Initiated by the recent observation of a flattened line shape of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><mn>0</mn><msup><mn>0</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup></math> around 1.4–1.5 GeV in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>K</mi><mi>S</mi></msub><msub><mi>K</mi><mi>S</mi></msub><msup><mi>π</mi><mn>0</mn></msup></math> invariant mass spectrum by BESIII, we make a systematic partial wave analysis of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mo stretchy="false">→</mo><mi>γ</mi><msub><mi>η</mi><mi>X</mi></msub><mo stretchy="false">→</mo><mi>γ</mi><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mi>π</mi></math> based on an isobaric approach. We demonstrate that in the scenario of the first radial excitations of the isoscalar pseudoscalar from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mi>π</mi></math> threshold to about 1.6 GeV the non-trivial <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>K</mi><mi>S</mi></msub><msub><mi>K</mi><mi>S</mi></msub><msup><mi>π</mi><mn>0</mn></msup></math> invariant mass spectrum can be explained by the coupled-channel effects with the presence of the triangle singularity mechanism. It shows that a combined fit of the Dalitz plots, three-body and two-body spectra can be achieved, which suggests that the one-state solution around 1.4–1.5 GeV proposed before still holds well. In particular, we show that the coupled-channel effects between the three important quasi-two-body decay channels, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo></mrow></msup><mover accent="true"><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mo>+</mo><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi><mo>.</mo></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>κ</mi><mover accent="true"><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mo>+</mo><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi><mo>.</mo></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo><mi>π</mi></math>, can be well described by taking into account the one-loop corrections in the isobaric approach. This is because the isoscalar pseudoscalar states are coupled to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mo>+</mo><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi><mo>.</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo><mi>π</mi></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>κ</mi><mover accent="true"><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mo>+</mo><mi mathvariant="normal">c</mi><mo>.</mo><mi mathvariant="normal">c</mi><mo>.</mo></mrow></math>) channels via the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math> waves, respectively. As a consequence, the coupled-channel effects can be largely absorbed into the redefinition of the tree-level effective couplings with the transition amplitudes computed to the order of one-loop corrections. Then, the coupled-channel effects can be estimated by the contributions from the one-loop rescattering amplitudes in comparison with the tree-level ones, where we find that the rescattering contributions from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math> wave into the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math> wave, or vice versa, are apparently suppressed in the kinematic region near threshold.

China

Yin Cheng

Lin Qiu

Qiang Zhao

Understanding the nontrivial isoscalar pseudoscalar structures in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>K</mi></mrow><mrow><mi>S</mi></mrow></msub><msub><mrow><mi>K</mi></mrow><mrow><mi>S</mi></mrow></msub><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> spectra in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> radiative decay

The Cabibbo-favored hadronic weak decay of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Ξ</mi><mn>0</mn></msup><msup><mi>π</mi><mo>+</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Ξ</mi><mo>−</mo></msup><msup><mi>π</mi><mo>+</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Ξ</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Ξ</mi><mn>0</mn></msup><msup><mi>η</mi><mrow><msup><mo stretchy="false">(</mo><mo>′</mo></msup><mo stretchy="false">)</mo></mrow></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><msup><mi mathvariant="normal">Ξ</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> are studied in the nonrelativistic constituent quark model. By analyzing their decay mechanisms at the quark level we show that the pole terms are essential for understanding the transition dynamics in addition to the usually considered direct meson emission process and color suppressed process in the charmed baryon hadronic weak decays. The experimentally measurable asymmetry parameters are also predicted in order to further pin down the decay mechanism.

Peng-Yu Niu

Japan

Qian Wang

Cabibbo-favored hadronic weak decays of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>c</mi></msub></math> in the quark model

