By combining the effective Lagrangian and Bethe-Salpeter framework, we studied the mass spectra, wave functions, and strong decay widths of the two pentaquark states $${P}_{\psi }^{N}{\left({444}0\right)}^{+}$$ and $${P}_{\psi }^{N}{\left({4457}\right)}^{+}$$ reported by LHCb in 2019. Taking into account both the mass ordering and the decay widths, our results favor the interpretation of $${P}_{\psi }^{N}{\left({444}0\right)}^{+}$$ and $${P}_{\psi }^{N}{\left({4457}\right)}^{+}$$ as the isospin- $$\frac{1}{2}$$ $$\left[{\overline{D} }^{*}{\Sigma}_{c}\right]$$ molecular states with $\textit{J}$ configuration $${\left(\frac{3}{2}\right)}^{-}$$ and $${\left(\frac{1}{2}\right)}^{-}$$ , respectively. We first calculate the one-boson-exchange interaction kernel of $$\left[{\overline{D} }^{*}{\Sigma}_{c}\right]$$ in the isospin- $$\frac{1}{2}$$ configuration. Then we present the Bethe-Salpeter equation (BSE) and wave functions for the bound states of a vector meson and a $$\frac{1}{2}$$ baryon with $${J}^{P}=\frac{1}{2}^{-}$$ and $$\frac{3}{2}^{-}$$ . The obtained mass results for the $${\left(\frac{3}{2}\right)}^{-}$$ and $${\left(\frac{1}{2}\right)}^{-}$$ are 4.442 and 4.457 GeV, respectively. Combining the effective Lagrangians and the BS wave functions, we further calculate the strong decay channels $${\overline{D} }^{(*)0}{\Lambda}_{c}^{+}$$ , $\textit{J}$/$\textit{ψ}$($\textit{η}$ )$\textit{p}$, and $$\overline{D}{\Sigma }_{c}^{(*)}$$ for the two $${P}_{\psi }^{N}$$ states. In the favored $$\frac{3}{2}^{-}$$ and $$\frac{1}{2}^{-}$$ configuration, the obtained total widths are 21.8 MeV and 13.0 MeV, respectively, which are substantially consistent with the LHCb data. Our results suggest that $${\overline{D} }^{0}{\Lambda}_{c}^{+}$$ and $${\overline{D} }^{(*)0}{\Lambda}_{c}^{+}$$ are the dominant decay channels to detect $${P}_{\psi }^{N}{\left({444}0\right)}^{+}$$ and $${P}_{\psi }^{N}{\left({4457}\right)}^{+}$$ , respectively.

China

Qiang Li

Chao-Hsi Chang

Xin Tong

Germany

Xiao-Ze Tan

Tianhong Wang

Guo-Li Wang

Strong decays of $${P}_{\psi }^{N}{\left({444}0\right)}^{+}$$ and $${P}_{\psi }^{N}{\left({4457}\right)}^{+}$$ within the Bethe-Salpeter framework

Large-scale organic liquid scintillator detectors are highly efficient in the detection of MeV-scale electron antineutrinos. These signal events can be detected through inverse beta decay on protons, which produce a positron accompanied by a neutron. A noteworthy background for antineutrinos coming from nuclear power reactors and from the depths of the Earth (geoneutrinos) is generated by ( $$\alpha ,\,n$$ ) reactions. In organic liquid scintillator detectors, $$\alpha $$ particles emitted from intrinsic contaminants such as $$^{238}$$ U, $$^{232}$$ Th, and $$^{210}$$ Pb/ $$^{210}$$ Po, can be captured on $$^{13}$$ C nuclei, followed by the emission of a MeV-scale neutron. Three distinct interaction mechanisms can produce prompt energy depositions preceding the delayed neutron capture, leading to a pair of events correlated in space and time within the detector. Thus, ( $$\alpha ,\,n$$ ) reactions represent an indistinguishable background in liquid scintillator-based antineutrino detectors, where their expected rate and energy spectrum are typically evaluated via Monte Carlo simulations. This work presents results from the open-source SaG4n software, used to calculate the expected energy depositions from the neutron and any associated de-excitation products. Also simulated is a detailed detector response to these interactions, using a dedicated Geant4-based simulation software from the JUNO experiment. An expected measurable $$^{13}$$ C $$(\alpha ,\,n)^{16}$$ O event rate and reconstructed prompt energy spectrum with associated uncertainties, are presented in the context of JUNO, however, the methods and results are applicable and relevant to other organic liquid scintillator neutrino detectors.

