Examination of the physical pictures of the field theories with nonlinearly realized symmetries by the Wilsonian renormalization group method

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We propose a method of determining the power counting rule for Nuclear Effective Field Theory, which reflects chiral symmetry of QCD, the fundamental theory of strong interactions. The method is based on the scaling dimensions obtained by the nonperturbative, or Wilsonian, renormalization group analysis. We show that the resulting power counting rule turns out to be very similar to that proposed by Kaplan, Savage, and Wise. We also propose a practical scheme of calculating the nucleon-nucleon scattering phase shift on the basis of the analysis and perform the calculations.