S. Szpigel

Symmetries of the similarity renormalization group for nuclear forces

We review the role played by long-distance symmetries within the context of the similarity renormalization group approach. This is based on phase-shift-preserving continuous unitary transformations that evolve Hamiltonians with a cutoff on energy differences. We find that there is a similarity cutoff of 3/fm for which almost perfect fulfillment of Wigner SU(4) symmetry is found at the two body level. This suggests to look for similar symmetry patterns for three- and four-body forces. We also analyze the impact of potentials based on Chiral Perturbation Theory in Nuclear Structure calculations.

Implicit vs explicit renormalization and effective interactions

Abstract Effective interactions can be obtained from a renormalization group analysis in two complementary ways. One can either explicitly integrate out higher energy modes or impose given conditions at low energies for a cut-off theory. While the first method is numerically involved, the second one can be solved almost analytically. In both cases we compare the outcoming effective interactions for the two nucleon system as functions of the cut-off scale and find a strikingly wide energy region where both approaches overlap, corresponding to relevant scales in light nuclei Λ ≲ 200 MeV . This amounts to a great simplification in the determination of the effective interaction parameters.

Similarity renormalization group evolution of chiral effective nucleon–nucleon potentials in the subtracted kernel method approach

Abstract 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.

THE CONTRIBUTION OF MICROBUNCHING INSTABILITY TO SOLAR FLARE EMISSION IN THE GHz TO THz RANGE OF FREQUENCIES

Recent solar flare observations in the sub-terahertz range have provided evidence of a new spectral component with fluxes increasing for larger frequencies, separated from the well-known microwave emission that maximizes in the gigahertz range. Suggested interpretations explain the terahertz spectral component but do not account for the simultaneous microwave component. We present a mechanism for producing the observed double spectra. Based on coherent enhancement of synchrotron emission at long wavelengths in laboratory accelerators, we consider how similar processes may occur within a solar flare. The instability known as microbunching arises from perturbations that produce electron beam density modulations, giving rise to broadband coherent synchrotron emission at wavelengths comparable to the characteristic size of the microbunch structure. The spectral intensity of this coherent synchrotron radiation (CSR) can far exceed that of the incoherent synchrotron radiation (ISR), which peaks at a higher frequency, thus producing a double-peaked spectrum. Successful CSR simulations are shown to fit actual burst spectral observations, using typical flaring physical parameters and power-law energy distributions for the accelerated electrons. The simulations consider an energy threshold below which microbunching is not possible because of Coulomb repulsion. Only a small fraction of the radiating charges accelerated to energies above the threshold is required to produce the microwave component observed for several events. The ISR/CSR mechanism can occur together with other emission processes producing the microwave component. It may bring an important contribution to microwaves, at least for certain events where physical conditions for the occurrence of the ISR/CSR microbunching mechanism are possible.

Power counting and renormalization group invariance in the subtracted kernel method for the two-nucleon system

We apply the subtracted kernel method (SKM), a renormalization approach based on recursive multiple subtractions performed in the kernel of the scattering equation, to the chiral nucleon–nucleon (NN) interactions up to next-to-next-to-leading-order. We evaluate the phase-shifts in the 1S0 channel at each order in Weinberg’s power counting scheme and in a modified power counting scheme which yields a systematic power-law improvement. We also explicitly demonstrate that the SKM procedure is renormalization group invariant under the change of the subtraction scale through a non-relativistic Callan–Symanzik flow equation for the evolution of the renormalized NN interactions.

Unitary neutron matter in the on-shell limit

We compute the Bertsch parameter for neutron matter by using nucleon-nucleon interactions that are fully diagonal in momentum space. We analyze the on-shell limit with the similarity renormalization group and compare the results for a simple separable toy model to realistic calculations with high precision NN potentials.

Contribution from Drell-Yan processes to the emission spectrum in solar flares

The recent discovery of a new and intense solar flare radiation spectral component with a maximum in the terahertz range has raised a great deal of interest. The origin of this component is still unknown, constituting a problem that goes beyond the application of canonical models used to describe the well-known microwave spectrum. In this work, we present preliminary results on the investigation of a possible contribution from electron-positron pairs produced in a Drell-Yan process to the emission of the terahertz component observed in solar flares.

Running of the contact interactions in chiral N3LO potentials from subtractive renormalization

In this work a subtracted kernel renormalization procedure (SKM) is applied to the chiral NN potential up to next-to-next-to-next-to-leading-order (N3 LO) to obtain the running of the renormalized contact strengths with the subtraction scale μ and the phase shifts for all uncoupled waves with contact interaction (S,P,D). We use two potentials constructed within the framework of Weinbergs approach to ChEFT, which provide a very accurate description of NN scattering data below laboratory energies E ~ 350 MeV, namely Epelbaum, Glockle and Meissner (N3LO-EGM) and Entem and Machleidt (N3LO-EM). For both potentials, we consider a large cutoff (30 fm-1) and analyze the phases and the running of the contact strengths with the subtraction point μ by making a fit of the K-matrix with five subtractions to the K-matrix from the Nijmegen II potential at low energies (E ≤ 20 MeV).

Renormalization Group Invariance in Pionless Effective Field Theory for the NN System

We consider the NN interaction in pionless effective field theory (EFT) up to next-to-next-to-leading order (NNLO) and use a recursive subtractive renormalization scheme to describe NN scattering in the 1S0 channel. We fix the strengths of the contact interactions at a reference scale, chosen to be the one that provides the best fit for the phase-shifts, and then slide the renormalization scale by evolving the driving terms of the subtracted Lippmann–Schwinger equation through a non-relativistic Callan–Symanzik equation. The results show that such a systematic renormalization scheme with multiple subtractions is fully renormalization group invariant.

RENORMALIZATION TOOLS FOR THE NN INTERACTION

In this work we apply the similarity renormalization group (SRG) approach to evolve an effective nucleon–nucleon (NN) potential in leading-order (LO) chiral effective field theory (ChEFT). We present the results obtained for a NN potential in the 1S0 channel derived within the framework of the subtracted kernel method (SKM).