France

Thomas Adam

Kai Adamowicz

Pakistan

Shakeel Ahmad

Rizwan Ahmed

Italy

Sebastiano Aiello

Fengpeng An

United Kingdom

Costas Andreopoulos

Giuseppe Andronico

Russia

Nikolay Anfimov

Vito Antonelli

Tatiana Antoshkina

João Athayde Marcondes de André

Didier Auguste

Weidong Bai

Nikita Balashov

Andrea Barresi

Davide Basilico

Eric Baussan

Marco Beretta

Antonio Bergnoli

Nikita Bessonov

Daniel Bick

Lukas Bieger

Svetlana Biktemerova

Thilo Birkenfeld

Simon Blyth

Anastasia Bolshakova

Mathieu Bongrand

Matteo Borghesi

Dominique Breton

Augusto Brigatti

Riccardo Brugnera

Riccardo Bruno

Marcel Büchner

Antonio Budano

Jose Busto

Anatael Cabrera

Barbara Caccianiga

Hao Cai

Xiao Cai

Yanke Cai

Zhiyan Cai

Stéphane Callier

Steven Calvez

United Arab Emirates

Antonio Cammi

Chuanya Cao

Guofu Cao

Jun Cao

Yaoqi Cao

Rossella Caruso

Cédric Cerna

Vanessa Cerrone

Jinfan Chang

Taiwan

Yun Chang

Thailand

Auttakit Chatrabhuti

Chao Chen

Guoming Chen

Jiahui Chen

Jian Chen

Jing Chen

Junyou Chen

Pingping Chen

Shaomin Chen

Shiqiang Chen

Xin Chen

Yiming Chen

Yixue Chen

Yu Chen

Ze Chen

Zhangming Chen

Zhiyuan Chen

Jie Cheng

Yaping Cheng

Yu Cheng

Alexander Chepurnov

Alexey Chetverikov

Davide Chiesa

Brazil

Pietro Chimenti

Po-Lin Chou

Ziliang Chu

Artem Chukanov

Gérard Claverie

Catia Clementi

Belgium

Barbara Clerbaux

Claudio Coletta

Selma Conforti Di Lorenzo

Simon Csakli

Chenyang Cui

United States

Olivia Dalager

Christophe Taille

Zhi Deng

Ziyan Deng

Xiaoyu Ding

Xuefeng Ding

Yayun Ding

Bayu Dirgantara

Carsten Dittrich

Sergey Dmitrievsky

David Doerflinger

Dmitry Dolzhikov

Simulation of the background from $$^{13}$$ C $$(\alpha ,\,n)^{16}$$ O reaction in the JUNO scintillator

We study $ \cos2\phi $ azimuthal asymmetry in doubly longitudinally polarized proton-proton Drell-Yan collisions within the transverse momentum dependent factorization framework. The asymmetry arises from the convolution of the longitudinal transversity distribution $ h_{1L}^{\perp} $ for both protons. Using the Bacchetta-Delcarro-Pisano-Radici-Signori parameterization for the nonperturbative Sudakov form factor and the Wandzura-Wilczek approximation for collinear $ h_{1L}^{\perp} $ , we predict the double spin asymmetry $ A_{LL}^{\cos2\phi} $ at RHIC and NICA kinematics. Our results demonstrate sensitivity to sea quark distributions, with the asymmetry reaching up to 25% for maximal sea quark contributions. These predictions highlight the potential of polarized Drell-Yan measurements to probe sea quark dynamics and advance our understanding of nucleon structures.

Hui Li

Ting Hu

Liang-Liang Liu

Xiao-Yu Wang

Zhun Lu

Asymmetry ${{\boldsymbol A}_{\boldsymbol{LL}}^{\bf\cos2\boldsymbol\phi}} $ in the polarized proton-proton Drell-Yan process within TMD factorization * Hui Li is supported by Fundamental Research Program of Shanxi Province (202203021222224) and Natural Science Foundation of Shanxi Normal University (JCYJ2023021). Xiao-Yu Wang is supported by the Natural Science Foundation of Henan Province (242300421377, 232300421140)

