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有效红外相互作用模型中夸克传播子的解析性质

The analytic properties of the quark propagator from an effective infrared interaction model

Andreas Windisch

发表信息：
Phys. Rev. C 95, 045204 (2017)
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摘要：

本文研究了朗道规范中夸克传播子Dyson-Schwinger方程的解析性质。在夸克自能中，胶子传播子和夸克-胶子顶点的结合由有效相互作用（所谓的Maris-Tandy相互作用）模拟，其中忽略了紫外项。这使得夸克自能的圈被积函数在切面上解析-Pi < arg（x）<外动量平方的Pi。利用截断的简单性，我研究了夸克传播子在[-5.1，0] GeV^2 X i[0，10.2] GeV^2中的解。由于一个复杂的共轭对称性，这个区域完全覆盖了抛物积分域的Bethe-Salpeter方程（BSE）的束缚态质量高达4.5 GeV。采用一种新的数值技术，是基于高度并行计算的图形处理单元（GPU），我提取超过6500极在这个地区，出现的裸夸克质量是变化在很大范围内的紧密间隔的值。这些极点被分成23个独立的“坐标”，随着裸露质量的变化，这些坐标捕捉了复杂区域中极点的运动。的极点位置和残留物的原始数据提供作为补充材料，它可以用来参数化的解决方案的复杂的夸克传播的裸质量值范围很广，大的束缚态质量。这项研究是对以前的工作的扩展微扰单圈积分的解析延续的第一步，长期目标是建立一个框架，允许数值提取的夸克传播子的解析性质的截断，延伸到彩虹以外的夸克自能的径向积分的轮廓进行适当的调整。

英文摘要：

In this paper I investigate the analytic properties of the quark propagator Dyson-Schwinger equation (DSE) in the Landau gauge. In the quark self-energy, the combined gluon propagator and quark-gluon vertex is modeled by an effective interaction (the so-called Maris-Tandy interaction), where the ultraviolet term is neglected. This renders the loop integrand of the quark self-energy analytic on the cut-plane -Pi < arg(x) < Pi of the square of the external momentum. Exploiting the simplicity of the truncation, I study solutions of the quark propagator in the domain x in [-5.1,0] GeV^2 X i[0,10.2] GeV^2. Because of a complex conjugation symmetry, this region fully covers the parabolic integration domain for Bethe-Salpeter equations (BSEs) for bound state masses of up to 4.5 GeV. Employing a novel numerical technique that is based on highly parallel computation on graphics processing units (GPUs), I extract more than 6500 poles in this region, which arise as the bare quark mass is varied over a wide range of closely spaced values. The poles are grouped in 23 individual 'trajectories', that capture the movement of the poles in the complex region as the bare mass is varied. The raw data of the pole locations and -residues is provided as supplemental material, which can be used to parametrize solutions of the complex quark propagator for a wide range of bare mass values and for large bound state masses. This study is a first step towards an extension of previous work on the analytic continuation of perturbative one-loop integrals, with the long-term goal of establishing a framework that allows for the numerical extraction of the analytic properties of the quark propagator with a truncation that extends beyond the rainbow by making adequate adjustments in the contour of the radial integration of the quark self-energy.

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