The so-called $\textit{X}$17 particle has been proposed in order to explain a very significant resonant behaviour (in both the angular separation and invariant mass) of $\textit{e}$ $\textit{e}$ pairs produced during a nuclear transition of excited Be, He and C nuclei. Fits to the corresponding data point, as most probable explanation, to a spin-1 object, which is protophobic and has a mass of approximately 16.7 MeV, which then makes the $\textit{X}$17 potentially observable in Coherent Elastic neutrino ($\textit{ν}$) Nucleus Scattering (CE$\textit{ν}$NS) at the European Spallation Source (ESS). By adopting as theoretical framework a minimal extension of the Standard Model (SM) with a generic U(1)$\textit{′}$ gauge group mixing with the hypercharge one of the latter, which can naturally accommodate the $\textit{X}$17 state compliant with all available measurements from a variety of experiments, we predict that CE$\textit{ν}$NS at the ESS will constitute an effective means to probe this hypothesis, even after allowing for the inevitable systematics associated to the performance of the planned detectors therein.

Sweden

J. Cederkäll

United Kingdom

Türkiye

Y. Hiçyılmaz

E. Lytken

S. Moretti

J. Rathsman

Hunting the elusive $\textit{X}$17 in CE$\textit{ν}$NS at the ESS

Neutron stars (NSs) with their strong magnetic fields and hot dense cores could be powerful probes of axions, a classic benchmark of feebly coupled new particles, through abundant production of axions with the axion-nucleon coupling and subsequent conversion into x-rays due to the axion-photon coupling. In this Letter, we point out that the pulsation structures in both the intensity and polarization of x-rays from NSs could provide us additional information about axions and their couplings. We develop new analytical formalisms of pulsation-polarization structure applicable to a wide range of NSs in the axion scenario and argue that they hold in complicated astrophysical environments. As a case study, we apply our formalism to a representative X-ray Dim Isolated Neutron Star, RX J1856.6-3754, with an unexpected hard x-ray excess which might be axion induced. We show with an updated fit that the axion explanation is compatible with both the intensity and pulsation data available, and combining the pulsation data does not shift the posterior by more than <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>σ</mi></math>. Yet, the preferred parameter space is close to being excluded by other astrophysical constraints. With a 75% reduction of the uncertainties in the pulsation data, we could potentially draw a definite conclusion on the axion-induced x-rays at more than <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>3</mn><mi>σ</mi></math> level.

United States

JiJi Fan

Lingfeng Li

Italy

Chen Sun

Pulse and Polarization Structures in Axion-Converted X-Rays from Pulsars

In this work, we propose a new method to detect the composition of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math> state. Based on a widely accepted interpretation that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math> is a weakly bound <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave molecule of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup></math> (neutral) and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><msup><mi>D</mi><mo>−</mo></msup></math> (charged) configurations, the process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mo>*</mo><mn>0</mn></mrow></msup><msup><mi>D</mi><mn>0</mn></msup></math> is described by one-loop triangle diagrams with the corresponding components as intermediate particles, and with the parameters constrained by the experimental branching ratio. Unlike the mild behavior of the neutral component, the charged component manifests itself as a distinct structure near the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><msup><mi>D</mi><mo>−</mo></msup></math> threshold at 3.880 GeV, in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>M</mi><mrow><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mo>*</mo><mn>0</mn></mrow></msup><msup><mi>D</mi><mn>0</mn></msup></mrow></msub></math> invariant mass distribution of the spin density matrix element <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>ρ</mi><mn>00</mn><msup><mi>D</mi><mo>*</mo></msup></msubsup></math>. Hence, the line shape of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>ρ</mi><mn>00</mn><msup><mi>D</mi><mo>*</mo></msup></msubsup></math> near this structure depends sensitively on the proportions of the two configurations. We propose high-precision measurements of this matrix element by future BESIII and Belle experiments to elucidate how a molecular <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math> state is composed.

