arXiv 1504.016242015-04hep-phcond-mat.str-elnucl-th

求解Minkowski空间中的非齐次Bethe-Salpeter方程：零能量极限

Solving the inhomogeneous Bethe-Salpeter Equation in Minkowski space: the zero-energy limit

T. Frederico, G. Salme', M. Viviani

备注：: 23 pages and 4 figures. Minor changes in the abstract, typos fixed and added a figure. Submitted for publication
DOI：: 10.1140/epjc/s10052-015-3616-1

摘要：

首次在Minkowski空间中，采用基于Nakanishi积分表示的方法，在梯形近似下数值研究了由两个质量标量交换一个质量标量组成的相互作用系统的非齐次Bethe-Salpeter方程.在本文中，零能态的极限情况下，被认为是成功地应用到束缚态的方法。利用Nakanishi框架内的两个不同的积分方程，计算了Yukawa耦合常数的几个值的散射长度的数值。这些低能量的观测值进行比较（i）类似的数量最近在文献中获得的，在一个完全不同的框架和（ii）非相对论性的评价，说明了相关的非微扰，真正的场理论处理在闵可夫斯基空间，即使在低能量政权。此外，还给出了动力学函数，如Nakanishi权函数和零能波前波函数的畸变部分。有趣的是，一个高度不平凡的问题有关的突然变化的宽度的支持的Nakanishi权重函数，当接近零能量极限，阐明，确保一个健全的基础，即将到来的评估相移。

英文摘要：

For the first time, the inhomogeneous Bethe-Salpeter Equation for an interacting system, composed by two massive scalars exchanging a massive scalar, is numerically investigated in ladder approximation, directly in Minkowski space, by using an approach based on the Nakanishi integral representation. In this paper, the limiting case of zero-energy states is considered, extending the approach successfully applied to bound states. The numerical values of scattering lengths, are calculated for several values of the Yukawa coupling constant, by using two different integral equations that stem within the Nakanishi framework. Those low-energy observables are compared with (i) the analogous quantities recently obtained in literature, within a totally different framework and (ii) the non relativistic evaluations, for illustrating the relevance of a non perturbative, genuine field theoretical treatment in Minkowski space, even in the low-energy regime. Moreover, dynamical functions, like the Nakanishi weight functions and the distorted part of the zero-energy Light-front wave functions are also presented. Interestingly, a highly non trivial issue related to the abrupt change in the width of the support of the Nakanishi weight function, when the zero-energy limit is approached, is elucidated, ensuring a sound basis to the forthcoming evaluation of phase-shifts.

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