We analyze the recent data from the BESIII collaboration on the $ X(3872) $ state in the $ J/\psi\pi^+\pi^- $ and $ D^0\bar{D}^0\pi^0 $ decay channels. The quantum number and mass of the $ X(3872) $ state allow us to exploit the universal feature of the very near-threshold $ D\bar D^* $ scattering in the $\textit{S}$ wave. The analysis of $ J/\psi\pi^+\pi^- $ and $ D^0\bar{D}^0\pi^0 $ data separately, as well as the combined analysis of these data together, all support the conclusion that $ X(3872) $ is an extremely weakly bound charm meson molecule.

China

Xian-Wei Kang

Jin-Zhe Zhang

Xin-Heng Guo

Nature of $\textit{X}$(3872) from recent BESIII data: considering the universal feature of an $\textit{S}$-wave threshold resonance * Supported by the National Natural Science Foundation of China (12275023)

Motivated by the discovery of hidden-charm strange pentaquarks, we conduct a systematic study of the magnetic moments of the hidden-bottom strange pentaquarks in molecular picture. We calculate magnetic moments of hidden-bottom strange pentaquarks with strangeness-1 and 2. Magnetic moment gives valuable information about the inner structure and shape of the hadron. The obtained results may be helpful to determine the inner structure of these hypothetical states.

Türkiye

Halil Mutuk

Unveiling the structure of hidden-bottom strange pentaquarks via magnetic moments

We study the radiative decay of <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math> based on the assumption that <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math> is regarded as a <math><mi>c</mi><mover><mrow><mi>c</mi></mrow><mo>‾</mo></mover></math> charmonium with quantum number <math><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mrow><mn>1</mn></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msup></math> (<math><mi>J</mi><mo>,</mo><mspace width="0.2em"></mspace><mi>P</mi><mo>,</mo><mspace width="0.2em"></mspace><mi>C</mi></math> represent the spin, parity and charge conjugation, respectively). The form factors of <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math> transitions to <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>γ</mi></math> and <math><msup><mrow><mi>ψ</mi></mrow><mrow><mo>′</mo></mrow></msup><mi>γ</mi></math> (<math><msup><mrow><mi>ψ</mi></mrow><mrow><mo>′</mo></mrow></msup></math> denotes <math><mi>ψ</mi><mo>(</mo><mn>2</mn><mi>S</mi><mo>)</mo></math> throughout the paper) are calculated in the framework of the covariant light-front quark model. The phenomenological wave function of a meson depends on the parameter β, whose inverse essentially describes the confinement scale. In the present work, the parameters β for the vector <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> and <math><msup><mrow><mi>ψ</mi></mrow><mrow><mo>′</mo></mrow></msup></math> mesons will be determined through their decay constants, which are obtained from the experimental values of their partial decay widths to the electron-positron pair. For <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math>, we determined the value of β by the decay width of <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo><mo>→</mo><msup><mrow><mi>ψ</mi></mrow><mrow><mo>′</mo></mrow></msup><mi>γ</mi></math>. Then, we examined the width of <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>γ</mi></math> in a manner of parameter-free prediction and compared it with the experimental value. As a result, an inconsistency or contradiction occurs between the widths of <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>γ</mi></math> and <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo><mo>→</mo><msup><mrow><mi>ψ</mi></mrow><mrow><mo>′</mo></mrow></msup><mi>γ</mi></math>. We thus conclude that <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math> cannot be a pure <math><mi>c</mi><mover><mrow><mi>c</mi></mrow><mo>‾</mo></mover></math> resonance and that other components are necessary in its wave function.

