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arXiv 2001.07113hep-phhep-lat
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奇异标量共振的相对论Cornell型机制

The Relativistic Cornell-type Mechanism of Exotic Scalar Resonances

A. M. Badalian, M. S. Lukashov, Yu. A. Simonov

备注：
v2: 22 pages, 5 figures; new explanations are added, several important insertions are made, the list of references is enlarged
发表信息：
Phys. Rev. D 102, 094012 (2020)
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摘要：

耦合$q\bar q$和$φφ( π-π$，$K\bar K, πK,...$）标量通道的形式主义制定，考虑到地面和径向激发$q\bar q$极点。的基本作用是由过渡系数$k^{(I)} (q\bar q, |φφ)$，这是使用夸克手征拉格朗日计算没有自由参数。所得到的方法称为极点投影机制（PPM），确保：1）每个$φφ$通道从基本$q\bar q$极点有一个谐振，例如$ππ$通道中的$f_0 (500)$谐振; 2）当在介子-介子沟道中考虑沟道耦合时，具有耦合到相同$q\bar q$态的两个$φφ$共振的可能性，其从大约1GeV的相同$n\bar n$极产生$f_0 (500)$和$f_0(980)$; 3）由于在没有自由参数的情况下以该形式计算的大的过渡系数$k^{(I)}$，对于特殊的（$ππ, πK)$）通道，极向下的强偏移。计算的复极点参数与共振态$f_0(500)$、$f_0(980)$、$a_0(980)$、$a_0(1450)$、$K^*_0(700)$、$K^*_0(1430)$、$f_0(1370)$和$f_0(1710)$的实验数据符合较好。

英文摘要：

The formalism of the coupled $q\bar q$ and the $φφ( π-π$, $K\bar K, πK,...$) scalar channels is formulated, taking into account the ground and radial excited $q\bar q$ poles. The basic role is shown to be played by the transition coefficients $k^{(I)} (q\bar q, |φφ)$, which are calculated using the quark-chiral Lagrangian without free parameters. The resulting method, called the pole projection mechanism (PPM), ensures: 1) one resonance for each $φφ$ channel from the basic $q\bar q$ pole, e.g. the $f_0 (500)$ resonance in the $ππ$ channel; 2) a possibility to have two $φφ$ resonances, coupled to the same $q\bar q$ state, when the channel coupling is taken into account in the meson-meson channels, which yields $f_0 (500)$ and $f_0(980)$ from the same $n\bar n$ pole around 1 GeV; 3) the strong pole shift down for special ($ππ, πK)$ channels due to large transition coefficients $k^{(I)}$, computed in this formalism without free parameters. The parameters of calculated complex poles are in reasonable agreement with the experimental data of the resonances $f_0(500)$, $f_0(980)$, $a_0(980)$, $a_0(1450)$, $K^*_0(700)$, $K^*_0(1430)$, $f_0(1370)$ and $f_0(1710)$.

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