arXiv subjects

Guo-Li Wang

Publications and source records attributed to Guo-Li Wang.

At least 37 records · Page 2Linked to original sources

arXiv2024

The decay property of the $X(3842)$ as the $ψ_{_3}(1^3D_{_3})$ state

In this paper, the new particle $X(3842)$ discovered by the LHCb Collaboration is identified to be the $ψ_{_3}(1^3D_{_3})$ state. We study its strong decays with the combination of the Bethe-Salpeter method and the $^3P_{_0}$ model. Its electromagnetic (EM) decay is also calculated by the Bethe-Salpeter method within Mandelstam formalism. The strong decay widths are {$Γ[X(3842)\rightarrow D^{0}\bar{D}^{0}]=1.28$ MeV}, $Γ[X(3823)\rightarrow D^{+}D^{-}]=1.08$ MeV, and the ratio ${\cal B}[X(3842)\rightarrow D^{+}D^{-}]/{\cal B}[X(3823)\rightarrow D^{0}\bar{D}^{0}]=0.84$. The EM decay width is $Γ[X(3842)\rightarrowχ_{_{c2}}γ]=0.29$ MeV. We also estimate the total width to be 2.87 MeV, which is in good agreement with the experimental data $2.79^{+0.86}_{-0.86}$ MeV. Since the used relativistic wave functions include different partial waves, we also study the contributions of different partial waves in electromagnetic decay.

hep-ph↗

arXiv2023

Partial wave effects in the heavy quarkonium radiative electromagnetic decays

In a previous paper \cite{Bc}, it was pointed out that the wave functions of all particles are not pure waves, besides the main partial waves, they all contain {other partial waves}. It is very interesting to know what role these different partial waves play in particle transitions. Therefore, by using the Bethe-Salpeter equation method, we study the radiative electromagnetic decays $ψ\rightarrowγχ_{_{cJ}}$ and $Υ\rightarrowγχ_{_{bJ}}$ ($J=0,1,2$). We find that for the $S$ and $P$ wave dominated states, like the $ψ(2S)$, $Υ(2S)$, $χ_{_{cJ}}(1P)$, and $χ_{_{bJ}}(1P)$ etc., the dominant $S$ and $P$ waves provide main and nonrelativistic contrition to the decays; other partial waves mainly contribute to the relativistic correction. For the states like the $ψ(1D)$, $Υ(2D)$, $χ_{c2}(1F)$, and $χ_{b2}(1F)$ etc., they are the $S-P-D$ mixing state dominated by $D$ wave or the $P-D-F$ mixing state dominated by $F$ wave. Large decay widths are found in the transitions $ψ(2D)\to χ_{c2}(1F)$, $Υ(1D)\to χ_{bJ}(1P)$, and $Υ(2D)\to χ_{bJ}(2P)$ etc., which may be helpful to study the missing states $χ_{c2}(1F)$, $Υ(1D)$, and $Υ(2D)$.

hep-ph↗

arXiv2023

A proposal to the '$\frac{1}{2}$ vs. $\frac{3}{2}$ puzzle'

We reconsider the semileptonic decays of $B\to D_1^{(\prime)}l\bar ν_l$. The previous theoretical calculations predict a significantly smaller rate for the semileptonic decay of $B$ to $D'_1(J_l=\frac{1}{2})$ compared with that to the $D_1(J_l=\frac{3}{2})$, which is not consistent with the current experimental data. This conflict is the so-called `$\frac{1}{2}$ vs. $\frac{3}{2}$ puzzle'. In this work, we propose a simple scheme to fix this problem, where we suppose that the strong eigenstates $D_1^{(\prime)}$ do not coincide with the eigenstate of the weak interaction, since no experimental results show the weak and the strong interactions have to share the same eigenstates. Within the framework of this tentative scheme, meson $B$ first weakly decays to {the weak eigenstates} $D_{α(β)}$ and then the latter are detected as the $D_1^{(\prime)}$ by the strong products $D^*π$. We predict that there exist two new particles $D_{α(β)}$ with $J^P=1^+$ which were not previously identified. The good performance of the new scheme in describing the experimental data may hint at new symmetry in the weak decays of $B_{q}$ to $1^+$ heavy-light mesons. To test the scheme proposed here, we suggest an experiment to detect the difference in the invariant mass spectra of $D_1$ reconstructed from the $B$ weak decay and from the strong decay products.