China

Ke Wang

Yu-Fei Wang

Bo-Chao Liu

Fei Huang

Sifting out the neutral and charged components of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math> from a spin observable

We perform a phenomenological study of helicity-dependent parton distribution functions (PDFs) using small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> helicity evolution equations, incorporating for the first time single-inclusive jet production data in polarized proton-proton (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math>) scattering at parton momentum fractions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi><mo>&lt;</mo><mn>0.1</mn></math>. We also simultaneously include double-longitudinal spin asymmetries in inclusive and semi-inclusive deep-inelastic scattering probing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi><mo>&lt;</mo><mn>0.1</mn></math>. Employing the polarized small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> pure-glue calculation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi><mo stretchy="false">→</mo><mi>g</mi><mi>X</mi></math> for the jet production cross section, we modify the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>&amp;</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>f</mi></mrow></msub></mrow></math> KPS-CTT evolution equations by setting <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>0</mn></math> to replicate the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> (pure-glue) limit, while retaining external quark flavors for the spinor field operators. We find that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math> data have a considerable impact on the helicity PDFs at small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>, reducing their uncertainties and leading to a total quark and gluon helicity in the proton for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi><mo>&lt;</mo><mn>0.1</mn></math> of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>0.04</mn><mo>±</mo><mn>0.23</mn></math>. Combining our analysis with a recent JAM helicity PDF analysis of the world polarized data, which includes <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi><mo>&gt;</mo><mn>0.1</mn></math>, we find a total quark and gluon helicity contribution for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi><mo>&gt;</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>7</mn></mrow></msup></math> of between 0.02 and 0.51.

Daniel Adamiak

Nicholas Baldonado

Yuri V. Kovchegov

Ming Li

W. Melnitchouk

Daniel Pitonyak

Nobuo Sato

Matthew D. Sievert

Andrey Tarasov

Thailand

Yossathorn Tawabutr

First study of polarized proton-proton scattering with small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> helicity evolution

We investigate the photon structure functions via the photon-photon and photon-vector meson scattering within the framework of holographic QCD, focusing on the small Bjorken <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> region and assuming that the Pomeron exchange dominates. The quasireal photon structure functions are formulated as the convolution of the known U(1) vector field wave function with the Brower-Polchinski-Strassler-Tan (BPST) Pomeron exchange kernel in the five-dimensional AdS space. Assuming the vector meson dominance, the photon structure functions can be calculated in a different way with the BPST kernel and vector meson gravitational form factor, which can be obtained in a bottom-up AdS/QCD model, for the Pomeron-vector meson coupling. It is shown that the obtained <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mn>2</mn></msub></math> structure functions in the both ways agree with the experimental data, which implies the realization of the vector meson dominance within the present model setup. Calculations for the longitudinal structure function and the longitudinal-to-transverse ratio are also presented.

Wei Gao

Siming Liu

Wenbin Lin

Japan

Akira Watanabe

Vector meson dominance in photon structure functions at small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> from holography

In this work the production of the state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math> is estimated via the reaction <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math> through triangle mechanisms described by the sequence <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msubsup><mi>D</mi><mi>s</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>+</mo></mrow></msubsup><mo stretchy="false">(</mo><mo stretchy="false">→</mo><msup><mi>K</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>+</mo></mrow></msup><mo stretchy="false">)</mo><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>−</mo></mrow></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup><mo stretchy="false">(</mo><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>+</mo></mrow></msup><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>−</mo></mrow></msup><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mspace linebreak="goodbreak"></mspace><msup><mi>K</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math>. The molecular configuration <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mi>D</mi><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup><mo>−</mo><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi><mo>.</mo><mo stretchy="false">)</mo></math> of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math> is considered. By means of the effective Lagrangian approach, the branching ratio <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mi>B</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math> is calculated as a function of the strength of the coupling of the charged components <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><msup><mi>D</mi><mo>+</mo></msup><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mo>*</mo><mo>−</mo></mrow></msup><mo>−</mo><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi><mo>.</mo><mo stretchy="false">)</mo></math> to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math> and compared with experimental data. Besides, employing the decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math> as a normalization channel, the ratio of branching fractions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo>=</mo><mfrac><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mi>B</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mrow><mo stretchy="false">*</mo><mn>0</mn></mrow></msup><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mi>B</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mrow><mo stretchy="false">*</mo><mn>0</mn></mrow></msup><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow></mfrac><mo>×</mo><mfrac><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>J</mi><mo stretchy="false">/</mo><mi>ψ</mi><msup><mi>π</mi><mo stretchy="false">+</mo></msup><msup><mi>π</mi><mo stretchy="false">−</mo></msup><mo stretchy="false">)</mo></mrow><mrow><mi mathvariant="script">B</mi><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>J</mi><mo stretchy="false">/</mo><mi>ψ</mi><msup><mi>π</mi><mo stretchy="false">+</mo></msup><msup><mi>π</mi><mo stretchy="false">−</mo></msup><mo stretchy="false">)</mo></mrow></mfrac></math> is also estimated. The findings provide another concrete example for the vital role of charged components in achieving a quantitatively correct description of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math>.

