We phenomenologically constrain the small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> and small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ξ</mi></math> gluon generalized parton distributions (GPDs) with the deeply virtual <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> production (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>DV</mi><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">P</mi></mrow></math>) in the framework of GPDs through universal moment parameterization (GUMP). We use a hybrid cross-section formula combining collinear factorization to the next-to-leading order (NLO) accuracy of the strong coupling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub></math>, with corrections from nonrelativistic QCD to account for the power corrections due to the heavy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> mass. We reach reasonable fit to the measured differential cross sections of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>DV</mi><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">P</mi></mrow></math> by H1 at the Hadron-Electron Ring Accelerator as well as forward gluon parton distribution functions (PDFs) from JAM22 global analysis. We find that both NLO and nonrelativistic corrections are significant for heavy vector meson productions. Of course, the gluon GPD we obtain still contains considerable freedom in need of inputs from other constraints, particularly in the distribution-amplitude-like region.

United States

Yuxun Guo

Xiangdong Ji

M. Gabriel Santiago

Jinghong Yang

China

Hao-Cheng Zhang

Small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> gluon GPD constrained from deeply virtual <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> production and gluon PDF through universal-moment parametrization

In this work, we have investigated the valence quark structure through chiral-even vector quark generalized parton distributions (GPDs) of light <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math> and heavy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> vector mesons using the light-cone quark model. By solving the quark-quark correlator, we have represented the quark GPDs in the light-front wave function (LFWFs) form. The charge, magnetic, and quadrupole form factors of these particles have been derived from the vector quark GPDs and compared with available theoretical predictions and lattice simulation data. The structure functions corresponding to the Rosenbluth scattering cross section of these mesons have also been calculated and compared with available NJL model predictions. All the results of our calculations are found to follow a similar trend to other model results. We have also calculated the parton distribution functions (PDFs) of these particles in the forward limit of GPDs. The calculated PDFs have also been evolved to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>5</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>GeV</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math> through next to next to leading order Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolutions.

India

 Tanisha

Satyajit Puhan

Anurag Yadav

Harleen Dahiya

Valence quark distribution of light <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math> and heavy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> vector mesons in a light-cone quark model

We report a study of the hadronic transitions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>b</mi><mi>J</mi></mrow></msub><mo stretchy="false">(</mo><mn>2</mn><mi>P</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>ω</mi><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo></mrow></math>, with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math>, using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>28.2</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>6</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>3</mn><mi>S</mi><mo stretchy="false">)</mo></mrow></math> mesons recorded by the Belle detector. We present the first evidence for the near-threshold transition <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>b</mi><mn>0</mn></mrow></msub><mo stretchy="false">(</mo><mn>2</mn><mi>P</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>ω</mi><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo></math>, the analog of the near-threshold charm sector decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>ω</mi><mi>J</mi><mo>/</mo><mi>ψ</mi></math>, with a branching fraction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo minsize="2ex" stretchy="true">(</mo><msub><mrow><mi>χ</mi></mrow><mrow><mi>b</mi><mn>0</mn></mrow></msub><mo stretchy="false">(</mo><mn>2</mn><mi>P</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>ω</mi><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo><mo minsize="2ex" stretchy="true">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>0.55</mn><mo>±</mo><mn>0.19</mn><mo>±</mo><mn>0.07</mn><mo stretchy="false">)</mo><mo>%</mo></mrow></math>. We also obtain branching fractions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mrow><mi>χ</mi></mrow><mrow><mi>b</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>2</mn><mi>P</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>ω</mi><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><msubsup><mrow><mn>2.39</mn></mrow><mrow><mo>−</mo><mn>0.19</mn></mrow><mrow><mo>+</mo><mn>0.20</mn></mrow></msubsup><mo>±</mo><mn>0.24</mn><mo stretchy="false">)</mo><mo>%</mo></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo minsize="2ex" stretchy="true">(</mo><msub><mrow><mi>χ</mi></mrow><mrow><mi>b</mi><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mn>2</mn><mi>P</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>ω</mi><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo><mo minsize="2ex" stretchy="true">)</mo><mo>=</mo><mspace linebreak="goodbreak"></mspace><mo stretchy="false">(</mo><msubsup><mrow><mn>0.47</mn></mrow><mrow><mo>−</mo><mn>0.12</mn></mrow><mrow><mo>+</mo><mn>0.13</mn></mrow></msubsup><mo>±</mo><mn>0.06</mn><mo stretchy="false">)</mo><mo>%</mo></mrow></math>, confirming the measurement of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi></math> transitions of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mi>P</mi></math>–wave states. The ratio for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>2</mn></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>1</mn></math> transitions is also measured and found to differ by 3.3 standard deviations from the expected value in the QCD multipole expansion.

