高密夸克物质与核物质中夸克配对和重子形成

Based on nonperturbetive theories and the constitunent quark model, we plan to investigate the properties of baryons, nuclear matter and their relation with color superconductivity. The static properties of baryons can be studied with the relativistic Faddeev equation. Different from the usual quasi-particle approach, we substitute the full diquark propagator obtained from Bethe-Salpeter equation into the Faddeev equation. In stead of directly solve the baryon eigen equation given by the Faddeev equation, the baryon vertex functions and the Faddeev amplitudes are decomposited corresponding to the spin and parity structures of baryon. The diquark self-energy are approximated with two dimensional Chebyshev polynomials, which is validated to significantly reduce the numerical complexity. We plan to study on the following issues: (1)how does the stablity of diquark influence on the properties of baryons and their excited state. (2)the properties of baryon and nuclear matter at finite temperature and finite density, especially in the phase transition region of QCD phase diagram. (3)baryon static properties in color superconducting phase and the effect of BEC-BCS crossover on stability of baryon bound state.

利用非微扰方法和重子的夸克对模型，在有限温度有限密度下计算重子性质、核物质性质以及它们和色超导态的关系。有别于传统的用准粒子近似处理夸克对的方法，我们在重子Faddeev方程中使用Bethe-Salpeter方程导出的夸克对全传播子。对带有Dirac结构的重子的顶角函数和波函数进行因子化，而不是直接的去解多维的本征方程。在数值上，利用Chebyshev近似来处理夸克对的自能项，经验证这种近似在处理夸克对传播子时有很好的收敛性，可以大大减少数值计算的复杂度。要解决的关键问题：(1) 夸克对的稳定性对重子及其激发态性质的影响；(2) 有限温度有限密度下在相变区域的重子和核物质性质；(3)色超导夸克物质中的重子性质以及BEC-BCS转变对重子性质的影响。此课题与FAIR/CBM实验有密切联系，是色超导领域的一个自然延伸。

本课题中，我们在光前平面中研究了玻色子三体束缚态的形成及其在不同耦合和束缚能区域的行为。运用本征矩阵法求解积分方程，并利用Cauchy-Swartz不等式以及数值逼近的方法对矩阵的奇异性及其对本征值的影响进行分析。在弱耦合情形下，不稳定的两体束缚态可以形成稳定的三体束缚态。在相对论情形下，当束缚能趋于零并且两玻色子束缚态即将形成时,三玻色子体系中可能会出现的类Efimov态的束缚态个数发散的现象。本质上，出现该现象的原因是零束缚能时在两体束缚态即将形成的区域，两玻色子传播子的奇异性使本征积分方程核的整体奇异性发生了变化,从而导致了体系的激发态分布发生了改变。