Physics – Nuclear Physics – Nuclear Theory
Scientific paper
1997-09-26
Nucl.Phys.A632:445-469,1998
Physics
Nuclear Physics
Nuclear Theory
25 pages LaTeX, 3 figures (uses epsf)
Scientific paper
10.1016/S0375-9474(98)00007-4
We study an effective field theory of interacting nucleons at distances much greater than the pion's Compton wavelength. In this regime the NN potential is conjectured to be the sum of a delta function and its derivatives. The question we address is whether this sum can be consistently truncated at a given order in the derivative expansion, and systematically improved by going to higher orders. Regularizing the Lippmann-Schwinger equation using a cutoff we find that the cutoff can be taken to infinity only if the effective range is negative. A positive effective range---which occurs in nature---requires that the cutoff be kept finite and below the scale of the physics which has been integrated out, i.e. O(m_\pi). Comparison of cutoff schemes and dimensional regularization reveals that the physical scattering amplitude is sensitive to the choice of regulator. Moreover, we show that the presence of some regulator scale, a feature absent in dimensional regularization, is essential if the effective field theory of NN scattering is to be useful. We also show that one can define a procedure where finite cutoff dependence in the scattering amplitude is removed order by order in the effective potential. However, the characteristic momentum in the problem is given by the cutoff, and not by the external momentum. It follows that in the presence of a finite cutoff there is no small parameter in the effective potential, and consequently no systematic truncation of the derivative expansion can be made. We conclude that there is no effective field theory of NN scattering with nucleons alone.
Beane Silas R.
Cohen Thomas D. .
Phillips Daniel R.
No associations
LandOfFree
The potential of effective field theory in NN scattering does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The potential of effective field theory in NN scattering, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The potential of effective field theory in NN scattering will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-118517