arXiv subjects

Guo-Li Wang

Publications and source records attributed to Guo-Li Wang.

At least 19 recordsLinked to original sources

arXiv2026

Dalitz decays of vector heavy quarkonia into $χ_{QJ}(1P)$ in the Bethe-Salpeter approach

We systematically investigate the Dalitz decays of vector heavy quarkonia into $χ_{QJ}(1P)\ell^+\ell^-$ ($Q=c,b$; $J=0,1,2$; $\ell=e,μ$) within the instantaneous Bethe--Salpeter framework. The study covers $ψ(2S)$, $ψ(1D)$, $Υ(2S)$, and the so-far unobserved $Υ(1D)$ states. For $ψ(2S)$ electron channels, our predictions are in excellent agreement with BESIII data. We further provide the first relativistic predictions for $ψ(1D)$ decays, with branching ratios for several electron channels reaching the $10^{-5}$ level, which is accessible at current BESIII statistics. For bottomonium, $Υ(2S)\toχ_{bJ}e^+e^-$ decays yield branching fractions of $\mathcal{O}(10^{-4})$, suggesting potential observability at Belle~II. Muonic channels are also discussed, with kinematic constraints carefully addressed. Our results establish a coherent theoretical basis for future experimental searches for heavy quarkonium Dalitz decays.

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arXiv2026

Improved covariant analysis of $B_c^+ \to χ_{c1}(nP)$ decays and implications for the nature of $χ_{c1}(3872)$

We study the weak decays $B_c^+\toχ_{c1}(nP)\ell^+ ν_{\ell}$ and $B_c^+\toχ_{c1}(nP)X$ (n=1,2,3) within the Bethe-Salpeter formalism, treating $χ_{c1}(3872)$ as the conventional $χ_{c1}(2P)$ charmonium. We upgrade the covariant hadronic transition amplitude to consistently evaluate the final-state wave function in its rest frame, enabling a reliable description of large-recoil processes and sizable relativistic corrections pertinent to highly excited charmonium. Our results provide a novel platform to probe the internal structure of $χ_{c1}(3872)$ via $B_c$ decays. While the LHCb search for $B_c^+\toχ_{c1}(3872)π^+$ yielded only an upper limit, we demonstrate that this is primarily due to insufficient luminosity, approximately 20 times the current $B_c$ data sample would be required for a definitive observation. In contrast, we identify the semileptonic mode $B_c^+\toχ_{c1}(3872)μ^+ν_μ$ as a far more promising channel, which could become accessible with merely twice the existing data set. Our predictions offer concrete guidance for upcoming LHCb analyses and complement ongoing efforts to resolve the nature of $χ_{c1}(3872)$.

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arXiv2026

$S-P-D$ Mixing in Vector Quarkonia from the Salpeter Equation with Optimized Wave Function Representations

This paper proposes a novel mechanism based on the instantaneous Bethe-Salpeter (Salpeter) equation for investigating wave function mixing in vector mesons such as $ψ(3770)$. Conventional theories typically treat $ψ(3770)$ as a $2S-1D$ mixed state; however, considering only tensor forces or relativistic corrections alone often leads to mixing angles that are too small and inconsistent with experimental data. Phenomenological $2S-1D$ mixing requires experimental data as input to determine the mixing angles, resulting in limited theoretical studies on states like $Υ(1D, 2D)$ in the absence of experimental data. To more accurately describe $S-D$ mixing and its relativistic effects, this paper systematically compares four relativistic wave function representations ($φ_1$, $φ_2$, $φ_3$, and $φ_4$) by solving the Salpeter equation and calculates the mass spectra and dileptonic decay widths of charmonium and bottomonium. The study finds that the wave function representation $φ_2$ can simultaneously reproduce the experimental data of both charmonium and bottomonium well. Further analysis reveals that, in addition to $S-D$ mixing, the wave functions of vector mesons contain a non-negligible $P$-wave component, meaning they are $S-P-D$ mixed states. We predict the mixing angles for bottomonium $Υ(1D)$ and $Υ(2D)$ to be $(1.78^{+0.32}_{-0.25})^\circ$ and $(5.44^{+1.10}_{-0.76})^\circ$, with dileptonic decay widths of $2.29^{+0.86}_{-0.69}$ eV and $10.5^{+4.2}_{-3.1}$ eV, respectively.

