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arXiv 2007.06495hep-ph
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$σ$ -介子：四夸克与二夸克成分和衰变宽度的Bethe-Salpeter方法

The $σ$-meson: four-quark vs. two-quark components and decay width in a Bethe-Salpeter approach

Nico Santowsky, Gernot Eichmann, Christian S. Fischer, Paul C. Wallbott, Richard Williams

备注：
10 pages, 7 figures, v2: minor changes, version accepted by PRD
发表信息：
Phys. Rev. D 102, 056014 (2020)
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摘要：

研究了两夸克态和四夸克态混合的同位旋单重态通道中共振态的动力学产生。为此，我们概括了贝特-萨尔彼得的方法，以前采用的四夸克态\cite{Heupel:2012ua}，以适应混合图。Bethe-Salpeter波函数的$q\bar{q}q\bar{q}$和$q\bar{q}$分量（含轻夸克$q\in\{u,d\}$）在Dyson-Schwinger方程的保序截断中一致地确定。作为一个突出的例子，我们研究了含有轻夸克的同位旋单重态$0^{++}$介子。我们发现，四夸克分量的$ππ$贡献是导致低质量（实部）的主要原因。我们还研究了在复杂的动量平面的分析结构，并发现一个分支削减在两个π阈值和奇异性的第二个黎曼表表示相当大的衰变宽度。我们的研究结果是在良好的定性协议的$σ/f_0(500)$出现在过去二十年的分散方法\cite{Pelaez:2015qba}的一般图片。

英文摘要：

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}.

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