Nucleon-nucleon potentials evolved to low momentum, which show great promise in few- and many-body calculations, have generally been formulated with a sharp cutoff on relative momenta. However, a sharp cutoff has technical disadvantages and can cause convergence problems at the 10-100 keV level in the deuteron and triton. This motivates using smooth momentum-space regulators as an alternative. We generate low-momentum interactions with smooth cutoffs both through energy-independent renormalization group methods and using a multi-step process based on the Bloch-Horowitz approach. We find greatly improved convergence for calculations of the deuteron and triton binding energies in a harmonic oscillator basis compared to results with a sharp cutoff. Even a slight evolution of chiral effective field theory interactions to lower momenta is beneficial. The renormalization group preserves the long-range part of the interaction, and consequently the renormalization of long-range operators, such as the quadrupole moment, the radius and 1/r, is small. This demonstrates that low-energy observables in the deuteron are reproduced without short-range correlations in the wave function.Comment: 29 pages, 19 figure

Abstract. We present a general formalism for deriving bounds on the shape parameters of the weak and electromagnetic form factors using as input correlators calculated from perturbative QCD, and exploiting analyticity and unitarity. The values resulting from the symmetries of QCD at low energies or from lattice calculations at special points inside the analyticity domain can be included in an exact way. We write down the general solution of the corresponding Meiman problem for an arbitrary number of interior constraints and the integral equations that allow one to include the phase of the form factor along a part of the unitarity cut. A formalism that includes the phase and some information on the modulus along a part of the cut is also given. For illustration we present constraints on the slope and curvature of the K l3 scalar form factor and discuss our findings in some detail. The techniques are useful for checking the consistency of various inputs and for controlling the parameterizations of the form factors entering precision predictions in flavor physics.

The nonperturbative nature of nucleon-nucleon interactions as a function of a momentum cutoff is studied using Weinberg eigenvalues as a diagnostic. This investigation extends an earlier study of the perturbative convergence of the Born series to partial waves beyond the 3 S 1 -3 D 1 channel and to positive energies. As the cutoff is lowered using renormalization-group or model-space techniques, the evolution of nonperturbative features at large cutoffs from strong short-range repulsion and the iterated tensor interaction are monitored via the complex Weinberg eigenvalues. When all eigenvalues lie within the unit circle, the expansion of the scattering amplitude in terms of the interaction is perturbative, with the magnitude of the largest eigenvalue setting the rate of convergence. Major decreases in the magnitudes of repulsive eigenvalues are observed as the Argonne v 18 , CD-Bonn or Nijmegen potentials are evolved to low momentum, even though two-body observables are unchanged. For chiral EFT potentials, running the cutoff lower tames the impact of the tensor force and of new nonperturbative features entering at N 3 LO. The efficacy of separable approximations to nuclear interactions derived from the Weinberg analysis is studied as a function of cutoff, and the connection to inverse scattering is demonstrated.

We study pure neutron matter in the BEC-BCS crossover regime using renormalization group based low-momentum interactions within the Nozières-Schmitt-Rink framework. This is an attempt to go beyond the mean field description for low-density matter. We work in the basis of so-called Weinberg eigenvectors where the operator G0V is diagonal, which proves to be an excellent choice that allows one to use non-local interactions in a very convenient way. We study the importance of correlations as a function of density. We notice that there is a significant reduction of the BCS critical temperature at low-densities as the neutron matter approaches the unitary limit.

We study pairing in low-density neutron matter including the screening interaction due to the exchange of particle-hole and RPA excitations. As bare force we employ the effective low-momentum interaction V low k , while the Fermi-liquid parameters are taken from a phenomenological energy density functional (SLy4) which correctly reproduces the equation of state of neutron matter. At low density, we find screening, i.e., pairing is reduced, while at higher densities, we find antiscreening, i.e., pairing is enhanced. This enhancement is mostly due to the strongly attractive Landau parameter f0. We discuss in detail the critical temperature Tc in the limit of low densities and show that the suppression of Tc predicted by Gor'kov and Melik-Barkhudarov can only be reproduced if the cutoff of the V low k interaction is scaled with the Fermi momentum. We also discuss the effect of non-condensed pairs on the density dependence of Tc in the framework of the Nozières-Schmitt-Rink theory.