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arXiv2026

Relativistic Bethe-Salpeter study of OZI-rule allowed strong decays: determination of total width of $h_{c}(2P)$ and $^{3}P_{0}$ model parameter

Strong decays allowed by the Okubo-Zweig-Iizuka rule play a decisive role in determining the properties of particles. The widely used $^{3}P_{0}$ model is non-relativistic and contains unknown adjustable parameter $γ$ that need to be determined experimentally. Based on the Bethe-Salpeter equation, we have derived a relativistic calculation formula in which the effective strength related to the $^{3}P_{0}$ parameter $γ$ is not introduced as an independent fitting parameter, but is consistently determined by the interaction kernel of the Bethe-Salpeter equation. Using this method, we present the total width of $h_{c}(2P)$ and allows a theoretical determination of the parameter $γ$ in the $^{3}P_{0}$ model within the present framework.

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arXiv2026

Large Relativistic Corrections to Nonrelativistic $M1$ Transitions in Heavy Quarkonium

As double heavy quarkonia, charmonium and bottomonium are generally considered to have small relativistic corrections and can be treated using nonrelativistic models. However, this is not always the case. In this paper, we employ the relativistic Bethe-Salpeter (BS) equation method to calculate the electromagnetic (EM) radiative decays of heavy quarkonium where the $M1$ transition provides the leading-order contribution. Compared to nonrelativistic method which only computes $M1$ transition, our calculations include $M1+E2+M3+E4$ transitions, where the higher-order multipoles, $E2$, $M3$, and $E4$, account for relativistic corrections. The study finds that relativistic effects are large in such transitions even for bottomonium. For instance: the relativistic corrections in the decays $ψ(nS)\rightarrowγη_c(mS)$ ($n\geq m$) range from $68.1\%$ to $83.2\%$, while those for $Υ(nS)\rightarrowγη_b(mS)$ range between $65.9\%$ and $75.2\%$.

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arXiv2025

Meson properties and symmetry emergence based on the deep neural network

As a key property of hadrons, the total width is quite difficult to obtain in theory due to the extreme complexity of the strong and electroweak interactions. In this work, a deep neural network model with the Transformer architecture is built to precisely predict meson widths in the range of $10^{-14} \sim 625$ MeV based on meson quantum numbers and masses. The relative errors of the predictions are $0.12\%, 2.0\%,$ and $0.54\%$ in the training set, the test set, and all the data, respectively. We present the predicted meson width spectra for the currently discovered states and some theoretically predicted ones. The model is also used as a probe to study the quantum numbers and inner structures for some undetermined states including the exotic states. Notably, this data-driven model is investigated to spontaneously exhibit good charge conjugation symmetry and approximate isospin symmetry consistent with physical principles. The results indicate that the deep neural network can serve as an independent complementary research paradigm to describe and explore the hadron structures and the complicated interactions in particle physics alongside the traditional experimental measurements, theoretical calculations, and lattice simulations.

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arXiv2025

Identification of $D^_2(3000)$ as the $D_2^(2^3P_2)$ and exploring potential of undiscovered $2^+$ mesons via $B$ decays

Following the discovery of the $D^*_2(3000)$, its mass and full width have been extensively studied. Yet its nature remains undetermined to date. Since it was discovered through nonleptonic decay of $B$ meson and the corresponding cascade process, we therefore in this paper investigate the nonleptonic and semileptonic decays of $B$ meson to $J^P = 2^+$ charmed mesons using the Bethe-Salpeter equation approach. Our calculations on nonleptonic $B$ decays reveal that the unconfirmed resonance $D^*_2(3000)$ aligns well with $D^*_2(2^3P_2)$ predictions. Other candidates, including $D^*_2(1^3F_2)$, $D^*_2(3^3P_2)$, and $D^*_2(2^3F_2)$, are excluded due to their very small branching ratios in $B$ decays. Considering that the $D^*_2(1F)$, $D^*_2(3P)$, and $D^*_2(2F)$ have not yet been experimentally observed, we investigate the feasibility of their detection in $B$-meson decays.