We propose a search strategy at the HL-LHC for a new neutral particle $\textit{X}$ that couples to $\textit{W}$-bosons, using the process $ p p \to W^{\pm} X (\to W^{+} W^{-}) $ with a tri-$\textit{W}$-boson final state. Focusing on events with two same-sign leptonic $\textit{W}$-boson decays into muons and a hadronically decaying $\textit{W}$-boson, our method leverages the enhanced signal-to-background discrimination achieved through a machine-learning-based multivariate analysis. Using the heavy photophobic axion-like particle (ALP) as a benchmark, we evaluate the discovery sensitivities on both production cross section times branching ratio $ \sigma(p p \to W^{\pm} X) \times \text{Br}(X \to W^{+} W^{-}) $ and the coupling $ g_{aWW} $ for particle mass over a wide range of 170–3000 GeV at the HL-LHC with center-of-mass energy $ \sqrt{s} = 14 \, \text{ TeV} $ and integrated luminosity $ {\cal{L}} = 3 \, \text{ab}^{-1} $ . Our results show significant improvements in discovery sensitivity, particularly for masses above 300 GeV, compared to existing limits derived from CMS analyses of Standard Model (SM) tri-$\textit{W}$-boson production at $ \sqrt{s} = 13 \, \text{ TeV} $ . This study demonstrates the potential of advanced selection techniques in probing the coupling of new particles to $\textit{W}$-bosons and highlights the HL-LHC's capability to explore physics beyond the SM.

Ying-nan Mao

Kechen Wang

Yiheng Xiong

Sensitivities of new resonance couplings to $\textit{W}$-bosons at the LHC * Ying-nan Mao and Yihen Xiong are supported by the National Natural Science Foundation of China (12205227). Kechen Wang is supported by the National Natural Science Foundation of China (11905162), the Excellent Young Talents Program of the Wuhan University of Technology (40122102), and the research program of the Wuhan University of Technology (2020IB024). The simulation and analysis work of this article was completed with the computational cluster provided by the Theoretical Physics Group at the Department of Physics, School of Physics and Mechanics, Wuhan University of Technology

The production of heavy-quark (HQ) jets is a new area that addresses the mass effect of jet quenching in heavy-ion physics. This paper presents a theoretical study of HQ jet yield suppression in Pb+Pb collisions at the Large Hadron Collider (LHC) and focuses on the energy loss of HQ jets produced by different mechanisms. The $\textit{p+p}$ baseline is provided by the generator simulation of high-energy reactions of particles (SHERPA), and the jet-medium interactions are described by the SHELL transport model, which considers the elastic and inelastic partonic energy loss in the quark-gluon plasma (QGP). In $\textit{p+p}$ collisions, our numerical results indicate that the HQ jets from gluon splitting ( $ g \rightarrow Q $ -jet) are the dominant contribution at high $ p_T $ , displaying more dispersive structures than the HQ-initiated ( $ Q \rightarrow Q $ -jet). In nucleus-nucleus collisions, our calculations were consistent with the inclusive and b-jet $ R_{AA} $ recently measured by the ATLAS collaboration, revealing a remarkable manifestation of the mass effect of jet energy loss. As a result of the dispersive substructure, the $ g \rightarrow Q $ -jet loses more energy than the $ Q \rightarrow Q $ -jet in the QGP. Due to the significant contribution of $ g \rightarrow c $ -jet, the $ R_{AA} $ of $\textit{c}$-jet is comparable or even smaller than that of inclusive jet. To experimentally distinguish the $ g \rightarrow Q $ -jet and $ Q \rightarrow Q $ -jet, we propose event selection strategies based on their topological features and test their performances. By isolating the $ c \rightarrow c $ -jet, $ b \rightarrow b $ -jet, and the jets initiated by heavy quarks, we predicted that the order of their $ R_{AA} $ are in line with the mass hierarchy of energy loss. Future measurements on the $ R_{AA} $ of $ Q \rightarrow Q $ -jet and $ g \rightarrow Q $ -jet will provide a unique opportunity for testing the flavor/mass dependence of energy loss at the jet level.