Z.S. Stottler

T.K. Pedlar

B.G. Fulsom

I. Adachi

K. Adamczyk

H. Aihara

S. Al Said

D.M. Asner

H. Atmacan

T. Aushev

R. Ayad

V. Babu

Sw. Banerjee

M. Bauer

P. Behera

K. Belous

J. Bennett

F. Bernlochner

M. Bessner

T. Bilka

D. Biswas

A. Bobrov

D. Bodrov

G. Bonvicini

J. Borah

A. Bozek

P. Branchini

T.E. Browder

A. Budano

M. Campajola

L. Cao

D. Červenkov

M.C. Chang

B.G. Cheon

K. Chilikin

H.E. Cho

K. Cho

S.K. Choi

Y. Choi

S. Choudhury

D. Cinabro

S. Das

G. De Nardo

G. De Pietro

R. Dhamija

F. Di Capua

Z. Doležal

T.V. Dong

S. Dubey

P. Ecker

D. Epifanov

T. Ferber

D. Ferlewicz

V. Gaur

A. Garmash

A. Giri

P. Goldenzweig

E. Graziani

T. Gu

Y. Guan

K. Gudkova

C. Hadjivasiliou

T. Hara

K. Hayasaka

S. Hazra

M.T. Hedges

D. Herrmann

W.S. Hou

C.L. Hsu

K. Inami

N. Ipsita

A. Ishikawa

R. Itoh

M. Iwasaki

Y. Iwasaki

W.W. Jacobs

S. Jia

Y. Jin

A.B. Kaliyar

T. Kawasaki

C. Kiesling

C.H. Kim

D.Y. Kim

K.H. Kim

Y.K. Kim

P. Kodyš

A. Korobov

S. Korpar

E. Kovalenko

P. Križan

P. Krokovny

T. Kuhr

M. Kumar

R. Kumar

K. Kumara

A. Kuzmin

Y.J. Kwon

Y.T. Lai

T. Lam

M. Laurenza

Study of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>b</mi><mi>J</mi></mrow></msub><mo stretchy="false">(</mo><mn>2</mn><mi>P</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>ω</mi><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo></mrow></math> at Belle

Ultraperipheral collisions (UPCs) of ions provide new opportunities to study the quarkonium production mechanism in photon-photon scattering. In this paper, we investigate the exclusive process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mo>+</mo><mi>γ</mi><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>+</mo><mi>γ</mi></math> up to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msub><mi>α</mi><mi>s</mi></msub><msup><mi>v</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math> accuracy within the nonrelativistic quantum chromodynamics factorization framework. We evaluate the corresponding cross sections for Pb-Pb and p-p UPCs at the Large Hadron Collider. Numerical results show that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msub><mi>α</mi><mi>s</mi></msub><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mi>v</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msub><mi>α</mi><mi>s</mi></msub><msup><mi>v</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math> corrections are about <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>50</mn><mo>%</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>33</mn><mo>%</mo></math>, and 15% of the leading-order (LO) contribution, respectively, showing reasonable convergence in both <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>v</mi><mn>2</mn></msup></math> expansion. Collectively, these corrections suppress the LO cross section by a factor of about <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>/</mo><mn>3</mn></math>, which is a crucial effect for reliable phenomenological analysis. Our results suggest that future experimental measurements of this process are feasible.

Zi-Qiang Chen

Long-Bin Chen

Exclusive <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>+</mo><mi>γ</mi></math> production in ultraperipheral ion collisions

With Bayesian inference, we investigate the impact of recent near-threshold <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> production measurements by the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi><mn>007</mn></mrow></math> experiment and GlueX Collaboration on the extraction of proton gravitational form factors. We apply the generalized parton distribution framework at the next to leading order and demonstrate a stable expansion for the near-threshold kinematics. We find that the experimental constraints are in good agreement with the state-of-the-art lattice simulations, where negative <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>C</mi><mi>q</mi></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi>g</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></math> are strongly preferred. This highlights a great potential to extract them from future high-precision experiments.