hep-ph↗

arXiv2023

The electromagnetic decays of $X(3823)$ as the $ψ_2(1^{3}D_{2})$ state and its radial excited states

We study the electromagnetic (EM) decays of $X(3823)$ as the $ψ_2(1^{3}D_{2})$ state by using the relativistic Bethe-Salpeter method. Our results are $Γ[X(3823)\rightarrowχ_{_{c0}}γ]=1.2$ keV, $Γ[X(3823)\rightarrowχ_{_{c1}}γ]=265$ keV, $Γ[X(3823)\rightarrowχ_{_{c2}}γ]=57$ keV and $Γ[X(3823)\rightarrowη_{_c}γ]=1.3$ keV. The ratio ${\cal B}[X(3823)\rightarrowχ_{_{c2}}γ]/{\cal B}[X(3823)\rightarrowχ_{_{c1}}γ]=0.22$, agrees with the experimental data. Similarly, the EM decay widths of $ψ_{_2}(n^{3}D_{_2})$, $n=2,3$, are predicted, and we find the dominant decays channels are $ψ_{_2}(n^{3}D_{_2})\rightarrowχ_{_{c1}}(nP)γ$, where $n=1,2,3$. The wave function include different partial waves, which means the relativistic effects are considered. We also study the contributions of different partial waves.

hep-ph↗

arXiv2023

Decay properties of $D_{s0}^*(2317)^+$ as a conventional $c\bar s$ meson

Taking $D_{s0}^{*}(2317)^{+ }$ as a conventional $c\bar s$ meson, we calculate its dominant strong and electromagnetic decays in the framework of the Bethe-Salpeter method. Our results are $Γ(D_{s0}^{*+}\to D_s^+π^0) = 7.83^{+1.97}_{-1.55}$ keV and $Γ(D_{s0}^{*+}\to D_s^{*+}γ) = 2.55^{+0.37}_{-0.45}$ keV. The contributions of the different partial waves from the initial and final state wave functions to the decay width are also calculated, and we find that the relativistic corrections in both decay processes are very large.

hep-ph↗

arXiv2023

Strong decays of $P_ψ^N(4312)^+$ to $J/ψ(η_c) p$ and $\bar D^{(*)}Λ_c$ within the Bethe-Salpeter framework

Based on the effective Lagrangian in the heavy quark limit, we calculate the one-boson-exchange interaction kernel of $P_ψ^N(4312)^+$ as the $\bar DΣ_c$ molecular state in isospin-$\frac12$. We present the Bethe-Salpeter equation and wave function for the constituent particles to be a (pseudo)scalar meson and a $\frac12$ baryon. By solving the Bethe-Salpeter equation, we obtain $P_ψ^N(4312)^+$ as the $\bar DΣ_c$ molecular state with $J^P=(\frac{1}{2})^-$. Combining the effective Lagrangian and the obtained BS wave function, the partial decay widths of $P_ψ^N(4312)^+$ to $J/ψp$, $η_c p$, $\bar D^{*0}Λ_c^+$ and $\bar D^0Λ_c^+$ are calculated to be $0.17$, $0.085$, $8.8$, and $0.026$ MeV, respectively, which are roughly consistent with the LHCb experimental measurements and some other theoretical researches. The obtain results indicate the fraction of $\bar D^{*0}Λ_c^+$ channel amounts to $\sim90\%$ of $P_ψ^N(4312)^+$, and is a highly promising channel to be discovered in the near future experiments. Our results favor the interpretation of $P_ψ^N(4312)^+$ as the $\bar DΣ_c$ molecular state with $J^P=(\frac{1}{2})^-$ and isospin $I=\frac12$.