Shuo-Ying Yu

Nature of (3872) From its Radiative Decay

The form factors of the semileptonic <math><mi>B</mi></math>, <math><msub><mi>B</mi><mi>s</mi></msub></math>, and <math><msub><mi>B</mi><mi>c</mi></msub></math> meson decays are calculated in the framework of the relativistic quark model based on the quasipotential approach in QCD. They are expressed through the overlap integrals of the meson wave function. All relativistic effects are consistently taken into account. The momentum transfer <math><msup><mi>q</mi><mn>2</mn></msup></math> behavior of form factors is determined in the whole accessible kinematical range. We do not use any extrapolations, heavy quark <math><mn>1</mn><mo>/</mo><msub><mi>m</mi><mi>Q</mi></msub></math> expansion, or model assumptions about the shape of form factors. Convenient analytic expressions of the form factors are given, which very accurately reproduce the numerical results of our calculation. On the basis of these form factors and helicity formalism, the differential and total branching fractions of various semileptonic decays of bottom meson are calculated. The mean values of the forward-backward asymmetry <math><mo>⟨</mo><msub><mi>A</mi><mrow><mi>FB</mi></mrow></msub><mo>⟩</mo></math>, lepton-side convexity parameter <math><mo>⟨</mo><msubsup><mi>C</mi><mi>F</mi><mo>ℓ</mo></msubsup><mo>⟩</mo></math>, longitudinal <math><mo>⟨</mo><msubsup><mi>P</mi><mi>L</mi><mo>ℓ</mo></msubsup><mo>⟩</mo></math> and transverse <math><mo>⟨</mo><msubsup><mi>P</mi><mi>T</mi><mo>ℓ</mo></msubsup><mo>⟩</mo></math> polarization of the charged lepton, and the longitudinal polarization fraction <math><mo>⟨</mo><msub><mi>F</mi><mi>L</mi></msub><mo>⟩</mo></math> for final-state vector meson are also evaluated. We present a detailed comparison of the obtained predictions with the calculations based on the covariant light-front quark model and confront them to available lattice QCD and experimental data. It is found that although both models predict close values of the total branching fractions, the differential distributions and forward-backward asymmetry and polarization parameters differ significantly, especially for the heavy-to-light semileptonic decays. We identify observables which measurement can help to discriminate between models.

Russia

R. N. Faustov

V. O. Galkin

Relativistic description of the semileptonic decays of bottom mesons

We use a near-threshold parameterization with explicit inclusion of the Castillejo–Dalitz–Dyson poles, which is more general than the effective range expansion, to study the bottomonium-like states  $$Z_b(10610)$$  <math> <mrow> <msub> <mi>Z</mi> <mi>b</mi> </msub> <mrow> <mo>(</mo> <mn>10610</mn> <mo>)</mo> </mrow> </mrow> </math>   and  $$Z_b(10650)$$  <math> <mrow> <msub> <mi>Z</mi> <mi>b</mi> </msub> <mrow> <mo>(</mo> <mn>10650</mn> <mo>)</mo> </mrow> </mrow> </math>  . In terms of the partial-wave amplitude, we fit the event number distribution of  $$B^{(*)}{\bar{B}}^*$$  <math> <mrow> <msup> <mi>B</mi> <mrow> <mo>(</mo> <mrow></mrow> <mo>∗</mo> <mo>)</mo> </mrow> </msup> <msup> <mrow> <mover> <mrow> <mi>B</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>∗</mo> </msup> </mrow> </math>   system to the experimental data for these resonances from Belle Collaboration. The data could be described very well in our method, which supports the molecular interpretation. Then the relevant physical quantities are obtained, including the  $$B^{(*)}\bar{B}^*$$  <math> <mrow> <msup> <mi>B</mi> <mrow> <mo>(</mo> <mrow></mrow> <mo>∗</mo> <mo>)</mo> </mrow> </msup> <msup> <mrow> <mover> <mrow> <mi>B</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>∗</mo> </msup> </mrow> </math>   scattering length (a), effective range (r), and residue squared ( $$\gamma _s^2$$  <math> <msubsup> <mi>γ</mi> <mi>s</mi> <mn>2</mn> </msubsup> </math>  ) of the pole in the complex plane. In particular, we find the compositeness can range from about 0.4 up to 1 for the  $$B{\bar{B}}^*$$  <math> <mrow> <mi>B</mi> <msup> <mrow> <mover> <mrow> <mi>B</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>∗</mo> </msup> </mrow> </math>   ( $$B^*{\bar{B}}^*$$  <math> <mrow> <msup> <mi>B</mi> <mo>∗</mo> </msup> <msup> <mrow> <mover> <mrow> <mi>B</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>∗</mo> </msup> </mrow> </math>  ) component in the resonance  $$Z_b(10610)$$  <math> <mrow> <msub> <mi>Z</mi> <mi>b</mi> </msub> <mrow> <mo>(</mo> <mn>10610</mn> <mo>)</mo> </mrow> </mrow> </math>   ( $$Z_b(10650)$$  <math> <mrow> <msub> <mi>Z</mi> <mi>b</mi> </msub> <mrow> <mo>(</mo> <mn>10650</mn> <mo>)</mo> </mrow> </mrow> </math>  ).

