arXiv 1005.56712010-05hep-phhep-ex

矢量介子辐射衰变的$η-η^{\prime}$混合角

$η-η^{\prime}$ Mixing Angle from Vector Meson Radiative Decays

T. N. Pham

备注：: LaTeX, 11 pages, v3, minor typos corrected, PLB version
发表信息：: Phys.Lett.B694:129-133,2010
DOI：: 10.1016/j.physletb.2010.09.053

摘要：

八重态单重态$η-η^{\prime}$混合质量项可以有一个衍生的$η-η^{\prime}$项，如最近对$η-η^{\prime}$系统的分析所发现的。该项引起附加的动量相关极贡献，其被相对于$η^{\prime}$幅度的$η$的因子$m_η^{2}/m_{η^{\prime}}^{2}$抑制。与$η$介子的过程可以用动量无关的混合质量项来描述，以达到很好的近似，该混合质量项产生新的$η-η^{\prime}$混合角$θ_{P}$，就像过去使用的旧的$η-η^{\prime}$混合角一样，但是动量相关的混合项$d$，就像当前文献中用于参数化赝标介子衰变常数的双角混合方案中的$\sin(θ_{0}-θ_{8})$，用$η^{\prime}$描述幅值。在本文中，我们得到了与$η$和$η^{\prime}$有关的物理矢量介子辐射衰变的求和规则，正如我们以前对$η$介子双光子衰变所做的工作一样，并且在$η^{\prime}$振幅具有九阶对称性的情况下，我们从$ρ\toηγ$和$η^{\prime}\toργ$衰变得到了一个混合角$θ_{P}=-(18.76\pm 3.4)^{\circ}$，$d=0.10\pm 0.03$，对于$ω$，$θ_{P}=-(15.81\pm 3.1)^{\circ}$，$d=0.02\pm 0.03$，以及对于$ϕ$，$θ_{P}=-(13.83\pm 2.1)^{\circ}$，$d=0.08\pm 0.03$。从$η^{\prime}\toωγ$振幅的九阶对称表达式中直接获得$d$的较大$0.06\pm 0.02$值。这表明更精确的矢量介子辐射衰变测量的分支比和高阶SU（3）破缺效应可以使$θ_{P}$的这些值更接近，并允许更好地确定$d$。

英文摘要：

The octet-singlet $η-η^{\prime}$ mixing mass term could have a derivative $O(p^{2})$ term as found in recent analysis of the $η-η^{\prime}$ system. This term gives rise to an additional momentum-dependent pole contribution which is suppressed by a factor $m_η^{2}/m_{η^{\prime}}^{2}$ for $η$ relative to the $η^{\prime}$ amplitude. The processes with $η$ meson can then be described, to a good approximation, by the momentum-independent mixing mass term which gives rise to a new $η-η^{\prime}$ mixing angle $θ_{P}$, like the old $η-η^{\prime}$ mixing angle used in the past, but a momentum-dependent mixing term $d$, like $\sin(θ_{0}-θ_{8})$ in the two-angle mixing scheme used in the parametrization of the pseudo-scalar meson decay constants in the current literature, is needed to describe the amplitudes with $η^{\prime}$. In this paper, we obtain sum rules relating $θ_{P}$ and $d$ to the physical vector meson radiative decays with $η$ and $η^{\prime}$, as done in our previous work for $η$ meson two-photon decay, and with nonet symmetry for the $η^{\prime}$ amplitude, we obtain a mixing angle $θ_{P}=-(18.76\pm 3.4)^{\circ}$, $d=0.10\pm 0.03$ from $ρ\toηγ$ and $η^{\prime}\toργ$ decays, for $ω$, $θ_{P}=-(15.81\pm 3.1)^{\circ}$, $d=0.02\pm 0.03$, and for $ϕ$, $θ_{P}=-(13.83\pm 2.1)^{\circ}$, $d=0.08\pm 0.03$. A larger value of $0.06\pm 0.02$ for $d$ is obtained directly from the nonet symmetry expression for the $η^{\prime}\toωγ$ amplitude. This indicates that more precise vector meson radiative decay measured branching ratios and higher order SU(3) breaking effects could bring these values for $θ_{P}$ closer and allows a better determination of $d$.

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