2,027 research outputs found
Chiral Expansion, Renormalization and the Nuclear Force
The renormalization of singular chiral potentials as applied to NN scattering
and the structure of the deuteron is discussed. It is shown how zero range
theories may be implemented non-perturbatively as constrained from known long
range NN forces.Comment: Talk at International IUPAP Conference on Few-Body Problems in
Physics (FB18), Santos-Sao Paulo (Brasil), 21-26 August 200
Deuteron radial moments for renormalized chiral potentials
We calculate deuteron positive and negative radial moments involving any
bilinear function of the deuteron S and D wave functions for renormalized OPE
and TPE chiral potentials. The role played by the strong singularities of the
potentials at the origin and the short distance insensitivity of the results
when the potentials are fully iterated is emphasized as compared to realistic
potentials.Comment: 3 pages, 2 figures. Poster presented at 4th International Conference
on Quarks and Nuclear Physics (QNP06), Madrid, Spain, 5-10 Jun 200
Power Counting of Contact-Range Currents in Effective Field Theory
We analyze the power counting of two-body currents in nuclear effective field
theories (EFTs). We find that the existence of non-perturbative physics at low
energies, which is manifest in the existence of the deuteron and the 1S0 NN
virtual bound state, combined with the appearance of singular potentials in
versions of nuclear EFT that incorporate chiral symmetry, modifies the
renormalization-group flow of the couplings associated with contact operators
that involve nucleon-nucleon pairs and external fields. The order of these
couplings is thereby enhanced with respect to the naive-dimensional-analysis
estimate. Consequently, short-range currents enter at a lower order in the
chiral EFT than has been appreciated up until now, and their impact on
low-energy observables is concomitantly larger. We illustrate the changes in
the power counting with a few low-energy processes involving external probes
and the few-nucleon systems, including electron-deuteron elastic scattering and
radiative neutron capture by protons.Comment: 5 pages. Minor revisions. Conclusions unchanged. Version to appear in
Physical Review Letter
Renormalization Group Analysis of Boundary Conditions in Potential Scattering
We analyze how a short distance boundary condition for the Schrodinger
equation must change as a function of the boundary radius by imposing the
physical requirement of phase shift independence on the boundary condition. The
resulting equation can be interpreted as a variable phase equation of a
complementary boundary value problem. We discuss the corresponding infrared
fixed points and the perturbative expansion around them generating a short
distance modified effective range theory. We also discuss ultraviolet fixed
points, limit cycles and attractors with a given fractality which take place
for singular attractive potentials at the origin. The scaling behaviour of
scattering observables can analytically be determined and is studied with some
emphasis on the low energy nucleon-nucleon interaction via singular pion
exchange potentials. The generalization to coupled channels is also studied.Comment: 31 pages, 8 figure
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