Feng Yuan

Wenbin Zhao

Bayesian Inferring Nucleon Gravitational Form Factors via Near-Threshold <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> Photoproduction

We study the initial state radiation (ISR) process, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mo stretchy="false">→</mo></mrow><mrow><mo>*</mo></mrow></msup><mi>γ</mi><mo stretchy="false">→</mo><mi>γ</mi><mo>+</mo><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> observed at high luminosity <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> colliders such as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> factories, with the ISR photon being emitted through the initial electron or positron, prior to their annihilation. The emitted <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi mathvariant="normal">Ψ</mi></math> is produced through the photon fragmentation process, with the produced <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> in turn decaying into a pair of leptons, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>μ</mi><mo>−</mo></msup><mo>+</mo><msup><mi>μ</mi><mo>+</mo></msup></math> through the leptonic decay process, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>/</mo><mi mathvariant="normal">Ψ</mi><mo stretchy="false">→</mo><msup><mrow><mi>γ</mi></mrow><mrow><mo>*</mo></mrow></msup><mo stretchy="false">→</mo><mi>γ</mi><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math>. The cross section for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi mathvariant="normal">Ψ</mi></math> production, and the branching ratio for the leptonic decay of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi mathvariant="normal">Ψ</mi><mo stretchy="false">→</mo><msup><mi>μ</mi><mo>−</mo></msup><msup><mi>μ</mi><mo>+</mo></msup></math>, both calculated in the framework of Bethe-Salpeter equation are used to work out the cross section for the complete 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>γ</mi><mo>+</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi>γ</mi><mo>+</mo><msup><mi>μ</mi><mo>−</mo></msup><mo>+</mo><msup><mi>μ</mi><mo>+</mo></msup></math>. Our results are compared with the BABAR data, and other models. This study is then extended to production and decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo></math> through the ISR process.

Shashank Bhatnagar

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> production through the initial state radiation process in electron-positron annihilation at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> factories

In this study, we investigate the production of doubly charmed baryons from anti-bottom charmed mesons. Using the effective Lagrangian approach, we discuss triangle diagrams at the hadronic level to access the branching ratios of $\overline{B}_c\to {\cal{B}}_{ccq}+{\cal{B}}_{\bar c\bar q\bar q}$ . Apparently, the specific process $\overline {B}_c \to \Xi_{cc}^{+} \, \overline {\Xi}_{\bar c}^{'0}$ occupies the largest possibility on the order of $9.1\times 10^{-5}$ . In addition, although the production of undiscovered $\Omega_{cc}^+$ is Cabibbo suppressed in $\overline B_c\to \Omega_{cc}^+ \, \overline {\Xi}_{\bar c}^0$ , its branching ratio can still reach a level of $10^{-7}$ . These results are expected to provide valuable support for future experiments.

Ye Xing

Ji Xu

Searching for doubly charmed baryons from ${ \overline{\boldsymbol B}_{\boldsymbol c}}$ meson decays * Y. X. support by National Natural Science Foundation of China (12005294), and the Fundamental Funds for Key disciplines in Physics (2022WLXK05). J. X. supported by National Natural Science Foundation of China (12105247)

Recently, a number of exotic hadrons have been reported in the experiments, and most of these states lie slightly below the threshold. Therefore, these states are considered to be hadronic molecules composed of mesons or baryons. In 2022, the doubly charmed tetraquark <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> was reported by the LHCb experiment, which is considered to be composed of two heavy quarks and two light antiquarks, and located slightly below the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> threshold. The observation motivates us to study the bound and resonant states of the doubly heavy tetraquarks as two meson systems. We employ the one boson exchange potential as an interaction between two mesons, where one free parameter has been determined to reproduce <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> reported by the LHCb experiment. In our previous work, bound states of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msup><mi>B</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> molecules were studied, where we respected the heavy quark spin symmetry (HQS). Using the same framework, we study not only bound but also resonant states with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>≤</mo><mn>2</mn></math> in this paper. Furthermore, we discuss the HQS partner structures of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</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>T</mi><mrow><mi>b</mi><mi>b</mi></mrow></msub></math> obtained in our study by introducing the light cloud basis.

Japan

Manato Sakai

Yasuhiro Yamaguchi

Analysis of bound and resonant states of doubly heavy tetraquarks with spin <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>≤</mo><mn>2</mn></math>