We carry out a combined study of the isospin-violating decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>*</mo></mrow></msubsup><mo stretchy="false">→</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow></msub><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> and radiative decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mo>*</mo></msubsup><mo stretchy="false">→</mo><msub><mi>D</mi><mi>s</mi></msub><mi>γ</mi></math> in an effective Lagrangian approach by taking into account the corrections from the one-loop transitions. By distinguishing the transition mechanisms of the long-distance interactions through the intermediate meson loops from the short-distance interactions through the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mo>−</mo><msup><mi>π</mi><mn>0</mn></msup></math> mixing at the tree level, the isospin-violating decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mo>*</mo></msubsup><mo stretchy="false">→</mo><msub><mi>D</mi><mi>s</mi></msub><msup><mi>π</mi><mn>0</mn></msup></math> can be well constrained. In our approach, the higher-order corrections to the isospin-violating effects can involve the intermediate <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></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> scatterings. We find that the contributions from the destructive interference of intermediate meson loops via <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mn>0</mn></mrow></msup><mo stretchy="false">(</mo><mi>c</mi><mover accent="true"><mrow><mi>u</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mo stretchy="false">)</mo><msup><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>+</mo></mrow></msup><mo stretchy="false">(</mo><mi>u</mi><mover accent="true"><mrow><mi>s</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mo stretchy="false">)</mo></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>+</mo></mrow></msup><mo stretchy="false">(</mo><mi>c</mi><mover accent="true"><mrow><mi>d</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mo stretchy="false">)</mo><msup><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mn>0</mn></mrow></msup><mo stretchy="false">(</mo><mi>d</mi><mover accent="true"><mrow><mi>s</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mo stretchy="false">)</mo></mrow></math> rescatterings are significant. Within the commonly accepted UV cutoff range, we obtain the partial decay width <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">Γ</mi><mo stretchy="false">[</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>*</mo></mrow></msubsup><mo stretchy="false">→</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow></msub><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">]</mo><mo>=</mo><msubsup><mrow><mn>9.92</mn></mrow><mrow><mo>−</mo><mn>0.66</mn></mrow><mrow><mo>+</mo><mn>0.76</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>eV</mi></mrow></math>. This approach allows us to describe the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mo>*</mo></msubsup></math> radiative decay in the same framework via the vector-meson-dominance model. We demonstrate that both the tree-level and one-loop transitions can be self-consistently determined if we adopt the experimental data for the branching ratio fraction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mo>*</mo></msubsup><mo stretchy="false">→</mo><msub><mi>D</mi><mi>s</mi></msub><msup><mi>π</mi><mn>0</mn></msup></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mo>*</mo></msubsup><mo stretchy="false">→</mo><msub><mi>D</mi><mi>s</mi></msub><mi>γ</mi></math>. It then leads to a reliable estimate of the total decay width of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mo>*</mo></msubsup></math>, i.e., <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">Γ</mi></mrow><mrow><mtext>total</mtext></mrow></msub><mo stretchy="false">(</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>*</mo><mo>+</mo></mrow></msubsup><mo stretchy="false">)</mo><mo>=</mo><mn>17</mn><msubsup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>12</mn></mrow><mrow><mo>+</mo><mn>13</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>eV</mi></mrow></math>.

Jun Wang

Combined study of the isospin-violating decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>*</mo></mrow></msubsup><mo stretchy="false">→</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow></msub><msup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> and radiative decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>*</mo></mrow></msubsup><mo stretchy="false">→</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow></msub><mi>γ</mi></mrow></math> with intermediate meson loops

Motivated by the work of Cardoso et al. (2022) <cross-ref refid='br0150' id='crf0030'>[15]</cross-ref> on black holes in galaxies, we derive a new black hole solution surrounded by a Dekel-Zhao (DZ) dark matter profile. The derived metric, influenced by DZ profile parameters, exhibits two distinct regimes: for <math altimg='si1.svg'><mi>r</mi><mo>&#8810;</mo><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math> ( <math altimg='si2.svg'><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math> is a characteristic radius), exponential corrections dominate, producing significant deviations from the Schwarzschild solution near dense cores, while for <math altimg='si3.svg'><mi>r</mi><mo>&#8811;</mo><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math>, these corrections vanish, restoring the Schwarzschild metric at large distances. These findings ensure consistency with general relativity in vacuum. The black hole shadow and deflection angle are analyzed, demonstrating that the shadow radius increases with black hole mass ( <math altimg='si4.svg'><msub><mrow><mi>M</mi></mrow><mrow><mi mathvariant='normal'>BH</mi></mrow></msub></math>), while higher central densities ( <math altimg='si5.svg'><msub><mrow><mi>&#961;</mi></mrow><mrow><mi mathvariant='normal'>ch</mi></mrow></msub></math>) result in smaller shadows, reflecting the environmental impact of dense dark matter halos. Photon dynamics reveal how DZ profiles modify critical impact parameters and effective potentials, with gravitational lensing effects highly sensitive to the characteristic radius ( <math altimg='si2.svg'><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math>). Smaller <math altimg='si2.svg'><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math> values lead to larger deflection angles due to stronger gravitational effects near compact cores. This work highlights the significance dark matter profiles in shaping black hole observables, providing a theoretical foundation for future observational studies and advancing the understanding of dark matter-black hole interactions in astrophysical and cosmological contexts.

