论文标题
（$γ$，$花
($γ$, $χ_{cJ}(J=0,1)$) and ($γ$, $η_c$) production in electron-positron annihilation at $\sqrt{s}=10.6$ GeV and $4.6$ GeV in the framework of Bethe-Salpeter equation
论文作者
论文摘要
在目前的工作中，我们研究了$ e^ - e^+ \rightarrowγχ_{cj}（np）（j = 0,1）$和$ e^ - e^ - e^+rightarrowγη_c（ns）$，通过领先订单（lo）图（通过c $ c $ cout $ cougplophite cougplothe）， $η_C/χ_{CJ} $通过三角夸克环图图，在$ 4 \ times 4 $ 4 $ bethe-salpeter方程（BSE）的框架中，位于质量Energies $ \ sqrt {s} = 10.6 $ gev（Belle Energy）和4.6 GEV（Belle Energy）和4.6 GEV（BESIIIIIIIIIIIIII）。就其形式而言，幅度简化为洛伦兹 - 搭配性所要求的一般形式。 The cross sections for these processes with leading order (tree level) diagrams alone at $\sqrt{s}$=10.6 GeV provide a sizable contribution, which might be mainly due to the BSE being a fully relativistic approach that incorporates the relativistic effect of quark spins and can also describe internal motion of constituent quarks within the hadron in a relativistically covariant manner.将我们的结果与最新的Belle数据在10.6 GEV中进行了比较，而BESIII数据为4.6 GEV以及其他模型。横截面与质量中心能量的图，$ \ sqrt {s} $揭示了低能（$ \ sqrt {s} $ = 4-6 GEV）区域的所有三个过程的轻度波动，并通过形式的形式进行分析。
In present work we study the production of ground and excited charmonium states in $e^- e^+ \rightarrow γχ_{cJ}(nP)(J=0,1)$, and $e^- e^+ \rightarrow γη_c(nS)$, through leading order (LO) diagrams, which proceed through exchange of a virtual photon that couples to $γ$ and $η_c/χ_{cJ}$ through the triangular quark loop diagram, in the framework of $4\times 4$ Bethe-Salpeter equation (BSE), at center of mass energies $\sqrt{s}=10.6$ GeV(Belle energy), and 4.6 GeV (BESIII energy). The amplitude simplifies to a general form required by Lorentz-covariance, in terms of its form factors. The cross sections for these processes with leading order (tree level) diagrams alone at $\sqrt{s}$=10.6 GeV provide a sizable contribution, which might be mainly due to the BSE being a fully relativistic approach that incorporates the relativistic effect of quark spins and can also describe internal motion of constituent quarks within the hadron in a relativistically covariant manner. Our results are compared with recent Belle data at 10.6 GeV, and BESIII data at 4.6 GeV, as well as other models. Plots of cross sections versus the center-of mass energy, $\sqrt{s}$ reveal mild fluctuations in their behaviour for all the three processes in the low energy ($\sqrt{s}$ = 4 - 6 GeV) region, and are analyzed in terms of the form factors.
