论文标题
$ 1/2 $ vs $ 3/2 $'难题的解决方案
The solution to the `$1/2$ vs $3/2$' puzzle
论文作者
论文摘要
使用基于伯特 - 盐的方程式的几乎完整的相对论方法，我们研究混合角$θ$，质量分裂$ \ bigtriangleup m $，强衰减宽度$γ（d^{（{\ prime}} _ 1）$ d^{（{\ prime}）} _ 1 \ellν_ {\ ell}）$的$ d_1（2420）$和$ d_1^{\ prime}（2430）$。我们发现，$^1p_1 $和$^3p_1 $ partial Waves在$ d_1^{\ prime}（2430）$的$^1p_1 $之间存在强烈的取消，并带有$θ\ sim-35.3^{\ circ} $，这导致了$ 1/2 $ vs $ 3/2 $'puine of to of $θ\ prime} $。无法通过仅添加相对论校正来克服难题，因为在$ \ bigtriangleup m $的较大参数范围内，线性变化而不是很小，$θ$，$γ（d^{（{\ prime}} _ 1）_ 1）$几乎没有变化，但与数据冲突。虽然在质量逆点附近的特殊范围内，$ \ bigtriangleup m = 0 $和$θ= \ pm 90^{\ circ} $，但它们会迅速变化，但我们找到了$ \ bigtriangleup m $，$γ（d^^{（{\ prime}} _ 1）_ 1）$ and $ br（bigtriangleup m $，$ \ bigtriangleup m $ d^{（{\ prime}）} _ 1 \ellν_ {\ ell}）$都与数据一致。通过实验确认的小$ \ bigtriangleup m $，对于解决$ 1/2 $ vs $ 3/2 $'拼图至关重要。
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.