Lu Zhang

Composite nature of  $$Z_b$$  <math> <msub> <mi>Z</mi> <mi>b</mi> </msub> </math>   states from data analysis

We study the weight or compositeness of the <math><mi>π</mi><mi>π</mi><mo>−</mo><mi>K</mi><mover><mi>K</mi><mo>¯</mo></mover></math> and <math><mi>π</mi><mi>η</mi><mo>−</mo><mi>K</mi><mover><mi>K</mi><mo>¯</mo></mover></math> in the composition of the <math><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo></math> and <math><msub><mi>a</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo></math> resonances, respectively. Either we use the saturation of the total width and compositeness, or we use a Flatté parametrization taking also into account the spectral function of a near-threshold resonance. We make connections and compare between these two methods. We take input values for the pole mass and width and, in addition, for the total compositeness or the decay-width branching ratio to the lighter channel for each resonance. It turns out that for the poles considered the meson-meson components are dominant for the <math><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo></math>, while for the <math><msub><mi>a</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo></math> resonance they are subdominant. We also provide partial decay widths and partial compositeness coefficients, so that the <math><mi>K</mi><mover><mi>K</mi><mo>¯</mo></mover></math> component is the most important one for the <math><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo></math>. Additionally, this study stresses the need to distinguish between the bare and dressed couplings and widths in a Flatté parametrization. We elaborate on the connection between the partial-decay widths calculated in terms of the dressed couplings and the actual measured ones. Due to the coupled-channel dynamics when the pole lies near the heavier threshold in the second Riemann sheet some changes are needed with respect to standard relations.

Ze-Qiang Wang

Spain

J. A. Oller

Analysis on the composite nature of the light scalar mesons <math><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo></math> and <math><msub><mi>a</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo></math>

The null signal from collider and dark matter (DM) direct detector experiments makes the interaction between DM and visible matter too small to reproduce the correct relic density for many thermal DM models. The remaining parameter space indicates that two almost degenerated states in the dark sector, the inelastic DM scenario, can co-annihilate in the early universe to produce the correct relic density. Regarding the direct detection of the inelastic DM scenario, the virialized DM component from the nearby halo is nonrelativistic and not able to excite the DM ground state, even if the relevant couplings can be considerable. Thus, a DM with a large mass splitting can evade traditional virialized DM direct detection. In this study, we connect the concept of cosmic-ray accelerated DM in our Milky Way and the direct detection of inelastic scattering in underground detectors to explore spectra that result from several interaction types of the inelastic DM. We find that the mass splitting   <math> <mi>δ</mi> <mo>&lt;</mo> <mi>O</mi> <mfenced> <mrow> <mn>1</mn> <mspace width="0.25em"></mspace> <mi>GeV</mi> </mrow> </mfenced> </math>  $$ \delta &lt;\mathcal{O}\left(1\ \mathrm{GeV}\right) $$  can still be reachable for cosmic ray accelerated DM with mass range 1 MeV &lt;   <math> <msub> <mi>m</mi> <msub> <mi>χ</mi> <mn>1</mn> </msub> </msub> </math>  $$ {m}_{\chi_1} $$  &lt; 100 GeV and sub-GeV light mediator using the latest PandaX-4T data, even though we conservatively use the astrophysical parameter (effective length) D eff = 1 kpc.

Jie-Cheng Feng

Chih-Ting Lu

Yue-Lin Tsai

Feng-Shou Zhang

Revising inelastic dark matter direct detection by including the cosmic ray acceleration

In this paper, we study the scattering amplitudes of <math><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><mtext>−</mtext><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo><mo>+</mo></mrow></msup><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> coupled channels based on the <math><mi>K</mi></math> matrix within the Chew-Mandelstam formalism. The <math><msup><mi>D</mi><mn>0</mn></msup><msup><mi>D</mi><mn>0</mn></msup><msup><mi>π</mi><mo>+</mo></msup></math> invariant mass spectrum of LHCb is fitted, and the pole parameters of the <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> are extracted. The analysis of pole behavior suggests that the <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> may originate from a <math><msup><mi>D</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><msup><mi>D</mi><mn>0</mn></msup></math> virtual state and is formed as a result of an interplay between an attractive interaction between <math><msup><mi>D</mi><mn>0</mn></msup></math> and <math><msup><mi>D</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup></math> and coupling to <math><msup><mi>D</mi><mn>0</mn></msup><msup><mi>D</mi><mn>0</mn></msup><msup><mi>π</mi><mo>+</mo></msup></math> channel.