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arXiv2025

Strong decays of $P_ψ^N(4440)^+$ and $P_ψ^N(4457)^+$ within the Bethe-Salpeter framework

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 $P_ψ^N(4440)^+$ and $P_ψ^N(4457)^+$ reported by LHCb in 2019. Taking into account both the mass ordering and the decay widths, our results favor the interpretation of $P_ψ^N(4440)^+$ and $P_ψ^N(4457)^+$ as the isospin-$\frac12$ $[\bar D^*Σ_c]$ molecular states with $J^P$ configuration $(\frac{3}{2})^-$ and $(\frac12)^-$, respectively. We first calculate the one-boson-exchange interaction kernel of $[\bar D^*Σ_c]$ in the isospin-$\frac12$ configuration. Then we present the Bethe-Salpeter equation (BSE) and wave functions for the bound states of a vector meson and a $\frac12$ baryon with $J^P={\frac12}^-$ and ${\frac32}^-$. The obtained mass results for the $(\frac32)^-$ and $(\frac12)^-$ are $4.442$ and $4.457$ GeV, respectively. Combining the effective Lagrangians and the BS wave functions, we further calculate the strong decay channels $\bar D^{(*)0}Λ_c^+$, $J/ψ(η_c) p$, and $\bar DΣ_c^{(*)}$ for the two $P_ψ^N$ states. In the favored $\frac32^-$ and $\frac12^-$ 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 $\bar D^{0}Λ_c^+$ and $\bar D^{(*)0}Λ_c^+$ are the dominant decay channels to detect $P_ψ^N(4440)^+$ and $P_ψ^N(4457)^+$, respectively.

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arXiv2025

Mass spectra and wave functions of toponia

In this article, {we solve the instantaneous Bethe-Salpeter equation with Cornell potential and Coulomb potential} and conduct a meticulous study of the mass spectrum and wave function of toponium. Our investigation reveals that, owing to the exceedingly heavy mass of the top quark, the mass splitting between singlet and triplet states, as well as within the triplet states, is negligible. Consequently, relativistic corrections can be safely disregarded in the study of toponium. As such, we present the nonrelativistic wave functions for $S$-wave, $P$-wave, and $D$-wave toponia and study the decays $η_t\to γγ$, $η_t\to gg$, and $Θ\to \ell^+\ell^-$.

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arXiv2025

Relativistic effects in the strong and electromagnetic decays of ${D^*}$ meson

In this paper, we solve the complete Salpeter equation and use the obtained relativistic wave function to calculate the strong and radiative electromagnetic decays of the ${D^*}$ meson. { We obtain the results $Γ(D^{*}(2007)^{0}\to D^{0}π^{0})=34.6~\rm{keV}$ and $Γ(D^{*}(2007)^{0}\rightarrow D^{0}γ)=19.4~\rm{keV}$, and the estimated full width is $Γ(D^{*}(2007)^{0})=54.0~\rm{keV}$.} The focus of this study is on the relativistic corrections. In our method, the wave function of the $D$ meson is not a pure $S$-wave, but includes both a non-relativistic $S$-wave and a relativistic $P$-wave, while the wave function of the $D^*$ meson includes a non-relativistic $S$-wave as well as both relativistic $P$-wave and $D$-wave. Therefore, in this case, the decay ${D^{*}\rightarrow{D}γ}$ is not a non-relativistic $M1$ transition, but rather an $M1+E2+M3+E4$ decay. We find that in a strong decay $D^{*}\rightarrow{D}π$, the non-relativistic contribution is dominant, while in an electromagnetic decay ${D^{*}\rightarrow{D}γ}$, the relativistic correction is dominant.

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arXiv2025

Basis light-front quantization for the $Λ_b$ and $Σ_b$ baryons

Within the basis light-front quantization framework, we compute the masses and light-front wave functions of the $Λ_b$ baryon and its isospin triplet counterparts $Σ_b^+$, $Σ_b^0$, and $Σ_b^-$ using a light-front effective Hamiltonian in the leading Fock sector. These wave functions are obtained as eigenstates of the effective Hamiltonian, which incorporates the one-gluon exchange interaction with fixed coupling and a three-dimensional confinement potential. With the quark masses and the couplings as adjustable parameters, the computed masses are set within the experimental range. The resulting predictions for their electromagnetic properties align well with other theoretical calculations. Additionally, the parton distribution functions (PDFs) of these baryons are obtained for the first time, with gluon and sea quark distributions dynamically generated through QCD evolution of the valence quark PDFs.