Türkiye

Ali Övgün

Philippines

Reggie C. Pantig

Black hole in the Dekel-Zhao dark matter profile

In this work, we systematically study both the mass spectra and strong decays of the nucleon and <math><mi>Δ</mi></math> resonances up to the <math><mi>N</mi><mo>=</mo><mn>2</mn></math> shell within a unified quark model framework with chiral dynamics. In this framework we achieve a good description of the strong decay properties of the well-established nucleon and <math><mi>Δ</mi></math> resonances. Meanwhile, the mass reversal between <math><mi>N</mi><mo>(</mo><mn>1440</mn><mo>)</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></math> as the first radial excitation state and the <math><mn>1</mn><mi>P</mi></math>-wave nucleon resonances can be explained. We show that the three-body spin-orbit potential arising from the one-gluon exchange can cause a large configuration mixing between <math><mi>N</mi><mo>(</mo><mn>1520</mn><mo>)</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> and <math><mi>N</mi><mo>(</mo><mn>1700</mn><mo>)</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> and is also responsible for the large splitting between <math><mi>Δ</mi><mo>(</mo><mn>1600</mn><mo>)</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> and <math><mi>Δ</mi><mo>(</mo><mn>1700</mn><mo>)</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math>. Some of these baryon resonances tend to weakly couple to the <math><mi>N</mi><mi>π</mi></math>, <math><mi>N</mi><mi>η</mi></math>, <math><mi>K</mi><mi>Λ</mi></math>, and <math><mi>K</mi><mi>Σ</mi></math> channels, which may answer the question of why they have not been established in these channels via the <math><mi>π</mi><mi>N</mi></math> and <math><mi>γ</mi><mi>N</mi></math> scatterings. It shows that these “missing resonances” may have large potentials to be established in the <math><mi>N</mi><mi>π</mi><mi>π</mi></math> final state due to their large decay rates into either the <math><mi>Δ</mi><mo>(</mo><mn>1232</mn><mo>)</mo></math> or <math><mn>1</mn><mi>P</mi></math>-wave nucleon resonances via the pionic decays. Further experimental search for their signals in charmonium decays at BESIII is thus strongly recommended.

Hui-Hua Zhong

Ming-Sheng Liu

Ru-Hui Ni

Mu-Yang Chen

Xian-Hui Zhong

Unified study of nucleon and <math><mi>Δ</mi></math> baryon spectra and their strong decays with chiral dynamics

The exact-exchange relativistic density functional theory (Ex-RDFT) of atomic nuclei has been solved in three-dimensional lattice space for the first time. The exchange energy is treated within the framework of the orbital-dependent relativistic Kohn-Sham density functional theory, wherein the local Lorentz scalar and vector potentials are derived using the relativistic optimized effective potential method. The solutions of binding energies, charge radii, and density distributions are benchmarked against the traditional relativistic Hartree-Fock approach for spherical and axially deformed nuclei. Furthermore, the triaxial neutron-rich <math><mmultiscripts><mrow><mtext>Ru</mtext></mrow><mprescripts></mprescripts><none></none><mrow><mn>104</mn><mo>−</mo><mn>120</mn></mrow></mmultiscripts></math> isotopes are investigated with the exchange correlations, which is beyond the current capacity of the traditional relativistic Hartree-Fock approach. The results notably indicate the γ-softness of these neutron-rich nuclei, which is consistent with experimental observations. This novel approach establishes a foundation for the study of nuclei without imposing any symmetry restrictions employing relativistic density functional with exchange correlations.

