论文标题
$σ$ -Meson：四夸克与两夸克组件和伯特 - 盐量的衰减宽度
The $σ$-meson: four-quark vs. two-quark components and decay width in a Bethe-Salpeter approach
论文作者
论文摘要
我们研究了Isospin Singlet通道中的共振动态产生，并在两个夸克状态之间进行混合。为此，我们将一种伯特 - 盐的方法推广到以前采用的四夸克国家\ cite {heupel：2012UA}以适应混合图。 $ q \ bar {q} q \ bar {q} $和$ q \ bar {q} $ bethe-salpeter Wave Wave函数的组件（带有Light Quarks $ Q \ in \ {u，d \} $）是在对称性否定的Dyson-Schwinger dysson-schwinger schwingwinger方程中的一致确定的。作为一个突出的例子，我们处理带有光夸克内容的isospin-singlet $ 0^{++} $梅森。我们发现，四夸克组件的$ππ$贡献主要负责所得状态的低（实际部分）质量。我们还研究了复杂动量平面中的分析结构，并在两杆阈值下切开一个分支，在第二个riemann板上的奇异性表明衰减宽度相当大。我们的发现与过去二十年来从分散方法\ cite {pelaez：2015qba}出现的$σ/f_0（500）$的一般图片达到了极好的定性协议。
We study the dynamical generation of resonances in isospin singlet channels with mixing between two- and four-quark states. To this end we generalise a Bethe-Salpeter approach to four-quark states employed previously \cite{Heupel:2012ua} to accommodate for mixing diagrams. The $q\bar{q}q\bar{q}$ and $q\bar{q}$ components of the Bethe-Salpeter wave function (with light quarks $q\in\{u,d\}$) are determined consistently in a symmetry-preserving truncation of the underlying Dyson-Schwinger equations. As a prominent example we deal with the isospin-singlet $0^{++}$ meson with light quark content. We find that the $ππ$ contribution of the four-quark component is mainly responsible for the low (real part of the) mass of the resulting state. We also study the analytic structure in the complex momentum plane and find a branch cut at the two-pion threshold and a singularity in the second Riemann sheet indicating a considerable decay width. Our findings are in excellent qualitative agreement with the general picture for the $σ/f_0(500)$ that emerged in the past two decades from dispersive approaches \cite{Pelaez:2015qba}.
