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.

该项目的主要目的是根据手学有效田间理论的原理制定和构建一个计划，并使用手性有效的拉格朗日式，可以在几个努克莱恩领域应用，主要要求是对Lagrangian的参数的明确重新构函数，并对可观察到的象征理论进行了明确的电力计数，并具有明确的功率计数。首先，研究了两个核子系统。通过解决lippmann-schinginger方程来迭代前阶电位，对受截止和某些接触项调节的领先潜在一杆交换以及某些接触术语进行了非扰动。多匹配交换的全部贡献与不受监管的接触相互作用与迭代的前阶电位之间的差异被视为扰动。所有其他高阶环图和接触术语贡献也被驱动地考虑在内。与常规方法相比，可观察到对监管机构形式和大小的依赖性弱得多，与常规方法相比，我们严格地证明，通过有效的lagrangianby分析相关的集成量的结构和计算量的结构，我们计划严格地证明有可能吸收所有违反违反的电力的贡献。我们将首先考虑次要领先的核子核子振幅，然后将分析扩展到近代到领导的临时和接下来的临时到领先顺序。之后，有可能将方法概括为两核系统与电流电流的相互作用。将所提出方法的适用性域扩展到明显更大的可能性，然后将研究硬刻度，以便找到``大'' - ''和``Small'' - 截止方案之间的匹配。我们还将检查是否有可能确定观察方法的可观察到的显式质量依赖性。至于实际应用，将考虑Deuteron形态和Deuteron光分散性。