Sa Wang

Shuang Li

Yao Li

Ben-Wei Zhang

Enke Wang

Probing the mass effect of heavy quark jets in high-energy nuclear collisions * Supported by the MajorProject of Basic and Applied Basic Research of Guangdong Province, China (2020B0301030008, 2023A1515011460), and the National Natural Science Foundation of China (11935007, 12035007, 12247127, 12375137). Sa Wang is supported by the Open Foundation of Key Laboratory of Quark and Lepton Physics (MOE) (QLPL2023P01) and the Talent Scientific Star-up Foundation of the China Three Gorges University, China (CTGU) (2024RCKJ013)

We study the possibility of finding axion-like particles (ALPs) through the leptonic decays of heavy mesons. The Standard Model (SM) predictions of the branching ratios of the leptonic decays of heavy mesons are less than the corresponding experimental upper limits. This provides some room for the existence of decay channels, of which the ALP is one of the products. Three scenarios are considered: First, the ALP is only coupled to one single charged fermion, namely, the quark, the antiquark, or the charged lepton; second, the ALP is only coupled to quark and antiquark with the same strength; and third, the ALP is coupled to all the charged fermions with the same strength. The constraints of the coupling strength in different scenarios are obtained by comparing the experimental data of the branching ratios of leptonic decays of   $B^-$  ,   $B^-$  , and   $B^-$   mesons with the theoretical predictions achieved by using the Bethe-Salpeter (BS) method. These constraints are further applied to predict the upper limits of the leptonic decay processes of the   $B^-$   meson in which the ALP participates.

Gang Yang

Probing axion-like particles in leptonic decays of heavy mesons  

The spin-singlet state <math><mrow><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo>(</mo><mmultiscripts><mrow><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow><mprescripts></mprescripts><none></none><mrow><mn>1</mn></mrow></mmultiscripts><mo>)</mo></mrow></math> has not been discovered in experiment and it is the only missing low-excited <math><mi>D</mi></math>-wave charmonium, so in this paper, we like to study its properties. Using the Bethe-Salpeter equation method, we obtain its mass as 3828.2 MeV and its electromagnetic decay widths as <math><mi>Γ</mi><mo>[</mo><msub><mi>η</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo>(</mo><mn>1</mn><mi>D</mi><mo>)</mo><mo>→</mo><msub><mi>h</mi><mi>c</mi></msub><mo>(</mo><mn>1</mn><mi>P</mi><mo>)</mo><mi>γ</mi><mo>]</mo><mo>=</mo><mn>284</mn><mtext> </mtext><mtext> </mtext><mi>keV</mi></math>, <math><mi>Γ</mi><mo>[</mo><msub><mi>η</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo>(</mo><mn>1</mn><mi>D</mi><mo>)</mo><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>γ</mi><mo>]</mo><mo>=</mo><mn>1.04</mn><mtext> </mtext><mtext> </mtext><mi>keV</mi></math>, <math><mi>Γ</mi><mo>[</mo><msub><mi>η</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo>(</mo><mn>1</mn><mi>D</mi><mo>)</mo><mo>→</mo><mi>ψ</mi><mo>(</mo><mn>2</mn><mi>S</mi><mo>)</mo><mi>γ</mi><mo>]</mo><mo>=</mo><mn>3.08</mn><mtext> </mtext><mtext> </mtext><mi>eV</mi></math>, and <math><mi>Γ</mi><mo>[</mo><msub><mi>η</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo>(</mo><mn>1</mn><mi>D</mi><mo>)</mo><mo>→</mo><mi>ψ</mi><mo>(</mo><mn>3770</mn><mo>)</mo><mi>γ</mi><mo>]</mo><mo>=</mo><mn>0.143</mn><mtext> </mtext><mtext> </mtext><mi>keV</mi></math>. Considering the strong decay widths are estimated to be <math><mi>Γ</mi><mo>(</mo><msub><mi>η</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo>(</mo><mn>1</mn><mi>D</mi><mo>)</mo><mo>→</mo><msub><mi>η</mi><mi>c</mi></msub><mi>π</mi><mi>π</mi><mo>)</mo><mo>=</mo><mn>144</mn><mtext> </mtext><mtext> </mtext><mi>keV</mi></math> and <math><mi>Γ</mi><mo>(</mo><msub><mi>η</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo>(</mo><mn>1</mn><mi>D</mi><mo>)</mo><mo>→</mo><mi>g</mi><mi>g</mi><mo>)</mo><mo>=</mo><mn>46.1</mn><mtext> </mtext><mtext> </mtext><mi>keV</mi></math>, we obtain the total decay width of 475 keV for <math><msub><mi>η</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo>(</mo><mn>1</mn><mi>D</mi><mo>)</mo></math>, and point out that the full width is very sensitive to the mass <math><msub><mi>M</mi><msub><mi>η</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub></msub></math>. In our calculation, the emphasis is put on the relativistic corrections. Our results show that <math><mrow><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo>→</mo><msub><mrow><mi>h</mi></mrow><mrow><mi>c</mi></mrow></msub><mi>γ</mi></mrow></math> is the nonrelativistic <math><mi>E</mi><mn>1</mn></math> transition dominated <math><mi>E</mi><mn>1</mn><mo>+</mo><mi>M</mi><mn>2</mn><mo>+</mo><mi>E</mi><mn>3</mn></math> decay, and <math><msub><mi>η</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo>→</mo><mi>ψ</mi><mi>γ</mi></math> is the <math><mi>M</mi><mn>1</mn><mo>+</mo><mi>E</mi><mn>2</mn><mo>+</mo><mi>M</mi><mn>3</mn><mo>+</mo><mi>E</mi><mn>4</mn></math> decay but the relativistic <math><mi>E</mi><mn>2</mn></math> transition contributes the most.

