arXiv subjects
Publications and source records attributed to Zhi-Gang Wang.
In the article, we calculate the hadronic coupling constants $G_{D_2^*Dπ}$, $G_{D_{s2}^*DK}$, $G_{B_2^*Bπ}$, $G_{B_{s2}^*BK}$ with the three-point QCD sum rules, then study the two body strong decays $D_2^*(2460)\to Dπ$, $D_{s2}^*(2573)\to DK$, $B_2^*(5741)\to Bπ$, $B_{s2}^*(5840)\to BK$, and make predictions to be confronted with the experimental data in the future.
In this article, we study the axial-vector mesons $Z_b(10610)$ and $Z_b(10650)$ with the $Cγ_μ-Cγ_5$ type and $Cγ_μ-Cγ_ν$ type interpolating currents respectively by carrying out the operator product expansion to the vacuum condensates up to dimension-10. In calculations, we explore the energy scale dependence of the QCD spectral densities of the hidden bottom tetraquark states in details for the first time, and suggest a formula $μ=\sqrt{M^2_{X/Y/Z}-(2{\mathbb{M}}_b)^2}$ with the effective mass ${\mathbb{M}}_b=5.13\,\rm{GeV}$ to determine the energy scales. The numerical results favor assigning the $Z_b(10610)$ and $Z_b(10650)$ as the $Cγ_μ-Cγ_5$ type and $Cγ_μ-Cγ_ν$ type hidden bottom tetraquark states, respectively. We obtain the mass of the $J^{PC}=1^{++}$ hidden bottom tetraquark state as a byproduct, which can be compared to the experimental data in the futures. Furthermore, we study the strong decays $Z_b^\pm(10610)\toΥπ^{\pm}\, ,\,η_bρ^{\pm}$ with the three-point QCD sum rules, the decay widths also support assigning the $Z_b(10610)$ as the $Cγ_μ-Cγ_5$ type hidden bottom tetraquark state.
In this article, we calculate the contributions of the vacuum condensates up to dimension-6 in the operator product expansion, study the masses and decay constants of the heavy tensor mesons $D_2^*(2460)$, $D_{s2}^*(2573)$, $B_2^*(5747)$, $B_{s2}^*(5840)$ using the QCD sum rules. The predicted masses are in excellent agreement with the experimental data, while the ratios of the decay constants $\frac{f_{D_{s2}^*}}{f_{D_{2}^*}}\approx\frac{f_{B_{s2}^*}}{f_{B_{2}^*}}\approx\frac{f_{D_{s}}}{f_{D}}\mid_{\rm exp}$, where the exp denotes the experimental value.
In this article, we calculate the contributions of the vacuum condensates up to dimension-10 in the operator product expansion, and study the $J^{PC}=0^{++}$, $1^{+-}$, $2^{++}$ $D^*\bar{D}^*$, $D_s^*\bar{D}_s^*$, $B^*\bar{B}^*$, $B_s^*\bar{B}_s^*$ molecular states with the QCD sum rules. In calculations, we use the formula $μ=\sqrt{M^2_{X/Y/Z}-(2{\mathbb{M}}_Q)^2}$ to determine the energy scales of the QCD spectral densities. The numerical results favor assigning the $Z_c(4020)$ and $Z_c(4025)$ as the $J^{PC}=0^{++}$, $1^{+-}$ or $2^{++}$ $D^*\bar{D}^*$ molecular states, the $Y(4140)$ as the $J^{PC}=0^{++}$ $D^*_s{D}_s^*$ molecular state, the $Z_b(10650)$ as the $J^{PC}=1^{+-}$ $B^*\bar{B}^*$ molecular state, and disfavor assigning the $Y(3940)$ as the ($J^{PC}=0^{++}$) molecular state. The present predictions can be confronted to the experimental data in the futures.
In this article, we study the two-body strong decays of the bottom mesons with the heavy meson effective theory in the leading order approximation, and obtain all the analytical expressions of the decay widths of the light pseudoscalar mesons transitions among the S-wave, P-wave and D-wave bottom mesons. As an application, we tentatively assign the bottom meson $B(5970)$ as the $2{\rm S}\,1^-$, $1{\rm D}\,1^-$ and $1{\rm D}\,3^-$ states, respectively, and calculate the decay widths of the $B_1(5721)$, $B_2(5747)$, $B_{s1}(5830)$, $B_{s2}(5840)$ and $B(5970)$, which can be confronted with the experimental data in the future.
