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

该项目的主要目标是根据手征有效场论的原理，使用手征有效拉格朗日量，制定和构建一个方案，该方案可应用于少核子扇区，主要要求是拉格朗日量参数的显式重整化和显式可观测量的幂次计数，并保持基础理论的对称性。首先，研究了双核子系统。通过求解迭代首阶势的Lippmann-Schwinger方程，非微扰地处理了由截断项和某些接触项调节的首阶势-一π交换。将多π交换和未调节的接触相互作用的全部贡献与迭代首阶势之差视为微扰，并考虑了所有其他高阶回路图和接触项的微扰贡献。与传统方法相比，微扰恢复原始相互作用导致观测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，严格证明通过有效拉格朗日参数的重整化吸收所有幂次计数违规贡献的可能性，并进行数值检验。我们将首先考虑次领先阶核子-核子振幅，然后将分析扩展到次领先阶和次领先阶。在此基础上，将该方法推广到两核子系统与电弱流的相互作用中。将研究将所提出的方法的适用范围扩展到明显大于硬标度的截止点的可能性，以便找到"大“和"小”截止点方案之间的匹配。我们还将检查是否有可能确定所考虑的方法内的observableswithin明确的π介子质量的依赖。至于实际应用，我们将考虑氘核的形状因子和氘核的光致衰变。

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.