South Korea

Germany

Zhengxue Ren

Pengwei Zhao

Kenichi Yoshida

Exact-exchange relativistic density functional theory in three-dimensional coordinate space

Whether the <math><mi>N</mi><mover><mi>N</mi><mo>¯</mo></mover></math> interaction could form a state or not is a long standing question, even before the observation of the <math><mi>p</mi><mover><mi>p</mi><mo>¯</mo></mover></math> threshold enhancement in 2003. The recent high statistic measurement in the <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><mi>γ</mi><mn>3</mn><mo>(</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo>)</mo></math> channel would provide a good opportunity to probe the nature of the peak structures around the <math><mi>p</mi><mover><mi>p</mi><mo>¯</mo></mover></math> threshold in various processes. By constructing the <math><mi>N</mi><mover><mi>N</mi><mo>¯</mo></mover></math> interaction respecting chiral symmetry, we extract the pole positions by fitting the <math><mi>p</mi><mover><mi>p</mi><mo>¯</mo></mover></math> and <math><mn>3</mn><mo>(</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo>)</mo></math> invariant mass distributions of the <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><mi>γ</mi><mi>p</mi><mover><mi>p</mi><mo>¯</mo></mover></math> and <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><mi>γ</mi><mn>3</mn><mo>(</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo>)</mo></math> processes. The threshold enhancement in the <math><mi>p</mi><mover><mi>p</mi><mo>¯</mo></mover></math> invariant mass distribution is from the pole on the third Riemann sheet, which more couples to the isospin triplet channel. The broader structure in the <math><mn>3</mn><mo>(</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo>)</mo></math> invariant mass comes from the pole on the physical Riemann sheet, which more couples to the isospin singlet channel. Furthermore, the large compositeness indicates that there should exist <math><mi>p</mi><mover><mi>p</mi><mo>¯</mo></mover></math> resonance based on the current experimental data. In addition, we also see a clear threshold enhancement in the <math><mi>n</mi><mover><mi>n</mi><mo>¯</mo></mover></math> channel, but not as significant as that in <math><mi>p</mi><mover><mi>p</mi><mo>¯</mo></mover></math> channel, which is useful and compared with further experimental measurement.

Zhen-Yu Zhang

Yi-Yao Li

Pole structures of the <math><mi>X</mi><mo>(</mo><mn>1840</mn><mo>)</mo></math> or <math><mi>X</mi><mo>(</mo><mn>1835</mn><mo>)</mo></math> and the <math><mi>X</mi><mo>(</mo><mn>1880</mn><mo>)</mo></math>

A novel approach is proposed to probe the nature of the double charm tetraquark through the prompt production asymmetry between $$T_{\bar{c}\bar{c}}^-$$ <math> <msubsup> <mi>T</mi> <mrow> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>-</mo> </msubsup> </math> and $$T_{cc}^+$$ <math> <msubsup> <mi>T</mi> <mrow> <mi>cc</mi> </mrow> <mo>+</mo> </msubsup> </math> in pp collisions. When comparing two theoretical pictures, i.e. the compact tetraquark and hadronic molecular pictures, we find that the former one exhibits a significantly larger production asymmetry, enabling the unambiguous determination of the tetraquark’s internal structure. Additionally, distinctive differences in the transverse momentum and rapidity distributions of $$T_{\bar{c}\bar{c}}^-$$ <math> <msubsup> <mi>T</mi> <mrow> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>-</mo> </msubsup> </math> and $$T_{cc}^+$$ <math> <msubsup> <mi>T</mi> <mrow> <mi>cc</mi> </mrow> <mo>+</mo> </msubsup> </math> cross sections emerge, particularly at $$p_\textrm{T}\approx 2~\textrm{GeV}$$ <math> <mrow> <msub> <mi>p</mi> <mtext>T</mtext> </msub> <mo>≈</mo> <mn>2</mn> <mspace width="3.33333pt"></mspace> <mtext>GeV</mtext> </mrow> </math> and $$y\approx \pm 6$$ <math> <mrow> <mi>y</mi> <mo>≈</mo> <mo>±</mo> <mn>6</mn> </mrow> </math> at a center-of-mass energy of 14 $$~\textrm{TeV}$$ <math> <mrow> <mspace width="3.33333pt"></mspace> <mtext>TeV</mtext> </mrow> </math> . The insignificant asymmetry in hadronic molecular picture is because that hadronic molecules are produced in hadronic phase, where the phase space of their constituents needs to be taken into account rigorously. Our work can be extended to the exploration of other double heavy tetraquark candidates, offering a versatile approach to advance our understanding of exotic hadrons.