Ling-Yun Dai

Xiang Sun

United States

A. P. Szczepaniak

Jie-Sheng Yu

Pole analysis on the doubly charmed meson in <math><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> mass spectrum

We reanalyze the problems in the assignment of <math><mrow><mn>3</mn><mmultiscripts><mrow><msub><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></mrow></math> and <math><mrow><mn>4</mn><mmultiscripts><mrow><msub><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></mrow></math> light mesons, which have not yet been well established with the <math><mi>q</mi><mover><mi>q</mi><mo>¯</mo></mover></math> quark model. Regge trajectories and the <math><mrow><mmultiscripts><mrow><msub><mrow><mi>P</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></mrow></math> decay model are used, respectively, to study the mass and width of the observed states and predict the missing ones. By comparing our calculations with the latest experiments, we suggest that the inconsistent data of <math><mi>ρ</mi><mo>(</mo><mn>2150</mn><mo>)</mo></math> may include two similar structures, <math><mrow><mi>ρ</mi><mo>(</mo><mn>4</mn><msub><mrow><mmultiscripts><mrow><mi>S</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow></math> and <math><mrow><mi>ω</mi><mo>(</mo><mn>4</mn><msub><mrow><mmultiscripts><mrow><mi>S</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow></math>. In addition, the problem of the <math><mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo></mrow></msup><mo>(</mo><mn>2</mn><msub><mrow><mmultiscripts><mrow><mi>S</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow></math> assignment, with two observed states <math><msup><mi>K</mi><mo>*</mo></msup><mo>(</mo><mn>1410</mn><mo>)</mo></math> and <math><msup><mi>K</mi><mo>*</mo></msup><mo>(</mo><mn>1680</mn><mo>)</mo></math>, is investigated, with several possible explanations.

Qi-Fang Lü

Possible assignment of excited light <math><mrow><msub><mrow><mmultiscripts><mrow><mi>S</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></mrow><mrow><mn>1</mn></mrow></msub></mrow></math> vector mesons

The semileptonic decay of heavy flavor mesons offers a clean environment for extraction of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements, which describes the CP-violating and flavor changing process in the Standard Model. The involved form factors where the dynamical information is encoded play an essential role in achieving any conclusive statement. That is, the knowledge of the form factors should be under good control, requiring one to examine more observables in addition to the branching fraction. In this paper, we provide the mean value and the q 2-dependent shape for further observables [differential decay distribution (dΓ/dq 2), forward-backward asymmetry   <math> <mfenced> <msubsup> <mi>A</mi> <mi>FB</mi> <mi>ls</mi> </msubsup> </mfenced> </math>  $$ \left({\mathcal{A}}_{FB}^{ls}\right) $$ , longitudinal   <math> <mfenced> <msubsup> <mi>P</mi> <mi>L</mi> <mi>l</mi> </msubsup> </mfenced> </math>  $$ \left({P}_L^l\right) $$  and transverse   <math> <mfenced> <msubsup> <mi>P</mi> <mi>T</mi> <mi>l</mi> </msubsup> </mfenced> </math>  $$ \left({P}_T^l\right) $$  polarization of a charged lepton, longitudinal polarization of a vector meson in the final state   <math> <mfenced> <mrow> <msubsup> <mi>F</mi> <mi>L</mi> <mi>l</mi> </msubsup> <mfenced> <mi>V</mi> </mfenced> </mrow> </mfenced> </math>  $$ \left({F}_L^l(V)\right) $$ , leptonic convexity parameter   <math> <mfenced> <msubsup> <mi>C</mi> <mi>F</mi> <mi>l</mi> </msubsup> </mfenced> </math>  $$ \left({C}_F^l\right) $$ , and trigonometric moments   <math> <mfenced> <msubsup> <mi>W</mi> <mi>i</mi> <mi>l</mi> </msubsup> </mfenced> </math>  $$ \left({W}_i^l\right) $$  in the decay of D (s) and B (s) to P/Vl + ν  l  (l = e, μ or τ)], based on the predictions of the relevant form factors from the covariant light-front quark model. P and V denote the pseudoscalar and vector meson, respectively. As a comparison, we find a good agreement with the results from the covariant confining quark model and the relativistic quark model in the literature. As it has been observed that the   <math> <msubsup> <mi>P</mi> <mi>L</mi> <mi>l</mi> </msubsup> </math>  $$ {P}_L^l $$  and   <math> <msubsup> <mi>F</mi> <mi>L</mi> <mi>l</mi> </msubsup> <mfenced> <mi>V</mi> </mfenced> </math>  $$ {F}_L^l(V) $$  are crucial quantities to discriminate various New Physics models, the reexamination of these observables from a different method is also essential and necessary.