. Lambrecht

D. Marckx

K. Skovpen

N. Bossche

J. Linden

J. Vandenbroeck

L. Wezenbeek

S. Bein

A. Benecke

A. Bethani

G. Bruno

A. Cappati

J. Favereau De Jeneret

C. Delaere

A. Giammanco

A. Guzel

Sa. Jain

V. Lemaitre

J. Lidrych

P. Mastrapasqua

S. Turkcapar

Brazil

G. Alves

E. Coelho

G. Correia Silva

C. Hensel

T. Menezes De Oliveira

C. Mora Herrera

Combined effective field theory interpretation of Higgs boson, electroweak vector boson, top quark, and multijet measurements