Brazil

Luciano M. Abreu

Production of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math> state via the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math> decay

Within the framework of the next-to-minimal supersymmetric (SUSY) extension of the Standard Model (SM) with a local B-L gauge symmetry (N-B-LSSM), we study lepton flavor violating (LFV) $ \tau\rightarrow e M^+ M^- $ decays: $ \tau \rightarrow e \pi^+\pi^- $ , $ \tau \rightarrow e \pi^+K^- $ , and $ \tau \rightarrow e K^+K^- $ . Based on the latest experimental data, the influence of different sensitive parameters on the branching ratios is considered. It can be seen from the numerical analysis that the main sensitive parameters and LFV sources are non-diagonal elements corresponding to the initial and final leptons. This work can provide a basis for discovering the existence of new physics (NP).

Rong-Zhi Sun

Shu-Min Zhao

Shuang Di

Portugal

Xing-Xing Dong

Study of ${\boldsymbol\tau\rightarrow {\boldsymbol e M^+ M^-}}$ decays in N-B-LSSM * Supported by National Natural Science Foundation of China (NNSFC) (12075074), Natural Science Foundation of Hebei Province (A2023201040, A2022201022, A2022201017, A2023201041), Natural Science Foundation of Hebei Education Department (QN2022173), Post-graduate's Innovation Fund Project of Hebei University (HBU2024SS042), the Project of the China Scholarship Council (CSC) (202408130113). X. Dong acknowledges support from Fundação para a Ciência e a Tecnologia (FCT, Portugal) through the projects CFTP FCT Unit (UIDB/00777/2020, UIDP/00777/2020)

Hidden-charm decays provide irreplaceable platforms for probing the structures of charmoniumlike states, such as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4260</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math>, and their heavy-quark-symmetry partners. In the hadronic molecular scenario, these hidden-charm decays are dominated by intermediate meson loops (IMLs), and the couplings of <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>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> are essential building blocks of the amplitudes for the pionic and radiative transitions of the charmoniumlike states to 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> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mi>c</mi></msub></math> states, e.g., <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mi>π</mi><mn>0</mn></msup><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo>,</mo><mi>π</mi><mi>π</mi><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub><mo>,</mo><mi>γ</mi><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4260</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mi>π</mi><mn>0</mn></msup><msub><mi>h</mi><mi>c</mi></msub><mo>,</mo><mi>η</mi><msub><mi>h</mi><mi>c</mi></msub></math>. These couplings cannot be extracted from the partial decay widths of 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> directly and only have estimated values from the vector meson dominance (VMD) model. Utilizing the recent precise determination of the pole position and the isospin breaking properties of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math>, we give an estimation on the upper bounds of the absolute values of 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><mo stretchy="false">→</mo><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> couplings. Our results show that the VMD model may overestimate 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><mo stretchy="false">→</mo><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> couplings considering the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math> as a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math> hadronic molecule with a binding energy about tens of keV. These upper limits can be used and tested in other hidden-charm transitions of the charmoniumlike states to 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> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>h</mi><mi>c</mi></msub></math>.

Zhao-Sai Jia

Gang Li

Zhen-Hua Zhang

Constrain 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><mo stretchy="false">→</mo><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> effective couplings via the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mi>π</mi><mn>0</mn></msup><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math> decays

