Explicit renormalization and power counting in the few-nucleon chiral effective field theory with a cutoff

带截止的少核子手性有效场理论中的显式重整化和功率计数

• 批准号: 426661267
• 负责人: Dr. Ashot Gasparyan
• 金额: --
• 依托单位: Institut für Theoretische Physik II: Hadronen- und Teilchenphysik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/426661267?language=en
• 关键词: Explicit; renormalization; power; counting; few

The main goal of this project is to formulate and construct a scheme based on the principles of chiral effective field theory and using the chiral effective Lagrangian that can be applied in the few-nucleon sector with the main requirements being an explicit renormalization of the parameters of the Lagrangian and explicit power counting for observables, and preserving the symmetries of the underlying theory. First, the two-nucleon system is studied. The leading-order potential-one-pion exchange regulated by a cutoff as well as some contact terms are treated non-perturbatively by solving the Lippmann-Schwinger equation iterating the leading-order potential. The difference between the full contribution of the multi-pion exchange together with the unregulated contact interactions and the iterated leading-order potential is regarded as a perturbation.All other higher order loop diagrams and contact-term contributions are also taken into account perturbatively. The perturbative restoration of the original interaction results ina much weaker dependence of observables on the form and the size of the regulator as compared to conventional approaches.We plan to rigorously prove the possibility of absorbing all power-counting violating contributions by a renormalization of the parameters of the effective Lagrangianby analyzing the structure of the relevant integrals in momentum space and check this numerically. We will first consider the next-to-leading order nucleon-nucleon amplitude and then extend the analysis to the next-to-next-to-leading and next-to-next-to-next-to-leading orders. After that, it will be possible to generalize the method to the interaction of the two-nucleon system with electroweak currents. The possibility to extend the applicability domain of the proposed method to the cutoffs significantly larger then the hard scale will be investigated in order to find a matching between the ``large''- and ``small''-cutoff schemes. We will also check whether it is possible to determine the explicit pion-mass dependence of the observableswithin the considered approach. As for the practical applications, deuteron form factors and deuteron photodisintegration will be considered.

这个项目的主要目标是根据手征有效场论的原理和使用手征有效拉格朗日来制定和构造一个方案，该方案可以应用于少数核子部门，主要要求是拉格朗日参数的显式重整化和对可观测到的显式功率计数，并保持基本理论的对称性。首先，研究了双核子系统。通过求解迭代前导阶势的Lippmann-Schwinger方程，非微扰地处理了受截断调节的前导级势-1-π交换以及一些接触项。多π交换的全部贡献与无规则的接触相互作用和迭代的领导阶势之差被视为微扰，所有其他高阶回路图和接触项的贡献也被微扰考虑。与传统方法相比，对原始相互作用的微扰恢复使得能观量对调节器的形式和大小的依赖性要弱得多。我们计划通过分析动量空间中相关积分的结构，严格证明通过重整化有效拉格朗日参数来吸收所有违反功率计算的贡献的可能性，并进行数值验证。我们将首先考虑次前级核子-核子振幅，然后将分析扩展到次前级和次前级。然后，将该方法推广到两核子系统与弱电流的相互作用。将研究将拟议方法的适用范围扩大到远大于硬规模的适用范围的可能性，以便找到“大”--和“小”-截止范围方案之间的匹配。我们还将检查是否有可能在所考虑的方法内确定可见粒子与质量的显式依赖关系。在实际应用中，我们将考虑重离子形状因子和重离子光解。