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arXiv2024

$η_{c2}(^1D_2)$ and its electromagnetic decays

The spin-singlet state $η_{c2}(^1D_2)$ has not been discovered in experiment and it is the only missing low-excited $D$-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 $Γ[η_{c2}(1D)\rightarrow h_{c}(1P)γ]=284$ keV, $Γ[η_{c2}(1D)\rightarrow J/ψγ]=1.04$ keV, $Γ[η_{c2}(1D)\rightarrowψ(2S)γ]=3.08$ eV, and $Γ[η_{c2}(1D)\rightarrowψ(3770)γ]=0.143$ keV. {Considering the strong decay widths are estimated to be $Γ(η_{c2}(1D)\toη_c ππ)=144~\rm{keV}$ and $Γ(η_{c2}(1D)\to gg)= 46.1~\rm{keV}$, we obtain the total decay width of $475$ keV for $η_{c2}(1D)$, and point out that the full width is very sensitive to the mass $M_{η_{c2}}$.} In our calculation, the emphasis is put on the relativistic corrections. Our results show that $η_{c2}\rightarrow h_{c}γ$ is the nonrelativistic $E1$ transition dominated $E1+M2+E3$ decay, and $η_{c2}\rightarrow ψγ$ is the $M1+E2+M3+E4$ decay but the relativistic $E2$ transition contributes the most.

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arXiv2024

Probing axion-like particles in leptonic decays of heavy mesons

We study the possibility of finding the 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 $B^-$, $D^+$, and $D_s^+$ 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 $B_c^-$ meson in which the ALP participates.

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arXiv2024

Radiative transitions of $χ_{_{cJ}}\toψγ$ and $χ_{_{bJ}}\toΥγ$

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}}$$\rightarrow$$γψ$ and $χ_{_{bJ}}$$\rightarrow$$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 $χ_{_{cJ}}(2P)\toγψ(1S)$ ($J=0,1,2$) are $\{49.7\%,~30.9\%,~37.5\%\}$, much larger than the corresponding $\{17.8\%,~7.08\%,~12.9\%\}$ of $χ_{_{bJ}}(2P)\rightarrowγΥ(1S)$. The decay of $χ_{_{cJ}}(2P)\toγψ$ 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)$$\rightarrow$$γψ(2S)$ is consistent with data, but the one of $χ_{_{c1}}(3872)$$\rightarrow$$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 $χ_{_{b0}}(2P)\rightarrowγΥ(1D)$ and $χ_{_{bJ}}(3P)\rightarrowγΥ(2D)$ ($J=0,1$), respectively. To search for $χ_{_{bJ}}(3P)$ $(J=0,1,2)$, the most competitive channels are the decays $χ_{_{bJ}}(3P)\rightarrowγΥ(3S)$. And the best way to find $χ_{_{b2}}(1F)$ is to search for the decay of $χ_{_{b2}}(1F)\rightarrowγΥ(1D)$.

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arXiv2024

Electron form factors in Basis Light-front Quantization

In this paper, we evaluate the electromagnetic and gravitational form factors as well as the corresponding generalized parton distributions of the electron using the Basis Light-front Quantization approach to QED. We compare our results with those from light-front perturbation theory. We adopt a novel basis with its scale depending on the constituents' longitudinal momentum fraction. We show that this basis improves convergence of the form factors with increasing basis dimension, compared to that calculated in the original basis with fixed scale. These results both validate the BLFQ approach and provide guidance for its efficient implementation in solving light-front Hamiltonian mass eigenstates for more complex systems in QED and QCD.

