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

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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.