论文标题
$φ^4 $理论中的三体共振
Three-body resonances in the $φ^4$ theory
论文作者
论文摘要
我们使用晶格复合体标量$φ^4 $理论研究了三体共振的特性，其中有两个标量，因此选择了一个重粒子，使一个重粒子可以腐烂成三个光。我们使用变分技术确定了几个晶格体积的两体和三体光谱，然后对它们进行两种版本的三粒子有限体积形式主义：相对论野外理论方法和有限量数量的单位性方法。我们发现两种方法都提供了对能级的等效描述，并且我们能够使用散射量的简单参数化拟合光谱。通过求解相应的三粒子形式主义的积分方程，我们确定共振在复杂能平面中的极点，从而确定其质量和宽度。我们发现，在理论耦合的不同值下，这两种方法之间的一致性非常好。
We study the properties of three-body resonances using a lattice complex scalar $φ^4$ theory with two scalars, with parameters chosen such that one heavy particle can decay into three light ones. We determine the two- and three-body spectra for several lattice volumes using variational techniques, and then analyze them with two versions of the three-particle finite-volume formalism: the Relativistic Field Theory approach and the Finite-Volume Unitarity approach. We find that both methods provide an equivalent description of the energy levels, and we are able to fit the spectra using simple parametrizations of the scattering quantities. By solving the integral equations of the corresponding three-particle formalisms, we determine the pole position of the resonance in the complex energy-plane and thereby its mass and width. We find very good agreement between the two methods at different values of the coupling of the theory.