Motivated by the recent LHCb measurements of the ratios between the branching ratios (BRs), <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mrow><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo>/</mo><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></msub><mo>≡</mo><mrow><mi>BR</mi></mrow><mo stretchy="false">(</mo><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><msup><mi>π</mi><mo>+</mo></msup><mo stretchy="false">)</mo><mo>/</mo><mrow><mi>BR</mi></mrow><mo stretchy="false">(</mo><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>π</mi><mo>+</mo></msup><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mrow><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo>/</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></mrow></msub><mo>≡</mo><mrow><mi>BR</mi></mrow><mo stretchy="false">(</mo><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><msup><mi>π</mi><mo>+</mo></msup><mo stretchy="false">)</mo><mo>/</mo><mrow><mi>BR</mi></mrow><mo stretchy="false">(</mo><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><msup><mi>π</mi><mo>+</mo></msup><mo stretchy="false">)</mo></math>, we analyze the decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">(</mo><mi>P</mi><mo>,</mo><mi>V</mi><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math> in the improved perturbative QCD (iPQCD) formalism, where <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> denotes the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi></math>-wave charmonia with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>=</mo><mn>0</mn></math>, 1, 2, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi><mo stretchy="false">(</mo><mi>V</mi><mo stretchy="false">)</mo></math> denotes the pseudoscalars <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math> (the vectors <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup></math>). Our results <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mrow><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo>/</mo><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></msub><mo>=</mo><mn>0.32</mn><mo>±</mo><mn>0.05</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mrow><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo>/</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></mrow></msub><mo>=</mo><mn>0.11</mn><mo>±</mo><mn>0.01</mn></math> at leading order in the strong coupling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub></math> agree well with the data within uncertainties. The result <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mrow><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub><mo>/</mo><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></msub><mo>≡</mo><mrow><mi>BR</mi></mrow><mo stretchy="false">(</mo><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub><msup><mi>π</mi><mo>+</mo></msup><mo stretchy="false">)</mo><mo>/</mo><mrow><mi>BR</mi></mrow><mo stretchy="false">(</mo><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>π</mi><mo>+</mo></msup><mo stretchy="false">)</mo><mo>=</mo><mn>0.17</mn><mo>±</mo><mn>0.02</mn></math> is lower than <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mn>1.41</mn><mrow><mo>−</mo><mn>0.45</mn></mrow><mrow><mo>+</mo><mn>0.50</mn></mrow></msubsup></math> inferred by the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub><msup><mi>π</mi><mo>+</mo></msup></math> measurement. The large longitudinal polarization fractions imply that these components dominate the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn><mo>,</mo><mi>c</mi><mn>2</mn></mrow></msub><msup><mi>ρ</mi><mo>+</mo></msup></math> BRs. A peculiar constructive (destructive) interference between the twist-2 and twist-3 contributions is identified in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><msup><mi>ρ</mi><mo>+</mo></msup></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><msup><mi>π</mi><mo>+</mo></msup></math>) mode, but not in the corresponding ones with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn><mo>,</mo><mi>c</mi><mn>2</mn></mrow></msub></math> mesons. Inputting the BRs of the strong decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn><mo>,</mo><mi>c</mi><mn>2</mn></mrow></msub><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo>/</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> and <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><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo stretchy="false">(</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo>/</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><mo stretchy="false">)</mo></math> reported by the BESIII Collaboration, we obtain those of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">(</mo><mi>ρ</mi><mo>,</mo><mi>π</mi><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math> followed by secondary decay chains under the narrow-width approximation. All the above iPQCD predictions can be confronted by more precise experiments in the future to deepen our understanding of QCD dynamics in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math> transitions.

Xin Liu

Hsiang-nan Li

Zhen-Jun Xiao

Study of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub><mo stretchy="false">→</mo><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo stretchy="false">(</mo><mi>P</mi><mo>,</mo><mi>V</mi><mo stretchy="false">)</mo></math> decays in the improved perturbative QCD formalism

A partial-wave analysis is performed on the decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi>γ</mi><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> within the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math> invariant-mass region below <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1.6</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>/</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math>, using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>10.09</mn><mo>±</mo><mn>0.04</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>9</mn></mrow></msup></mrow></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> events collected with the BESIII detector. Significant isospin-violating decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mo stretchy="false">(</mo><mn>1405</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1420</mn><mo stretchy="false">)</mo></math> into <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><msup><mi>π</mi><mn>0</mn></msup></math> are observed. For the first time, three axial vectors, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1285</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1420</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1510</mn><mo stretchy="false">)</mo></math>, are observed to decay into <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math>. The product branching fractions of these resonances are reported.

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

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

Study of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>f</mi></mrow><mn>1</mn></msub><mo stretchy="false">(</mo><mn>1420</mn><mo stretchy="false">)</mo></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mo stretchy="false">(</mo><mn>1405</mn><mo stretchy="false">)</mo></math> in the decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi>γ</mi><msup><mrow><mi>π</mi></mrow><mn>0</mn></msup><msup><mrow><mi>π</mi></mrow><mn>0</mn></msup><msup><mrow><mi>π</mi></mrow><mn>0</mn></msup></mrow></math>