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

本课题的主要目标是根据手性有效场论的原理，利用手性有效拉格朗日量，制定和构建一个可以应用于少核子领域的方案，主要要求是拉格朗日量参数的显式重整化和观测值的显式幂计数，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Lippmann-Schwinger方程，迭代了导阶势，对导阶势-单介子交换和一些接触项进行了非摄动处理。多介子交换的全部贡献以及不规范的接触相互作用与迭代的导阶势之间的差被视为扰动。所有其他高阶回路图和接触期贡献也被摄动地考虑在内。与传统方法相比，原始相互作用的微扰恢复导致可观测值对调节器的形式和大小的依赖性更弱。我们计划通过分析动量空间中相关积分的结构并进行数值验证，通过对有效拉格朗日函数参数的重整化来严格证明吸收所有幂计数违规贡献的可能性。我们将首先考虑次导阶核子-核子振幅，然后将分析扩展到次导阶和次导阶。在此之后，将有可能将该方法推广到两核子系统与弱电流的相互作用。为了找到“大”截止点和“小”截止点方案之间的匹配，将研究将所提出方法的适用范围扩展到比硬尺度大得多的截止点的可能性。我们还将检查是否有可能在考虑的方法中确定可观测值的显式介子质量依赖关系。在实际应用方面，将考虑氘核的形态因素和氘核的光分解。

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.