The next-to-leading order hard function for quarkonium electroproduction is calculated within the framework of transverse-momentum-dependent (TMD) factorization in the low-transverse-momentum regime. The structure of the TMD shape function in quarkonium leptoproduction is analyzed through its operator-level definition. Particular attention is given to the convolution of the unpolarized TMD gluon distribution with the TMD shape function, thereby illustrating the latter’s phenomenological role. Building on this framework, we provide predictions for the unpolarized differential cross-section of $\textit{J/ψ}$ electroproduction at the future Electron-Ion Collider in the region of small transverse momentum.

Spain

Miguel Echevarria

United States

Raj Kishore

Samuel Romera

Modeling the TMD shape function in $\textit{J}$/$\textit{ψ}$ electroproduction

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 study the processes $\textit{χ}$ $\textit{ ω}$ and $\textit{χ}$ ($\textit{π}$ $\textit{π}$ $\textit{π}$ ) ($\textit{J}$ = 0, 1, 2) at center-of-mass energies $$\sqrt{s}$$ from 10.73 to 11.02 GeV using a 142$\textit{.}$5 fb data sample collected with the Belle detector at the KEKB asymmetric-energy $\textit{e}$ $\textit{e}$ collider; and at $$\sqrt{s}\sim 10.75$$ GeV using a 19$\textit{.}$8 fb sample collected with Belle II at SuperKEKB. We find that the Υ(10753) state decays into $\textit{χ}$ $\textit{ ω}$ but not into $\textit{χ}$ ($\textit{π}$ $\textit{π}$ $\textit{π}$ ) , while the Υ(10860) state, in contrast, decays into $\textit{χ}$ ($\textit{π}$ $\textit{π}$ $\textit{π}$ ) but not into $\textit{χ}$ $\textit{ ω}$. The mass and width of the Υ(10753) state are measured to be (10756$\textit{.}$1 ± 3$\textit{.}$4(stat$\textit{.}$) ± 2$\textit{.}$7(syst$\textit{.}$)) MeV/$\textit{c}$ and (32$\textit{.}$2 ± 11$\textit{.}$3(stat$\textit{.}$) ± 14$\textit{.}$9(syst$\textit{.}$)) MeV. The products of the partial width to $\textit{e}$ $\textit{e}$ and branching fractions for Υ(10753) $\textit{→ χ}$ $\textit{ω}$ and Υ(10753) $\textit{→ χ}$ $\textit{ω}$ are (1$\textit{.}$57 $\textit{±}$ 0$\textit{.}$27(stat$\textit{.}$) $\textit{±}$ 0$\textit{.}$22(syst$\textit{.}$)) eV and (1$\textit{.}$39 $\textit{±}$ 0$\textit{.}$41(stat$\textit{.}$) $\textit{±}$ 0$\textit{.}$33(syst$\textit{.}$)) eV.

I. Adachi

L. Aggarwal

H. Ahmed

H. Aihara

N. Akopov

M. Alhakami

A. Aloisio

N. Althubiti

M. Angelsmark

N. Anh Ky

D. Asner

H. Atmacan

V. Aushev

M. Aversano

R. Ayad

V. Babu

H. Bae

N. Baghel

S. Bahinipati

P. Bambade

Sw. Banerjee

M. Barrett

M. Bartl

J. Baudot

A. Baur

A. Beaubien

F. Becherer

J. Becker

J. Bennett

F. Bernlochner

V. Bertacchi

M. Bertemes

E. Bertholet

M. Bessner

S. Bettarini

B. Bhuyan

F. Bianchi

D. Biswas

A. Bobrov

D. Bodrov

A. Bolz

A. Bondar

A. Boschetti

A. Bozek

M. Bračko

P. Branchini

R. Briere

T. Browder

A. Budano

S. Bussino

Q. Campagna

M. Campajola

G. Casarosa

C. Cecchi

J. Cerasoli

M.C. Chang

P. Chang

R. Cheaib

P. Cheema

B. Cheon

K. Chilikin

J. Chin

K. Chirapatpimol

H.E. Cho

K. Cho

S.J. Cho

S.K. Choi

S. Choudhury

J. Cochran

I. Consigny

L. Corona

J. Cui

E. Cruz-Burelo

S. Motte

G. Nardo

G. Pietro

R. Sangro

M. Destefanis

S. Dey

R. Dhamija

A. Canto

F. Capua

J. Dingfelder

Z. Doležal

I. Domínguez Jiménez

T. Dong

M. Dorigo

D. Dossett

K. Dugic

G. Dujany

P. Ecker

D. Epifanov

J. Eppelt

P. Feichtinger

T. Ferber

T. Fillinger

C. Finck

G. Finocchiaro

A. Fodor

F. Forti

Improved measurement of Born cross sections for $\textit{χ}$ $\textit{bJ}$ $\textit{ ω}$ and $\textit{χ}$ $\textit{bJ}$ ($\textit{π}$ + $\textit{π}$ $\textit{−}$ $\textit{π}$ 0)non$\textit{−ω}$ ($\textit{J}$ = 0, 1, 2) at Belle and Belle II

In this study, we analyze the first measurement of the electron-positron invariant mass spectrum in $$J/\psi \rightarrow \pi ^0 e^+e^-$$ by BESIII, using the framework of resonance chiral theory. Our results indicate that both strong interaction and electromagnetic transition are essential to accurately describe the data. We obtain the $$\pi ^0$$ transition form factor for $$J/\psi \rightarrow \pi ^0\gamma ^*$$ and the corresponding decay branching ratios for $$J/\psi \rightarrow \pi ^0 l^+l^-$$ . The decay process $$J/\psi \rightarrow \pi ^0 V$$ is also examined. It is found that $$J/\psi \rightarrow \pi ^0 \rho ^0$$ is dominated by the strong interaction, while the other two channels, $$J/\psi \rightarrow \pi ^0 \omega $$ and $$\pi ^0 \phi $$ , arise primarily from electromagnetic transitions.

China

Yi-Hao Zhang

Shao-Zhou Jiang

Ling-Yun Dai

An analysis on $$J/\psi \rightarrow \pi ^0\gamma ^*$$ within resonance chiral theory

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

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.

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

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

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

F. De Mori

X.X. Ding

Y. Ding

Y.X. Ding

J. Dong

L.Y. Dong

M.Y. Dong

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