hep-ph↗

arXiv2022

The solution to the `$1/2$ vs $3/2$' puzzle

Using an almost complete relativistic method based on the Bethe-Salpeter equation, we study the mixing angle $θ$, the mass splitting $\bigtriangleup M$, the strong decay widths $Γ(D^{({\prime})}_1)$ and the weak production rates $Br(B\to D^{({\prime})}_1\ellν_{\ell})$ of the $D_1(2420)$ and $D_1^{\prime}(2430)$. We find there is the strong cancellation between the $^1P_1$ and $^3P_1$ partial waves in $D_1^{\prime}(2430)$ with $θ\sim-35.3^{\circ}$, which leads to the `$1/2$ vs $3/2$' puzzle. The puzzle can not be overcome by adding only relativistic corrections since in a large parameter range where $\bigtriangleup M$ is linear varying and not small, the $θ$, $Γ(D^{({\prime})}_1)$ and $Br(B\to D^{({\prime})}_1\ellν_{\ell})$ remain almost unchanged but conflict with data. While in a special range around the mass inverse point where $\bigtriangleup M=0$ and $θ=\pm 90^{\circ}$, they change rapidly but we find the windows where $\bigtriangleup M$, $Γ(D^{({\prime})}_1)$ and $Br(B\to D^{({\prime})}_1\ellν_{\ell})$ are all consistent with data. The small $\bigtriangleup M$ confirmed by experiment, is crucial to solve the `$1/2$ vs $3/2$' puzzle.

hep-ph↗

arXiv2022

Two-Body Strong Decay of the 2P and 3P Charmonium states

Two-body open charm strong decays of the $2P$ and $3P$ charmonium states are studied by the Bethe-Salpeter(BS) method combined with the $^3P_0$ model. The wave functions and mass spectra of the $2P$ and $3P$ charmonium states are obtained by solving the BS equation with the relativistic correction. The strong decay widths and relative ratios of the $2P$ and $3P$ charmonium states are calculated. Comparing our results with the experimental data, we obtain some interesting results. Considering the $X^*(3860)$ as the $χ_{c0}(2P)$, the total strong decay width is smaller than the experimental data. But the strong decay width depends on the parameter $γ$ in the $^3P_0$ model, and the mass and width of the $X^*(3860)$ have large errors, we cannot rule out the possibility that the $X^*(3860)$ is the $χ_{c0}(2P)$. The $X(4160)$ is a good candidate for the $χ_{c0}(3P)$, not only the strong decay width of the $χ_{c0}(3P)$ is same as the experimental data, but the relative ratios $\frac{Γ(χ_{c0}(3P)\to D\bar D)}{Γ(χ_{c0}(3P)\to D^*\bar D^*)}\approx0.0019<0.09$, and $\frac{Γ({χ_{c0}(3P)\to D\bar D^*})}{Γ({χ_{c0}(3P)\to D^*\bar D^*})}=0<0.22$ are consistent with the experimental results of the $X(4160)$. Taking the $X(4274)$ as the $χ_{c1}(3P)$, the strong decay width is consistent with the experimental data, so the $X(4274)$ is a good candidate for the $χ_{c1}(3P)$. Assigning the $X(4350)$ as the $χ_{c2}(3P)$, the corresponding strong decay width is slightly larger than the experimental data. To identify if the $X(4350)$ is $χ_{c2}(3P)$, many more investigations are needed. All of the strong decay widths and relative ratios of the $2P$ and $3P$ charmonium states can provide the useful information to discover and confirm these particles in the future.