Xin-Yao Du

Su-Yan Pei

Wei Li

Man Jia

Bo Wang

<math><mrow><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo>(</mo><mmultiscripts><mrow><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow><mprescripts></mprescripts><none></none><mrow><mn>1</mn></mrow></mmultiscripts><mo>)</mo></mrow></math> and its electromagnetic decays

The average values of the powers of <math><mrow><mover><mrow><mo>|</mo><mover><mrow><mi>q</mi></mrow><mrow><mo>→</mo></mrow></mover><msup><mrow><mo>|</mo></mrow><mrow><mi>n</mi></mrow></msup></mrow><mrow><mo>¯</mo></mrow></mover><mo>≡</mo><msup><mrow><mi>q</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></math> and <math><mrow><mover><mrow><mo>|</mo><mover><mrow><mi>v</mi></mrow><mrow><mo>→</mo></mrow></mover><msup><mrow><mo>|</mo></mrow><mrow><mi>n</mi></mrow></msup></mrow><mrow><mo>¯</mo></mrow></mover><mo>≡</mo><msup><mrow><mi>v</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></math> are commonly used physical quantities, where <math><mover><mi>q</mi><mo>→</mo></mover></math> and <math><mover><mi>v</mi><mo>→</mo></mover></math> are the three-dimensional momentum and velocity of a quark inside a meson, respectively. For example, the average kinetic energy <math><msubsup><mi>μ</mi><mi>π</mi><mn>2</mn></msubsup><mo>=</mo><msup><mi>q</mi><mn>2</mn></msup></math> is an important quantity in the heavy quark effective theory, and the expansion of <math><msup><mi>v</mi><mi>n</mi></msup></math> is commonly used in the nonrelativistic quantum chromodynamics. In this paper, based on the instantaneous Bethe-Salpeter equation method, we calculate the average values <math><msup><mi>q</mi><mi>n</mi></msup></math> and <math><msup><mi>v</mi><mi>n</mi></msup></math> (<math><mi>n</mi><mo>=</mo><mn>1</mn></math>, 2, 3, 4) of a heavy quark inside <math><mi>S</mi></math> wave and <math><mi>P</mi></math> wave heavy-light mesons. We obtain the kinetic energy <math><mrow><msubsup><mrow><mi>μ</mi></mrow><mrow><mi>π</mi></mrow><mn>2</mn></msubsup><mo>=</mo><mn>0.455</mn><mtext> </mtext><mtext> </mtext><msup><mi>GeV</mi><mn>2</mn></msup></mrow></math> for the <math><mi>B</mi></math> meson, which is consistent with the experimental result <math><mrow><mn>0.464</mn><mo>±</mo><mn>0.076</mn><mtext> </mtext><mtext> </mtext><msup><mi>GeV</mi><mn>2</mn></msup></mrow></math>. For the <math><msub><mi>B</mi><mi>s</mi></msub></math>, <math><mi>D</mi></math>, and <math><msub><mi>D</mi><mi>s</mi></msub></math> mesons, the <math><msubsup><mi>μ</mi><mi>π</mi><mn>2</mn></msubsup></math> are 0.530, 0.317, and <math><mrow><mn>0.369</mn><mtext> </mtext><mtext> </mtext><msup><mi>GeV</mi><mn>2</mn></msup></mrow></math>, respectively, and <math><msup><mi>v</mi><mn>2</mn></msup><mo>=</mo><mn>0.0185</mn></math>, 0.0215, 0.121, and 0.140 for <math><mi>B</mi></math>, <math><msub><mi>B</mi><mi>s</mi></msub></math>, <math><mi>D</mi></math>, and <math><msub><mi>D</mi><mi>s</mi></msub></math>, respectively. We obtain some relationships, for example, <math><mrow><msubsup><mrow><mi>q</mi></mrow><mrow><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo></mrow></msup></mrow><mrow><mi>n</mi></mrow></msubsup><mo>(</mo><mi>m</mi><mi>S</mi><mo>)</mo><mo>≈</mo><msubsup><mrow><mi>q</mi></mrow><mrow><msup><mrow><mn>1</mn></mrow><mrow><mo>−</mo></mrow></msup></mrow><mrow><mi>n</mi></mrow></msubsup><mo>(</mo><mi>m</mi><mi>S</mi><mo>)</mo></mrow></math>, <math><mrow><msubsup><mrow><mi>q</mi></mrow><mrow><msup><mrow><mn>0</mn></mrow><mrow><mo>+</mo></mrow></msup></mrow><mrow><mi>n</mi></mrow></msubsup><mo>(</mo><mi>m</mi><mi>P</mi><mo>)</mo><mo>≈</mo><msubsup><mrow><mi>q</mi></mrow><mrow><msup><mrow><mn>1</mn></mrow><mrow><mo>+</mo><mo>′</mo></mrow></msup></mrow><mrow><mi>n</mi></mrow></msubsup><mo>(</mo><mi>m</mi><msup><mrow><mi>P</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo><mo>&gt;</mo><msubsup><mrow><mi>q</mi></mrow><mrow><msup><mrow><mn>1</mn></mrow><mrow><mo>+</mo></mrow></msup></mrow><mrow><mi>n</mi></mrow></msubsup><mo>(</mo><mi>m</mi><mi>P</mi><mo>)</mo><mo>≈</mo><msubsup><mrow><mi>q</mi></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mo>+</mo></mrow></msup></mrow><mrow><mi>n</mi></mrow></msubsup><mo>(</mo><mi>m</mi><mi>P</mi><mo>)</mo></mrow></math>, and <math><mrow><msup><mrow><mi>q</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>(</mo><mi>m</mi><mi>S</mi><mo>)</mo><mo>&lt;</mo><msup><mrow><mi>q</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>(</mo><mi>m</mi><mi>P</mi><mo>)</mo></mrow></math> (<math><mi>m</mi><mo>=</mo><mn>1</mn></math>, 2, 3), etc.

