We re-calculate the exclusive semileptonic and nonleptonic decays of $B_c$ meson to a $P$-wave charmonium in terms of the improved Bethe-Salpeter (B-S) approach, which is developed recently. Here the widths for the exclusive semileptonic and nonleptonic decays, the form factors, and the charged lepton spectrums for the semileptonic decays are precisely calculated. To test the concerned approach by comparing with experimental measurements when the experimental data are available, and to have comparisons with the other approaches the results obtained by the approach and those by some approaches else as well as the original B-S approach, which appeared in literature, are comparatively presented and discussed.
We calculate the double charmonium production cross section within the framework of $4\times 4$ Bethe-Salpeter Equation in the electron-positron annihilation, at center of mass energy $\sqrt{s}= 10.6$GeV, that proceeds through the exchange of a single virtual photon. In this calculation, we make use of the full Dirac structure of 4D BS wave functions of these charmonia, with the incorporation of all the Dirac covariants (both leading and sub-leading). The calculated cross-sections for the double charmonium productions for final states, ($J/Ψ, η_c$); ($Ψ',η_c$) ; ($J/Ψ, η_c'$); and ($Ψ',η_c'$) …
The Isgur-Wise function vastly reduces the weak-decay form factors of hadrons containing one heavy quark. In this paper, we extract the Isgur-Wise functions from the instantaneous Bethe-Salpeter method, and give the numerical results for the $B_c$ decays to charmonium where the final states include $1S$, $1P$, $2S$ and $2P$. The overlapping integral of the wave functions for the initial and final states is the Isgur-Wise function, as the heavy quark effective theory does. In the case of accurate calculation, describing form factors need to introduce more relativistic corrections which are the …
In a recent comment [1] Blankleider and Kvinikhidze claim that our work [2] is based on a set of inconsistent Bethe-Salpeter equations for the coupling of four-quark to two-quark states. Here we demonstrate that their argument is insubstantial.
We interpret the $X_1(2900)$ as an $S$-wave $\bar{D}_1K$ molecular state in the Bethe-Salpeter equation approach with the ladder and instantaneous approximations for the kernel. By solving the Bethe-Salpeter equation numerically with the kernel containing one-particle-exchange diagrams and introducing three different form factors (monopole, dipole, and exponential form factors) in the verties, we find the bound state exists. We also study the decay width of the decay $X_1(2900)$ to $D^-K^+$.
We study the scalar bound states of $D^{\ast}\bar{D}^{\ast}$ and $B^{\ast}\bar{B}^{\ast}$ in the Bethe-Salpeter formalism, with the effective interaction kernel extracted from the chiral perturbative theory and the heavy quark effective theory in the ladder approximation and the covariant instantaneous approximation. The results show that, in the scalar case ($J=0$), there can only exist $I = 0$ bound states for parameters in proper range, while there cannot exist the $I = 1$ bound states in the whole reasonable parameter range, due to more constraints arising from our definition of the Bethe-…
In this work, we study the $B\bar{K}$ molecule in the Bethe-Salpeter (BS) equation approach. With the kernel containing one-particle-exchange diagrams and introducing two different form factors (monopole form factor and dipole form factor) in the vertex, we solve the BS equation numerically in the covariant instantaneous approximation. We investigate the isoscalar and isovector $B\bar{K}$ systems, and we find $X(5568)$ cannot be a $B\bar{K}$ molecule.
In this work, we assume that the observed state $Ξ(1620)$ is a $s$-wave $Λ\bar{K}$ or $Σ\bar{K}$ bound state. Based on this molecule picture, we establish the Bethe-Salpeter equations for $Ξ(1620)$ in the ladder and instantaneous approximations. We solve the Bethe-Salpeter equations for the $Λ\bar{K}$ and $Σ\bar{K}$ systems numerically and find that the $Ξ(1620)$ can be explained as $Λ\bar{K}$ and $Σ\bar{K}$ bound states with $J^P=1/2^-$, respectively. Then we calculate the decay widths of $Ξ(1620)\rightarrowΞπ$ in these two different molecule pictures systems, respectively.
We review in detail modern numerical methods used in the determination and solution of Bethe-Salpeter and Dyson--Schwinger equations. The algorithms and techniques described are applicable to both the rainbow-ladder truncation and its non-trivial extensions. We discuss pedagogically the steps involved in constructing conventional mesons and baryons as systems of two- and three-quarks respectively. As further application we describe the self-consistent calculation of form-factors and highlight the challenges that remain therein.
$QQ^{\prime} \bar u \bar d$ bound state in the Bethe-Salpeter equation approach
在重夸克极限下，我们建立了含有一个重双夸克$QQ^{\prime}$（$Q, Q^{\prime}=b$或$c$）和一个轻反双夸克$\bar u \bar d$的基态$QQ^{\prime} \bar u \bar d$的Bethe-Salpeter方程.我们在协变瞬时近似下数值求解了Bethe-Salpeter方程，其核包含一个标量禁闭项和一个胶子交换项。数值解的Bethe-Salpeter波函数。结果表明，$bb \bar u \bar d$、$bc \bar u \bar d$和$cc \bar u \bar d$束缚态的质量分别低于$\bar{B}^{*0}\,B^-$或$B^0\,{B^*}^-$、$B^-D^+$或$\bar{B}^{0} D^0$、$D^+\,{D^*}^0$或${D^*}^+\,D^0$介子的阈值.基态$QQ^{\prime} \bar u \bar d$可能存在，我们预计即将到来的实验数据将证实它们。
The challenge to obtain from the Euclidean Bethe--Salpeter amplitude the amplitude in Minkowski is solved by resorting to un-Wick rotating the Euclidean homogeneous integral equation. The results obtained with this new practical method for the amputated Bethe--Salpeter amplitude for a two-boson bound state reveals a rich analytic structure of this amplitude, which can be traced back to the Minkowski space Bethe--Salpeter equation using the Nakanishi integral representation. The method can be extended to small rotation angles bringing the Euclidean solution closer to the Minkowski one and could…