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arXiv2024

Kinetic energy and speed powers $v^n$ of a heavy quark inside $S$ wave and $P$ wave heavy-light mesons

Based on the instantaneous Bethe-Salpeter equation method, we calculate the average values $\overline{|\vec{q}|^n}\equiv q^n$ and speed powers $\overline{|\vec{v}|^n} \equiv v^n$ ($n=1,2,3,4$) of a heavy quark inside $S$ wave and $P$ wave heavy-light mesons, where $\vec{q}$ and $\vec{v}$ are the three dimensional momentum and velocity of the heavy quark, respectively. We obtain the kinetic energy $μ^2_{_π}=0.455$ GeV$^2$ for the $B$ meson, which is consistent with the experimental result $0.464\pm 0.076$ GeV$^2$. For the $B_{s}$, $D$ and $D_{s}$ mesons, the $μ^2_{_π}$ are $0.530$ GeV$^2$, $0.317$ GeV$^2$ and $0.369$ GeV$^2$, respectively. And $v^2=0.0185$, $0.0215$, $0.121$, and $0.140$ for $B$, $B_{s}$, $D$, and $D_{s}$. We obtain some relationships, for example, $q^n_{_{0^-}}(mS)\approx q^n_{_{1^-}}(mS)$, $q^n_{_{0^+}}(mP)\approx q^n_{_{1^{+'}}}(mP^{'})> q^n_{_{1^+}}(mP)\approx q^n_{_{2^+}}(mP)$, and $q^n(mS)< q^n(mP)$ ($m=1,2,3$), etc.

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arXiv2024

Production of $D_{s0}(2590)^+$ in $B$ nonleptonic decays

In 2021, a new charm-strange meson, $D_{s0}(2590)^+$, has been discovered, it is believed to be the $D_s^+(2^1S_0)$. 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 to search for the $D_{s0}(2590)^+$ in the $B$ meson nonleptonic decays, $B_q\rightarrow D^{(*)}_qD_{s0}(2590)^+$ ($q=u,d$), followed by $D_{s0}(2590)^+\to D^*K$. We find $Br(B_q\rightarrow D^{(*)}_qD_{s0}(2590)^+)\times Br(D_{s0}(2590)^+\to D^{*}K)=(2.16\sim2.82)\times 10^{-3}$ is very large, and the result is not sensitive to the mass of $D_{s0}(2590)^+$. Due to large branching ratio, large amount of $D_{s0}(2590)^+$ events are expected. This study is based on the framework of instantaneous Bethe-Salpeter equation, and the used relativistic wave functions for mesons contain different partial waves. The contributions of different partial waves are also studied.

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arXiv2024

Semirelativistic study on the semileptonic decays of $B_q$ mesons to orbital excited heavy Tensors

Based on the method of solving the complete Salpeter equation, we study the semileptonic decays of a $0^-$ heavy meson to $1P$, $2P$, or $3P$ heavy tensor mesons, $B_q \to (\bar c q)(nP) \ell^+ ν_\ell$ $(q=u,d,s,c;n=1,2,3)$. The obtained branching ratio of $\mathcal{B} (B \rightarrow D_2^{\star}(2460)\ell^{+} ν_{\ell})$ agrees with the experimental data. We predict $\mathcal{B}\left(B_s^{0} \rightarrow D_{s2}^{\star-}(1P) \ell^{+} ν_{\ell}\right)$$=$$3.76\times 10^{-3}$ and $\mathcal{B}\left(B_c^+ \rightarrow χ_{c2}(1P)\ell^{+} ν_{\ell}\right)$$=$$1.82\times 10^{-3}$. The branching ratios of decays to $2P$ and $3P$ final states are found to be very small. The ratios $\mathcal{R}(\bar{D}_{2}^{\star 0})=0.045$, $\mathcal{R}({D}_{s2}^{\star})=0.048$ and $\mathcal{R}(χ_{c2})=0.059$ are also obtained. This study focuses on the contribution of relativistic corrections. The wave function of the pseudoscalar includes non-relativistic $S$-wave and relativistic $P$-wave. While for a tensor, it contains non-relativistic $P$-wave and relativistic $P$, $D$ and $F$ waves in its wave function. We find the individual contributions of relativistic partial waves are significant in the decay $B \to D_2^{\star }(2460)\ell^{+} ν_{\ell}$, but the overall contribution of the relativistic effect is $24.4\%$, which is small due to cancellation. Similarly, for the decay $B_s^{0} \rightarrow D_{s2}^{\star-}(1P) \ell^{+} ν_{\ell}$, the contribution of the relativistic effect is $28.8\%$. While for $B_c^+ \rightarrow χ_{c2}(1P)\ell^{+} ν_{\ell}$, the individual contributions of relativistic partial waves and the overall relativistic correction are both small, the later of which is $22.1\%$.

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