Tai-Fu Feng

Kinetic energy and speed powers <math><mrow><msup><mrow><mi>v</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></math> of a heavy quark inside <math><mi>S</mi></math> wave and <math><mi>P</mi></math> wave heavy-light mesons

In the framework of instantaneous Bethe-Salpeter equation, according to the J  PC  of quarkonia, we find that their wave functions all contain multiple partial waves, rather than pure waves. In the radiative electromagnetic transitions χ  cJ →γψ and χ  bJ →γΥ (J = 0, 1, 2), the main wave of quarkonium gives the non-relativistic contribution, while other waves provide the relativistic corrections. Our results indicate that the relativistic effect of charmonium, especially highly excited states, is significant. Such as the relativistic effects of χ  cJ (2P) → γψ(1S) (J = 0, 1, 2) are {49.7%, 30.9%, 37.5%}, much larger than the corresponding {17.8%, 7.08%, 12.9%} of χ  bJ (2P) → γΥ(1S). The decay of χ  cJ (2P) → γψ can be used to distinguish between χ  c0(3860) and χ  c0(3915), which particle is the charmonium χ  c0(2P). Although our result of χ  c1(3872)→γψ(2S) is consistent with data, but the one of χ  c1(3872)→γψ(1S) is much larger than data, so whether χ  c1(3872) is the conventional χ  c1(2P) remains an open question. The undiscovered Υ(1D) and Υ(2D) have large production rates in decays of χ  b0(2P) → γΥ(1D) and χ  bJ (3P) → γΥ(2D) (J = 0, 1), respectively. To search for χ bJ (3P) (J = 0, 1, 2), the most competitive channels are the decays χ  bJ (3P) → γΥ(3S). And the best way to find χ  b2(1F) is to search for the decay of χ  b2(1F) → γΥ(1D).

