Methods based on Wilson's renormalization group have been successfully applied in the context of nuclear physics to analyze the scale dependence of effective nucleon-nucleon ($NN$) potentials, as well as to consistently integrate out the high-momentum components of phenomenological high-precision $NN$ potentials in order to derive phase-shift equivalent softer forms, the so called $V_{low-k}$ potentials. An alternative renormalization group approach that has been applied in this context is the Similarity Renormalization Group (SRG), which is based on a series of continuous unitary transformations that evolve hamiltonians with a cutoff on energy differences. In this work we study the SRG evolution of a leading order (LO) chiral effective $NN$ potential in the $^1 S_0$ channel derived within the framework of the Subtracted Kernel Method (SKM), a renormalization scheme based on a subtracted scattering equation.
Power counting and renormalization group invariance in the subtracted kernel method for the two-nucleon system
我们应用减核方法（SKM），一种基于在散射方程的核中进行递归多次减法的重正化方法，手性核子核子（NN）相互作用的下一个到下一个到领先阶（NNLO）。我们评估的相移在1 S 0通道在每个顺序在温伯格的功率计数计划和修改后的功率计数计划，产生系统的幂律改进。我们还明确地表明，SKM程序是重整化群不变的减法规模的变化下，通过一个非相对论性的Callan-Symanzik流方程的重整化NN相互作用的演变。
We compare the subtractive renormalization and the Wilsonian renormalization group approaches in the context of an effective field theory for the two-nucleon system. Based on an exactly solvable model of contact interactions, we observe that the standard Wilsonian renormalization group approach with a single cutoff parameter does not cover the whole space spanned by the renormalization scale parameters of the subtractive formalism. In particular, renormalization schemes corresponding to Weinberg's power counting in the case of an unnaturally large scattering length are beyond the region covere…
Effects of T- and P-odd weak nucleon interaction in nuclei: renormalizations due to residual strong interaction, matrix elements between compound states and their correlations with P-violating matrix elements
We present a study of two-nucleon scattering in chiral effective field theory with a finite cutoff to next-to-leading order in the chiral expansion. In the proposed scheme, the contributions of the lowest-order interaction to the scattering amplitude are summed up to an arbitrary order, while the corrections beyond leading order are iterated only once. We consider a general form of the regulator for the leading-order potential including local and non-local structures. The main objective of the paper is to address formal aspects of renormalizability within the considered scheme. In particular, …
Effective Hamiltonians and effective electroweak operators are calculated with the Okubo-Lee-Suzuki formalism for two-nucleon systems. Working within a harmonic oscillator basis, first without and then with a confining harmonic oscillator trap, we demonstrate the effects of renormalization on observables calculated for truncated basis spaces. We illustrate the renormalization effects for the root-mean-square point-proton radius, electric quadrupole moment, magnetic dipole moment, Gamow-Teller transition and neutrinoless double-beta decay operator using nucleon-nucleon interactions from chiral …
Renormalization group invariance in pionless effective field theory for the NN system
我们考虑NN相互作用在无π有效场论（EFT）的次-首阶（NNLO）和使用递归减法重整化方案来描述NN散射在1 S 0通道。我们将接触相互作用的强度固定在一个参考尺度上，选择一个为相移提供最佳拟合的尺度，然后通过非相对论性Callan-Symanzik方程来演化减去的Lippmann-Schwinger方程的驱动项，从而滑动重整化尺度。结果表明，这种多重减项的系统重整化方案是完全重整化群不变的。
Nucleon-nucleon scattering in the $^1S_0$ partial wave is considered in chiral effective field theory within the renormalizable formulation of Ref. [1] beyond the leading-order approximation. By applying subtractive renormalization, the subleading contact interaction in this channel is taken into account non-perturbatively. For a proper choice of renormalization conditions, the predicted energy dependence of the phase shift and the coefficients in the effective range expansion are found to be in a good agreement with the results of the Nijmegen partial wave analysis.
The renormalization of iterated one-pion exchange (OPE) is studied in Chiral Effective Field Theory ($χ$EFT) for the antinucleon-nucleon ($\overline{N}\!N$) system. The OPE potential is cut off at a certain distance and contact interactions are represented by a complex spherical well with the same radius. We investigate the dependence on the cutoff radius of the phase shifts, inelasticities, and mixing angles for the low partial waves in $\overline{N}\!N$ scattering. We show that renormalization requires additional contact interactions compared to the expectation based on naive dimensional ana…
Unitary transformations of a Hamiltonian generally induce interaction terms beyond the particle rank present in the untransformed Hamiltonian that have to be captured and included in a many-body calculation. In systems with strangeness such as hypernuclei, the three-body terms induced by the hyperon-nucleon interaction are strong, so their inclusion is crucial. We present in detail a procedure for computing hyperon-nucleon-nucleon interaction terms that are induced during a similarity renormalization group (SRG) flow. The SRG is carried out in a basis spanned by antisymmetric harmonic-oscillat…
The Microscopic Otical Model Potential is evaluated within a relativistic scheme which provides a natural and consistent relation between the spin-orbit part and the central part of the potential. The Dirac-Brueckner-Hartree-Fock (DBHF) approach provides such a microscopic relativistic scheme, which is based on a realistic nucleon-nucleon interaction and reproduce the saturation properties of symmetric nuclear matter without any adjustable parameter. Its solution using the projection technique within the subtracted T-matrix (STM) representation provides a reliable extension to asymmetric nucle…
We investigate the axial-vector nucleon-to-delta transition form factors in the framework of relativistic baryon chiral perturbation theory at the one-loop order using the complex-mass renormalization scheme. We determine the available six free parameters by fitting to an empirical parametrization of the form factors obtained from the BNL neutrino bubble chamber experiments. A unique feature of our calculation is the prediction of a non-vanishing form factor $C_3^A(Q^2)$. Moreover, our results show a surprising sensitivity to the coupling constant $\texttt{g}_1$ of the leading-order Lagrangian…