hep-ph↗

arXiv2022

The partial waves of $B^{*}_{2}(5747)$ and their contributions in strong decays

By adopting the relativistic Bethe-Salpeter method, the OZI allowed strong decays of the $2^+$ state $B^{*}_{2}(5747)^{0}$ are studied, emphasis is paid to the relativistic corrections. We first study the partial waves in the wave functions used, find that there are $P$, $D$ and $F$ partial waves in $B^{*}_{2}(5747)^{0}$ meson, and the ratios $P:D:F=1:0.421:0.051$. We also find $S:P:D=1:0.354:0.046$ for $B^*$, and $S:P=1:0.343$ for $B$ meson. The large components of the $D$ wave in $B^{*}_{2}(5747)^{0}$ and $P$ wave in $B^{(*)}$ means that large relativistic effects existing in these states. Second, we calculate the strong decays, the obtained total decay width $Γ(B^{*}_{2}(5747)^{0})=25.9$ MeV and the branching fraction $Γ(B^{*}_{2}(5747)^{0} \to B^{*}π)$ / $Γ(B^{*}_{2}(5747)^{0} \to Bπ)=0.96$ are consistent well with experimental data. Third, we study the contributions of different partial waves in the initial and final wave functions, find that the relativistic effects are about $15\%$ and $11\%$ for $B^{*}_{2}(5747)^{0} \to Bπ$ and $B^{*}_{2}(5747)^{0} \to B^{*}π$, respectively, which are much smaller than our expected, showing that the relativistic corrections are cancelled to each other in these decays.

hep-ph↗

arXiv2022

Strong decays of excited $ 2^+ $ charmed mesons

The new charmed resonance $ D_2^*(3000) $ was observed by the LHCb Collaboration in $ B $ decays. In this paper, by assigning it as four possible excited states of the $ 2^+ $ family, we use the instantaneous Bethe-Salpeter method to calculate their Okubo-Zweig-Iizuka-allowed two-body strong decays. The results of $ 1^3F_2 $ and $ 3^3P_2 $ states deviate from the present experimental observation while $ 2^3P_2 $ and $ 2^3F_2 $ are in the error range. Our study also reveals that the widths of these states depend strongly on the masses. Due to the large uncertainties and different mass input, variable models get inconsistent conclusions at the moment. The analysis in this work can provide essential assistance for future measurements and investigations.

hep-ph↗

arXiv2022

The mass spectrum and wave functions of the $B_c$ system

The spectrum and relativistic wave functions of $B_c$ system are investigated via solving the complete Salpeter equation. Emphases are put on the study of the partial waves of each $J^P$ state. Our study shows that there are three categories of $J^P$ states. The first category contains $0^-$ and $0^+$ states, which are ${}^1S_0$ dominant state with a small amount of $P$ wave and ${}^3P_0$ dominant state with a small amount of $S$ wave, respectively. The second category includes the natural parity states, such as $1^-$, $2^+$, $3^-$, etc. Taking the $1^-$ state as an example, we study it in two cases. One is the ${}^3S_1$ dominant state with a small amount of $P$ and $D$ waves, and the other is the ${}^3D_1$ dominant state but contains a large amount of $S$ and $P$ wave components. The third category includes the unnatural parity states, such as $1^+$, $2^-$, $3^+$, etc. For the $1^+$ spectrum, the states are grouped into pairs with different radial quantum numbers. Each pair contains two ${}^1P_1-{}^3P_1$ mixing states, and the corresponding mixing angles are calculated by using the relativistic wave functions.

hep-ph↗

arXiv2022

The newly observed state $D_{s0}(2590)^{+}$

We choose the Reduction Formula, PCAC and Low Energy Theory to reduce the $S$ matrix of a OZI allowed two-body strong decay involving a light pseudoscalar, the covariant transition amplitude formula with relativistic wave functions as input is derived. After confirm this method by the decay $D^*(2010)\to Dπ$, we study the newly observed $D_{s0}(2590)^{+}$ with supposing it to be the state $D_s(2^1S_0)^+$, we find its decay width $Γ$ is highly sensitive to the $D_{s0}(2590)^{+}$ mass, which result in the meaningless comparison of widths by different models with various input masses. Instead of width, we studied the overlap integral over the wave functions of initial and final states, here we parameterized it as $X$ which is model-independent, and the ratio $Γ/{|{\vec P_f}|^3}$, both are almost mass independent, to give us useful information. The results show that, all the existing theoretical predictions $X_{D_s(2S) \to D^*K}=0.25\sim 0.41$ and $Γ/{|{\vec P_f}|^3}=0.81\sim1.77$ MeV$^{-2}$ are smaller than experimental data $0.585^{+0.015}_{-0.035}$ and $4.54^{+0.25}_{-0.52}$ MeV$^{-2}$. Further compared with $X^{ex}_{D^*(2010) \to Dπ}=0.540\pm0.009$, the current data $X^{ex}_{D_s(2S) \to D^*K}=0.585^{+0.015}_{-0.035}$ is too big to be an reasonable value, so it is early to say $D_{s0}(2590)^{+}$ is the conventional $D_s(2^1S_0)^+$ meson.