Xue-Li Hua

Shuai Yang

Bing-Song Zou

Revealing the mystery of the double charm tetraquark in pp collision

In recent years many vector charmonium(like) states were reported by different electron-positron collider experiments above 4.2 GeV. However, so far, there not only exists sizable tension in the parameters of those states, but there is also no consensus on the number of the vector states in this energy range. To some extend, this might be caused by the fact that the experimental data were typically analyzed in single channel analyses employing overlapping Breit-Wigner functions, in particular ignoring the effect of opening thresholds. In this study, we focus on the mass range between 4.2 GeV and 4.35 GeV, conducting a comprehensive analysis of eight different final states in <math><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> annihilation. Our findings demonstrate that, within this mass range, a single vector charmoniumlike state, exhibiting properties consistent with a <math><mrow><msub><mrow><mi>D</mi></mrow><mrow><mn>1</mn></mrow></msub><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> molecular structure and characterized by a pole location <math><mrow><msqrt><mrow><msubsup><mrow><mi>s</mi></mrow><mrow><mi>pole</mi></mrow><mrow><mi>Y</mi><mo>(</mo><mn>4230</mn><mo>)</mo></mrow></msubsup></mrow></msqrt><mo>=</mo><mrow><mo>(</mo><mn>4227</mn><mo>±</mo><mn>4</mn><mo>−</mo><mfrac><mrow><mi>i</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>(</mo><msubsup><mrow><mn>50</mn></mrow><mrow><mo>−</mo><mn>2</mn></mrow><mrow><mo>+</mo><mn>8</mn></mrow></msubsup><mo>)</mo><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></mrow></math>, can effectively describe all the collected data. This is made possible by allowing for an interference with the well-established vector charmonium <math><mi>ψ</mi><mo>(</mo><mn>4160</mn><mo>)</mo></math> along with the inclusion of the <math><msub><mi>D</mi><mn>1</mn></msub><mover><mi>D</mi><mo>¯</mo></mover></math> threshold effect. Moreover, in contrast to experimental analyses, our study reveals that the highly asymmetric total cross sections for <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>π</mi><mi>π</mi></math> and <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>K</mi><mover><mi>K</mi><mo>¯</mo></mover></math> around 4230 MeV stem from the same physics, rooted in the approximate SU(3) flavor symmetry of QCD.

Leon von Detten

Vadim Baru

Christoph Hanhart

Daniel Winney

How many vector charmoniumlike states lie in the mass range 4.2–4.35 GeV?

The weak radiative decay of <math><msup><mi>D</mi><mn>0</mn></msup><mo>→</mo><mi>V</mi><mi>γ</mi></math> with <math><mi>V</mi><mo>=</mo><msup><mover><mi>K</mi><mo>¯</mo></mover><mn>0</mn></msup></math>, and <math><mi>ϕ</mi></math>, <math><msup><mi>ρ</mi><mn>0</mn></msup></math>, and <math><mi>ω</mi></math>, is systematically studied in the vector meson dominance model. It allows us to distinguish the short-distance mechanisms which can be described by the tree-level transitions in the nonrelativistic constituent quark model, and the long-distance mechanisms which are related to the final-state interactions (FSIs). We find that the FSI effects play a crucial role in <math><msup><mi>D</mi><mn>0</mn></msup><mo>→</mo><mi>V</mi><mi>γ</mi></math> and the SU(3) flavor symmetry can provide a natural constraint on the relative phase between the short and long-distance transition amplitudes. Our analysis suggests that the <math><mi>D</mi></math>-meson weak radiative decays can serve as a good case for investigating the nonperturbative QCD mechanisms at the charm quark mass region.

Ye Cao

Study of weak radiative decays of <math><msup><mi>D</mi><mn>0</mn></msup><mo>→</mo><mi>V</mi><mi>γ</mi></math>