arXiv 1209.65072012-09-28hep-phnucl-th

$η(1405) \to π^{0} f_0(980)$反应中的同位旋断裂和$f_0(980)$混合

Isospin breaking and $f_0(980)$-$a_0(980)$ mixing in the $η(1405) \to π^{0} f_0(980)$ reaction

F. Aceti, W. H. Liang, E. Oset, J. J. Wu, B. S. Zou

DOI：: 10.1103/PhysRevD.86.114007

摘要：

我们对$η(1405) \to π^{0} f_0(980)$和$η(1405) \to π^{0} a_0(980)$反应进行了理论研究，目的是确定$f_0(980)$和$a_0(980)$共振的同位旋破坏和混合。我们利用手征么正的方法，这两个共振出现的复合状态的两个介子，动态生成的介子-介子相互作用提供的手征拉格朗日。我们得到一个非常窄的形状$f_0(980)$生产与北京谱仪实验。至于同位旋破坏的数量，或$f_0(980)$和$a_0(980)$混合，假设恒定的顶点的主要$η(1405)\rightarrow π^{0}K\bar{K}$和$η(1405)\rightarrow π^{0}π^{0}η$生产，我们发现的结果是远远小于发现在最近的实验BES文件，但与其他两个相关的BES实验中发现的结果一致。我们试图通过假设$f_0(980)$波函数中的I=1混合物来理解这种异常，但这导致$f_0(980)$质量分布的宽度比实验观察到的要大得多。通过使用由$η' \to K^* \bar K$驱动的初级产生和随后由$K^* \to K π$驱动的初级产生来解决该问题，这在产生$f_0(980)$和$a_0(980)$共振所需的回路函数中引起额外的奇异性。沿着同样的路线改进早期的工作，并使用手性酉方法，我们现在可以预测的比率$Γ(π^0, π^+ π^-)/Γ(π^0, π^0 η)$的绝对值，这是在公平的协议与实验。我们还表明，如果我们有$η(1475)$共振或这两种状态的混合物，同样的结果成立，似乎是在BES实验的情况下。

英文摘要：

We make a theoretical study of the $η(1405) \to π^{0} f_0(980)$ and $η(1405) \to π^{0} a_0(980)$ reactions with an aim to determine the isospin violation and the mixing of the $f_0(980)$ and $a_0(980)$ resonances. We make use of the chiral unitary approach where these two resonances appear as composite states of two mesons, dynamically generated by the meson-meson interaction provided by chiral Lagrangians. We obtain a very narrow shape for the $f_0(980)$ production in agreement with a BES experiment. As to the amount of isospin violation, or $f_0(980)$ and $a_0(980)$ mixing, assuming constant vertices for the primary $η(1405)\rightarrow π^{0}K\bar{K}$ and $η(1405)\rightarrow π^{0}π^{0}η$ production, we find results which are much smaller than found in the recent experimental BES paper, but consistent with results found in two other related BES experiments. We have tried to understand this anomaly by assuming an I=1 mixture in the $η(1405)$ wave function, but this leads to a much bigger width of the $f_0(980)$ mass distribution than observed experimentally. The problem is solved by using the primary production driven by $η' \to K^* \bar K$ followed by $K^* \to K π$, which induces an extra singularity in the loop functions needed to produce the $f_0(980)$ and $a_0(980)$ resonances. Improving upon earlier work along the same lines, and using the chiral unitary approach, we can now predict absolute values for the ratio $Γ(π^0, π^+ π^-)/Γ(π^0, π^0 η)$ which are in fair agreement with experiment. We also show that the same results hold if we had the $η(1475)$ resonance or a mixture of these two states, as seems to be the case in the BES experiment.

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摘要：

英文摘要：

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