We study the pion leading-twist distribution amplitude (DA) within the framework of SVZ sum rules under the background field theory. To improve the accuracy of the sum rules, we expand both the quark propagator and the vertex $(z\cdot \tensor{D})^n$ of the correlator up to dimension-six operators in the background field theory. The sum rules for the pion DA moments are obtained, in which all condensates up to dimension-six have been taken into consideration. Using the sum rules, we obtain $\left<ξ^2\right>|_{\rm 1\;GeV} = 0.338 \pm 0.032$, $\left<ξ^4\right>|_{\rm 1\;GeV} = 0.211 \pm 0.030$ and $\left<ξ^6\right>|_{\rm 1\;GeV} = 0.163 \pm 0.030$. It is shown that the dimension-six condensates shall provide sizable contributions to the pion DA moments. We show that the first Gegenbauer moment of the pion leading-twist DA is $a^π_2|_{\rm 1\;GeV} = 0.403 \pm 0.093$, which is consistent with those obtained in the literature within errors but prefers a larger central value as indicated by lattice QCD predictions.
In this article, we distinguish the charge conjugations of the interpolating currents, calculate the contributions of the vacuum condensates up to dimension-10 in the operator product expansion, and study the masses and pole residues of the $J^{PC}=1^{-\pm}$ hidden charmed tetraquark states with the QCD sum rules. We suggest a formula $μ=\sqrt{M^2_{X/Y/Z}-(2{\mathbb{M}}_c)^2}$ with the effective mass ${\mathbb{M}}_c=1.8\,\rm{GeV}$ to estimate the energy scales of the QCD spectral densities of the hidden charmed tetraquark states, which works very well. The numerical results disfavor assigning the $Z_c(4020)$, $Z_c(4025)$, $Y(4360)$ as the diquark-antidiquark (with the Dirac spinor structure $C-Cγ_μ$) type vector tetraquark states, and favor assigning the $Z_c(4020)$, $Z_c(4025)$ as the diquark-antidiquark type $1^{+-}$ tetraquark states. While the masses of the tetraquark states with symbolic quark structures $c\bar{c}s\bar{s}$ and $c\bar{c}(u\bar{u}+d\bar{d})/\sqrt{2}$ favor assigning the $Y(4660)$ as the $1^{--}$ diquark-antidiquark type tetraquark state, more experimental data are still needed to distinguish its quark constituents. There are no candidates for the positive charge conjugation vector tetraquark states, the predictions can be confronted with the experimental data in the future at the BESIII, LHCb and Belle-II.
In this article, we construct both the color singlet-singlet type and octet-octet type currents to interpolate the $X(3872)$, $Z_c(3900)$, $Z_b(10610)$, and calculate the vacuum condensates up to dimension-10 in the operator product expansion. Then we study the axial-vector hidden charmed and hidden bottom molecular states with the QCD sum rules, explore the energy scale dependence of the QCD sum rules for the heavy molecular states in details, and use the formula $μ=\sqrt{M^2_{X/Y/Z}-(2{\mathbb{M}}_Q)^2}$ with the effective masses ${\mathbb{M}}_Q$ to determine the energy scales. The numerical results support assigning the $X(3872)$, $Z_c(3900)$, $Z_b(10610)$ as the color singlet-singlet type molecular states with $J^{PC}=1^{++}$, $1^{+-}$, $1^{+-}$, respectively, more theoretical and experimental works are still needed to distinguish the molecule and tetraquark assignments; while there are no candidates for the color octet-octet type molecular states.
In this article, we distinguish the charge conjunctions of the interpolating currents, calculate the contributions of the vacuum condensates up to dimension-10 in a consistent way in the operator product expansion, study the masses and pole residues of the $J^{PC}=1^{+\pm}$ hidden charmed tetraquark states with the QCD sum rules, and explore the energy scale dependence in details for the first time. The predictions $M_{X}=3.87^{+0.09}_{-0.09}\,\rm{GeV}$ and $M_{Z}=3.91^{+0.11}_{-0.09}\,\rm{GeV}$ support assigning the $X(3872)$ and $Z_c(3900)$ (or $Z_c(3885)$) as the $1^{++}$ and $1^{+-}$ diquark-antidiquark type tetraquark states, respectively.
In this article, we study momentum dependence of the hadronic coupling constants $G_{B_c^* B_c Υ}$, $G_{B_c^* B_c J/ψ}$, $G_{B_c B_c Υ}$ and $G_{B_c B_c J/ψ}$ with the off-shell $Υ$ and $J/ψ$ using the three-point QCD sum rules. Then we fit the hadronic coupling constants into analytical functions and extrapolate them into deep time-like regions to obtain the on-shell values $ G_{B_c^*B_cΥ}(q^2=M_Υ^2)$, $ G_{B_c^*B_c J/ψ}(q^2=M_{J/ψ}^2)$, $ G_{B_cB_cΥ}(q^2=M_Υ^2)$ and $ G_{B_cB_c J/ψ}(q^2=M_{J/ψ}^2)$ for the first time. Those hadronic coupling constants can be taken as basic input parameters in phenomenological analysis.
In this article, we study the axial-vector tetraquark state and two-quark-tetraquark mixed state consist of light quarks using the QCD sum rules. The present predictions disfavor assigning the $a_1(1420)$ as the axial-vector tetraquark state with $J^{PC}=1^{++}$, while support assigning the $a_1(1420)$ as the axial-vector two-quark-tetraquark mixed state.