Radiative transitions of χ  cJ  → ψγ and χ  bj  → Υγ

In 2021, a new charm-strange meson,  $$D_{s0}(2590)^+$$  <math> <mrow> <msub> <mi>D</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mn>2590</mn> <mo>)</mo> </mrow> <mo>+</mo> </msup> </mrow> </math>  , was discovered, which is believed to be the  $$D_s^+(2^1S_0)$$  <math> <mrow> <msubsup> <mi>D</mi> <mi>s</mi> <mo>+</mo> </msubsup> <mrow> <mo>(</mo> <msup> <mn>2</mn> <mn>1</mn> </msup> <msub> <mi>S</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow> </math>  . However, its low mass and wide width are challenged by theoretical results. Given the small branching ratio of the current production channel, resulting in a small number of events and large errors, we suggest searching for the  $$D_{s0}(2590)^+$$  <math> <mrow> <msub> <mi>D</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mn>2590</mn> <mo>)</mo> </mrow> <mo>+</mo> </msup> </mrow> </math>   in the B meson nonleptonic decays,  $$B_q\rightarrow D^{(*)}_qD_{s0}(2590)^+$$  <math> <mrow> <msub> <mi>B</mi> <mi>q</mi> </msub> <mo>→</mo> <msubsup> <mi>D</mi> <mi>q</mi> <mrow> <mo>(</mo> <mrow></mrow> <mo>∗</mo> <mo>)</mo> </mrow> </msubsup> <msub> <mi>D</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mn>2590</mn> <mo>)</mo> </mrow> <mo>+</mo> </msup> </mrow> </math>   ( $$q=u,d$$  <math> <mrow> <mi>q</mi> <mo>=</mo> <mi>u</mi> <mo>,</mo> <mi>d</mi> </mrow> </math>  ), followed by  $$D_{s0}(2590)^+\rightarrow D^*K$$  <math> <mrow> <msub> <mi>D</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mn>2590</mn> <mo>)</mo> </mrow> <mo>+</mo> </msup> <mo>→</mo> <msup> <mi>D</mi> <mo>∗</mo> </msup> <mi>K</mi> </mrow> </math>  . We find that  $$Br(B_q\rightarrow D^{(*)}_qD_{s0}(2590)^+)\times Br(D_{s0}(2590)^+\rightarrow D^{*}K)=(2.16\sim 2.82)\times 10^{-3}$$  <math> <mrow> <mi>B</mi> <mi>r</mi> <mrow> <mo>(</mo> <msub> <mi>B</mi> <mi>q</mi> </msub> <mo>→</mo> <msubsup> <mi>D</mi> <mi>q</mi> <mrow> <mo>(</mo> <mrow></mrow> <mo>∗</mo> <mo>)</mo> </mrow> </msubsup> <msub> <mi>D</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mn>2590</mn> <mo>)</mo> </mrow> <mo>+</mo> </msup> <mo>)</mo> </mrow> <mo>×</mo> <mi>B</mi> <mi>r</mi> <mrow> <mo>(</mo> <msub> <mi>D</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mn>2590</mn> <mo>)</mo> </mrow> <mo>+</mo> </msup> <mo>→</mo> <msup> <mi>D</mi> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </msup> <mi>K</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>2.16</mn> <mo>∼</mo> <mn>2.82</mn> <mo>)</mo> </mrow> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </msup> </mrow> </math>   is very large, and the result is not sensitive to the mass of  $$D_{s0}(2590)^+$$  <math> <mrow> <msub> <mi>D</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mn>2590</mn> <mo>)</mo> </mrow> <mo>+</mo> </msup> </mrow> </math>  . Due to the large branching ratio, numerous  $$D_{s0}(2590)^+$$  <math> <mrow> <msub> <mi>D</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mn>2590</mn> <mo>)</mo> </mrow> <mo>+</mo> </msup> </mrow> </math>   events are expected. This study is based on the framework of the instantaneous Bethe–Salpeter equation, and the relativistic wave functions used for mesons contain different partial waves. The contributions of the different partial waves are also studied.

Shuang-Tao Wang

Production of  $$D_{s0}(2590)^+$$  <math> <mrow> <msub> <mi>D</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mn>2590</mn> <mo>)</mo> </mrow> <mo>+</mo> </msup> </mrow> </math>   in B nonleptonic decays