hep-ph↗

arXiv2022

Intensity-surged and Bandwidth-extended Terahertz Radiation in Two-foci Cascading Plasmas

The two-color strong-field mixing in gas medium is a widely-used approach to generate bright broadband terahertz (THz) radiation. Here, we present a new and counterintuitive method to promote THz performance in two-color scheme. Beyond our knowledge that the maximum THz generation occurs with two-color foci overlapped, we found that, when the foci of two-color beams are noticeably separated along the propagation axis resulting in cascading plasmas, the THz conversion efficiency is surged by one order of magnitude and the bandwidth is stretched by more than 2 times, achieving $10^{-3}$ conversion efficiency and $>$100 THz bandwidth under the condition of 800/400 nm, $\sim$35 fs driving lasers. With the help of the pulse propagation equation and photocurrent model, the observations can be partially understood by the compromise between THz generation and absorption due to the spatial redistribution of laser energy in cascading plasmas. Present method can be extended to mid-infrared driving laser, and the new records of THz peak power and conversion efficiency are expected.

physics.optics↗

arXiv2021

Mass spectra, wave functions and mixing effects of the $(bcq)$ baryon

Mass spectra and wave functions of the $J^P=\frac{1}{2}^+$ $(bcq)$ baryons are calculated by the relativistic Bethe-Salpeter equation\,(BSE) with considering the mixing effects between the $1^+$ and $0^+$ $(bc)$-diquarks inside. Based on the diquark picture, the three-body problem of baryons is transformed into two two-body problems. The BSE and wave functions of the $0^+$ diquark are given, and then solved numerically to obtain the effective mass spectra and form factors. Also we present the wave functions at zero point for the $(bc)$-diquark. Considering the obtained diquark form factors, the $(bcq)$ baryons are then described by the BSE as the bound state of a diquark and a light quark, where the interaction kernel includes the inner transitions between the $0^+$ and $1^+$ diquarks. The general wave function of the $\frac{1}{2}^+$ $(bcq)$ baryons is constructed and solved to obtain the corresponding mass spectra. Especially, by using the obtained wave functions, the mixing effects between $Ξ_{bc}(Ω_{bc})$ and $Ξ_{bc}'(Ω'_{bc})$ in ground states are computed and determined to be small ($\sim \!1\%$). The numerical results indicate that it is a good choice to take $Ξ_{bc}$ and $Ξ'_{bc}$ as the baryon states with the inside $(bc)$-diquarks occupying the definite spin.

hep-ph↗

arXiv2021

Mass spectra and wave functions of $T_{QQ\bar Q\bar Q}$ tetraquarks

The compact tetraquark states with fully heavy quark contents $QQ\bar Q\bar Q$ are studied as the bound states of the diquark-antidiquark within the Bethe-Salpeter framework. The (anti)diquark masses and form factors used are the same as we calculated the doubly heavy baryons in a previous work. Under the instantaneous approximation, the three-dimensional (Bethe-)Salpeter equation of the tetraquarks is derived and solved numerically to obtain the corresponding mass spectra and wave functions of the tetraquarks with $J^{PC}=0^{++}$, $1^{+-}$, and $2^{++}$. Our results show that the three ground states of $cc\bar c\bar c$ locate in the mass range of $6.4\sim6.5$GeV, and the $bb\bar b\bar b$ states in mass range of $19.2\sim19.3$GeV. The obtained relativistic wave functions naturally include the mixing effects from the possible $D$\,(or $G$) partial waves, and then can be further used to do precise calculations of the tetraquark decays. Based on the obtained results, the LHCb's observation $X(6900)$ is less likely to be the ground states of compact $cc\bar c\bar c$ tetraquarks but might be the first or second excited states. In addition, a widely used propagator-like form factor is also investigated and discussed.

