四夸克与三重翻转势共振，在碎玻璃近似下在樱桃中衰变
Tetraquark resonances with the triple flip-flop potential, decays in the cherry in a broken glass approximation
摘要：
我们发展了一个用三重翻转势研究四夸克态的么正化形式，它包括两个介子-介子势和四夸克态四体势。这可以与雅菲-威尔切克模型和卡林纳-利普金四夸克模型联系起来，在这些模型中我们也考虑了可能的开放通道，因为四个夸克和反夸克可以随时逃逸到一对介子中。在这里，我们研究了一个简化的两变量玩具模型，并探讨了与玻璃杯中的樱桃的类比，但樱桃可能会从破碎的玻璃杯中逃脱。让我们的系统在一个变量中是有限的或紧的，而在另一个变量中是无限的，这是很有趣的。在这个框架下，我们解决了两个变量的薛定谔方程的位形空间。用有限差分方法，我们计算的频谱，我们搜索的局域态，我们试图计算相移。然后，我们应用出射球面波的方法来计算详细的相移和，并确定衰减宽度。我们在等质量的情况下探索模型，我们发现窄共振。特别是，两个交换角动量的存在是导致我们的衰变宽度较小的原因。
英文摘要：
We develop a unitarized formalism to study tetraquarks using the triple flip-flop potential, which includes two meson-meson potentials and the tetraquark four-body potential. This can be related to the Jaffe-Wilczek and to the Karliner-Lipkin tetraquark models, where we also consider the possible open channels, since the four quarks and antiquarks may at any time escape to a pair of mesons. Here we study a simplified two-variable toy model and explore the analogy with a cherry in a glass, but a broken one where the cherry may escape from. It is quite interesting to have our system confined or compact in one variable and infinite in the other variable. In this framework we solve the two-variable Schrödinger equation in configuration space. With the finite difference method, we compute the spectrum, we search for localized states and we attempt to compute phase shifts. We then apply the outgoing spherical wave method to compute in detail the phase shifts and and to determine the decay widths. We explore the model in the equal mass case, and we find narrow resonances. In particular the existence of two commuting angular momenta is responsible for our small decay widths.
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