In this article, we recalculate the contributions of all vacuum condensates up to dimension-6, in particular the one-loop corrections to the quark condensates $α_s<\bar{q}q>$ and partial one-loop corrections to the four-quark condensates $α_s^2<\bar{q}q>^2$, in the operator product expansion. Then we study the masses and decay constants of the heavy pseudoscalar mesons $D$, $D_s$, $B$ and $B_s$ using the QCD sum rules with two choices: {\bf I} we choose the $\bar{MS}$ masses by setting $m=m(μ)$ and take perturbative corrections up to the order $\mathcal{O}(α_s)$; {\bf II} we choose the pole masses $m$, take perturbative corrections up to the order $\mathcal{O}(α_s^2)$ and set the energy-scale to be the heavy quark pole mass $μ=m_Q$. In the case of {\bf I}, the predictions $f_D=(208\pm11)\,\rm{MeV}$ and $f_B=(189\pm15)\,\rm{MeV}$ are consistent with the experimental data within uncertainties, while the prediction $f_{D_s}=(241\pm12)\,\rm{MeV}$ is below the lower bound of the experimental data $f_{D_s}=(260.0\pm5.4)\,\rm{MeV}$. In the case of {\bf II}, the predictions $f_D=(211\pm14)\,\rm{MeV}$, $f_B=(190\pm17)\,\rm{MeV}$, $f_{D_s}=(258\pm13)\,\rm{MeV}$ and $f_{D_s}/f_D=1.22\pm0.08$ are all in excellent agreements with the experimental data within uncertainties.
In this article, we assume that the two quarks have unequal masses and calculate the next-to-leading order contributions to the spectral densities of the mesonic two-point correlation functions of the vector, axialvector, scalar and pseudoscalar currents. We take dimensional regularization to regularize both the ultraviolet and infrared divergences, and use optical theorem to obtain the spectral densities directly, furthermore, we present some necessary technical details for readers convenience. The analytical expressions are applicable in many phenomenological analysis besides the QCD sum rules.
In this article, we study the radiative transitions among the vector and scalar heavy quarkonium states with the covariant light-front quark model. In calculations, we observe that the radiative decay widths are sensitive to the constituent quark masses and the shape parameters of the wave-functions, and reproduce the experimental data with suitable parameters.
In this article, we tentatively identify the charmed mesons $D_J(2580)$, $D_J^*(2650)$, $D_J(2740)$, $D^*_J(2760)$, $D_J(3000)$, $D_J^*(3000)$ observed by the LHCb collaboration according to their spin, parity and masses, then study their strong decays to the ground state charmed mesons plus light pseudoscalar mesons with the heavy meson effective theory in the leading order approximation, and obtain explicit expressions of the decay widths. The ratios among the decay widths can be used to confirm or reject the assignments of the newly observed charmed mesons. The strong coupling constants in the decay widths can be fitted to the experimental data in the future at the LHCb, BESIII, KEK-B and $\rm{\bar{P}ANDA}$.
In this article, we calculate the $B_c^* \to η_c$ form-factors with the three-point QCD sum rules, then study the semileptonic decays $B_c^* \to η_c \ell \barν_{\ell}$. The tiny decay widths may be observed experimentally in the future at the LHCb, while the $B_c^* \to η_c$ form-factors can be taken as basic input parameters in other phenomenological analysis.
In this article, we take the tensor currents $\bar{Q}(x)σ_{μν}Q(x)$ to interpolate the $P$-wave spin-singlet heavy quarkonium states $h_Q$, and study the masses and decay constants with the Borel sum rules and moments sum rules. The masses and decay constants from the Borel sum rules and moments sum rules are consistent with each other, the masses are also consistent with the experimental data. We can take the decay constants as basic input parameters and study other phenomenological quantities with the three-point correlation functions via the QCD sum rules. The heavy quarkonium states $h_Q$ couple potentially to the tensor currents $\bar{Q}(x)σ_{μν}Q(x)$, and have the quark structure $ε^{ijk}ξ^{\dagger}σ^kζ$ besides the quark structure $ik_2^i ξ^{\dagger}σ\cdot (\vec{k}_1-\vec{k}_2)ζ$. In calculations, we take into account the leading-order, next-to-leading-order perturbative contributions, and the gluon condensate, four-quark condensate contributions in the operator product expansion. The analytical expressions of the perturbative QCD spectral densities have applications in studying the two-body decays of a boson to two fermions with the vertexes $σ_{μν}γ_5$ and $σ_{μν}$.
In this article, we calculate the $B_c^* \to B_c$ electromagnetic form-factor with the three-point QCD sum rules, then study the radiative decays $ B_c^{*\pm} \to B_c^{\pm} γ$. Experimentally, we can study the radiative transitions using the decay cascades $B_c^{*\pm}\to B_c^{\pm} γ\to J/ψ\ell^{\pm}\barν_{\ell} γ\to μ^+ μ^- \ell^{\pm}\barν_{\ell} γ$ in the future at the LHCb.