hep-ph↗

arXiv2021

The light invisible boson in FCNC decays of $B$ and $B_c$ mesons

In this paper, we study the FCNC decay processes of $B$ and $B_c$ meson, in which one invisible particle is emitted. Both the spin-0 and spin-1 cases are considered. The model-independent effective Lagrangian is introduced to describe the coupling between the light invisible boson and quarks. The constraints of the coupling coefficients are extracted by experimental upper limits of the missing energy in $B$ meson decays. The bounds are used to predict the upper limits of branching fractions of corresponding $B_c$ decays, which are of the order of $10^{-6}$ or $10^{-5}$ when final meson is pseudoscalar or vector, respectively. The maximum branch ratios are achieved when $m_χ\approx3.5- 4$~GeV, where $m_χ$ is the mass of the invisible particle.

hep-ph↗

arXiv2021

CP violation in non-leptonic $B_c$ decays to excited final states

We study the CP violation in two-body nonleptonic decays of $B_c$ meson. We concentrate on the decay channels which contain at least one excited heavy meson in the final states. Specifically, the following channels are considered: $B_c\to c\bar c(2S, 2P)+\bar cq(1S, 1P)$, $B_c\to c\bar c(1S)+\bar cq(2S, 2P)$, $B_c\to c\bar c(1P)+\bar cq(2S)$, $B_c\to c\bar c(1D)+\bar cq(1S, 1P)$, and $B_c\to c\bar c(3S)+\bar cq(1S)$. The improved Bethe-Salpeter method is applied to calculate the hadronic transition matrix element. Our results show that some decay modes have large branching ratios, which is of the order of $10^{-3}$. The CP violation effect in $B_c \rightarrow η_c(1S)+D(2S)$, $B_c \rightarrow η_c(1S)+D_0^{*}(2P)$, and $B_c \rightarrow J/ψ+D^{*}(2S)$ are most likely to be found. If the detection precision of the CP asymmetry in such channels can reach the $3σ$ level, at least $10^7$ $B_c$ events are needed.

hep-ph↗

arXiv2021

Finding $B_c(3S)$ States via Their Strong Decays

The experimentally known $B_c$ states are all below open bottom-charm threshold, which experience three main decay modes, and all induced by weak interaction. In this work, we investigate the mass spectrum and strong decays of the $B_c(3S)$ states, which just above the threshold, in the Bethe-Salpeter formalism and $^3P_0$ model. The numerical estimation gives $M(B_c(3^1S_0))=7273\ {\rm MeV}$, $M(B_c^*(3^3S_1))=7304\ {\rm MeV}$, $Γ\left(B_c(3^1S_0)\to B^*D\right)=26.02^{+2.33}_{-2.21}\ {\rm MeV}$, $Γ\left(B_c^*(3^3S_1)\to BD\right)=3.39^{+0.27}_{-0.26}\ {\rm MeV}$, $Γ\left(B_c^*(3^3S_1)\to B^*D\right)=14.77^{+1.40}_{-1.33}\ {\rm MeV}$ and $Γ\left(B_c^*(3^3S_1)\to BD^*\right)=6.14^{+0.58}_{-0.54}\ {\rm MeV}$. Compared with previous studies in non-relativistic approximation, our results indicate that the relativistic effects are notable in $B_c(3S)$ exclusive strong decays. According to the results, we suggest to find the $B_c(3S)$ states in their hadronic decays to $B$ and $D$ mesons in experiment, like the LHCb.

hep-ph↗