The study of meson pairs produced with quantum correlations gives direct access to parameters that are challenging to measure in other systems. In this Letter, the existence of quantum correlations due to charge-conjugation symmetry <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi></math> are demonstrated in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="true">¯</mo></mover></math> pairs produced through the processes <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><mrow><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="true">¯</mo></mover></mrow></math>, <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><mrow><msup><mi>D</mi><mo>*</mo></msup><mover accent="true"><mi>D</mi><mo stretchy="true">¯</mo></mover></mrow></math>, and <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><mrow><msup><mi>D</mi><mo>*</mo></msup><mrow><msup><mover accent="true"><mi>D</mi><mo stretchy="true">¯</mo></mover><mo>*</mo></msup></mrow></mrow></math>, where the lack of charge superscripts refers to an admixture of neutral-charm-meson particle and antiparticle states, using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>7.13</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> 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></math> collision data collected by the BESIII experiment between center-of-mass energies of 4.13–4.23 GeV. Processes with either <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi></math>-even or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi></math>-odd constraints are identified and separated. A procedure is presented that harnesses the entangled production process to enable measurements of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup></math>-meson hadronic parameters. This Letter provides the first confirmation of quantum correlations in <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>X</mi><mrow><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="true">¯</mo></mover></mrow></math> processes and the first observation of a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi></math>-even constrained <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="true">¯</mo></mover></math> system. The procedure is applied to measure <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>δ</mi><mrow><mi>K</mi><mi>π</mi></mrow><mi>D</mi></msubsup></math>, the strong phase between the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><msup><mrow><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="true">¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup></mrow><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> decay amplitudes, which results in the determination of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>δ</mi></mrow><mrow><mi>K</mi><mi>π</mi></mrow><mrow><mi>D</mi></mrow></msubsup><mo>=</mo><mo stretchy="false">(</mo><msubsup><mrow><mn>192.8</mn></mrow><mrow><mo>−</mo><mn>12.4</mn><mo>−</mo><mn>2.4</mn></mrow><mrow><mo>+</mo><mn>11.0</mn><mo>+</mo><mn>1.9</mn></mrow></msubsup><mo stretchy="false">)</mo><mo>°</mo></mrow></math>. The potential for measurements of other hadronic decay parameters and charm mixing with these and future datasets is also discussed.

M. Ablikim

Russia

M.N. Achasov

P. Adlarson

X.C. Ai

Germany

R. Aliberti

A. Amoroso

Q. An

Y. Bai

JINR

O. Bakina

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

M.H. Cai

X. Cai

A. Calcaterra

G.F. Cao

N. Cao

S.A. Cetin

X.Y. Chai

J.F. 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.L. Chen

S.M. Chen

T. Chen

X.R. Chen

X.T. Chen

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z. Chen

Z.J. Chen

Z.K. Chen

South Korea

S.K. Choi

X. Chu

G. Cibinetto

F. Cossio

J. Cottee-Meldrum

J.J. Cui

H.L. Dai

J.P. Dai

A. Dbeyssi

R.E. de Boer

D. Dedovich

C.Q. Deng

Z.Y. Deng

A. Denig

I. Denysenko

M. Destefanis

F. De Mori

B. Ding

X.X. Ding

Y. Ding

Y.X. Ding

J. Dong

L.Y. Dong

M.Y. Dong

X. Dong

M.C. Du

S.X. Du

Y.Y. Duan

P. Egorov

G.F. Fan

J.J. Fan

Y.H. Fan

J. Fang

S.S. Fang

W.X. Fang

Y.Q. Fang

R. Farinelli

L. Fava

F. Feldbauer

G. Felici

C.Q. Feng

J.H. Feng

L. Feng

Q.X. Feng

First Observation of Quantum Correlations in <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>X</mi><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="true">¯</mo></mover></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi></math>-Even Constrained <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>D</mi><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="true">¯</mo></mrow></mover></mrow></math> Pairs

The longitudinal structure function for nucleons and nuclei is considered at fixed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Q</mi><mn>2</mn></msup></math> to the minimum value of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> given by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Q</mi><mn>2</mn></msup><mo>/</mo><mi>s</mi></math>. This is done using the expansion method and color dipole model in the next-to-leading order approximation. The extracted longitudinal structure functions were consistent with HERA hepdata and the determination of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mi>L</mi></msub></math> at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi><mo>=</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>/</mo><mi>s</mi></math> [Taylor, <a href="http://dx.doi.org/10.1103/PhysRevD.111.052001">Phys. Rev. D 111, 052001 (2025)</a>] at moderate and large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Q</mi><mn>2</mn></msup></math> values. The results, consistent with the dipole picture at low <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Q</mi><mn>2</mn></msup></math> values, show that the longitudinal structure function is small as expected due to the transverse polarization of the exchanged photon and the strong suppression of the dominant gluon component. Nonlinear corrections to the nuclear longitudinal structure function at low values of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Q</mi><mn>2</mn></msup></math> are also considered. These results may enhance the deep inelastic scattering neutral current data in future colliders at low <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> and low <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Q</mi><mn>2</mn></msup></math>. The longitudinal structure functions for deuterium at low four-momentum transfer squared, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Q</mi><mn>2</mn></msup><mo>&lt;</mo><mn>1</mn><mtext> </mtext><mtext> </mtext><msup><mi>GeV</mi><mn>2</mn></msup></math> at the leading order and next-to-leading order approximations are determined and compared with the JLab E00-002 data.

Iran

G.R. Boroun

Longitudinal structure function in the limit <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi><mo>=</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>/</mo><mi>s</mi></math>