n + p -> d + gamma in Effective Field Theory

The radiative capture process n+p-> d+gamma provides clear evidence for meson exchange currents in nuclear physics. We compute this process at low energies using a recently developed power counting for the effective field theory that describes nucleon-nucleon interactions. The leading order contribution to this process comes from the photon coupling to the nucleon magnetic moments. At subleading order there are other contributions. Among these are graphs where the photon couples directly to pions, i.e. meson exchange currents. These diagrams are divergent and require the presence of a local four-nucleon-one photon counterterm. The coefficient of this operator is determined by the measured cross section, 334.2 +- 0.5 mb, for incident neutrons with speed |v|=2200 m/s.Comment: 14 pages, 5 figures, late

Regularization and renormalization in effective field theories of the nucleon-nucleon interaction

Some form of nonperturbative regularization is necessary if effective field theory treatments of the NN interaction are to yield finite answers. We discuss various regularization schemes used in the literature. Two of these methods involve formally iterating the divergent interaction and then regularizing and renormalizing the resultant amplitude. Either a (sharp or smooth) cutoff can be introduced, or dimensional regularization can be applied. We show that these two methods yield different results after renormalization. Furthermore, if a cutoff is used, the NN phase shift data cannot be reproduced if the cutoff is taken to infinity. We also argue that the assumptions which allow the use of dimensional regularization in perturbative EFT calculations are violated in this problem. Another possibility is to introduce a regulator into the potential before iteration and then keep the cutoff parameter finite. We argue that this does not lead to a systematically-improvable NN interaction.Comment: 5 pages, LaTeX, uses espcrc1.sty, summary of talk given at the 15th International Conference on Few-Body Problems in Physic

The potential of effective field theory in NN scattering

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.Comment: 25 pages LaTeX, 3 figures (uses epsf

Effective Field Theory for Short-Range Forces

The method of effective field theories (EFTs) is developed for the scattering of two particles at wavelengths which are large compared to the range of their interaction. It is shown that the renormalized EFT is equivalent to the effective range expansion, to a Schroedinger equation with a pseudo-potential, and to an energy expansion of a generic boundary condition at the origin. The roles of regulators and potentials are also discussed. These ideas are exemplified in a toy model.Comment: 38 pages, 6 figure

Coulomb Effects in Low Energy Proton-Proton Scattering

Using a recently developed effective field theory for the interactions of nucleons at non-relativistic energies, we calculate non-perturbatively Coulomb corrections to proton-proton scattering. Including the dimension-eight derivative interaction in the PDS regularization scheme, we recover a modified form of the Blatt-Jackson relation between the scattering lengths. The effective range receives no corrections from the Coulomb interactions to this order. Also the case of scattering in channels where the Coulomb force is attractive, is considered. This is of importance for hadronic atoms.Comment: 29 pages, Late

Chiral Perturbation Theory in Few-Nucleon Systems

The low-energy effective theory of nuclear physics based on chiral symmetry is reviewed. Topics discussed include the nucleon-nucleon force, few-body potentials, isospin violation, pion-deuteron scattering, proton-neutron radiative capture, pion photoproduction on the deuteron, and pion production in proton-proton collisions.Comment: 15 pages, 2 figures, Latex, aipproc.sty and epsfig, invited talk at the 6th Conference on the Intersections of Particle and Nuclear Physics, Big Sky, May 199

Elastic and Inelastic Neutrino-Deuteron Scattering in Effective Field Theory

The differential cross-sections for elastic and inelastic neutrino-deuteron scattering are calculated analytically using nucleon-nucleon effective field theory. For elastic scattering, the deuteron axial form factor and the deuteron strange magnetic moment form factor are computed to next-to-leading order, including two-body currents. For inelastic scattering, two neutral current processes nu+d->nu+n+p, nubar+d->nubar+n+p and one charged current process nubar+d->(e^+)+n+n are computed to next-to-leading order. These depend on an isovector axial two-body matrix element whose value is yet to be fixed by experiment. Potential model calculations by Kubodera et al. and Ying et al. are reproduced for different values of the two-body matrix element. This implies that the differences between the two potential model calculations lie in their treatment of short distance physics. The charged current to neutral current nubar-d cross-section ratio is confirmed to be insensitive to short distance physics, and the same ratio is obtained by potential models and the calculation presented here, within 5%, for incident incident neutrino energies up to 20 MeV. The two-body matrix element could be fixed using the parity violating process epol+d->e+n+p.Comment: 29 pages, 11 figures; An error in the charged current cross section has been corrected. Figures and discussion have been modified accordingl

Low Energy Theorems For Nucleon-Nucleon Scattering

Low energy theorems are derived for the coefficients of the effective range expansion in s-wave nucleon-nucleon scattering valid to leading order in an expansion in which both $m_\pi$ and $1/a$ (where $a$ is the scattering length) are treated as small mass scales. Comparisons with phase shift data, however, reveal a pattern of gross violations of the theorems for all coefficients in both the $^1S_0$ and $^3S_1$ channels. Analogous theorems are developed for the energy dependence $\epsilon$ parameter which describes $^3S_1 - ^3D_1$ mixing. These theorems are also violated. These failures strongly suggest that the physical value of $m_\pi$ is too large for the chiral expansion to be valid in this context. Comparisons of $m_\pi$ with phenomenological scales known to arise in the two-nucleon problem support this conjecture.Comment: 12 pages, 1 figure, 1 table; appendix added to discuss behavior in chiral limit; minor revisions including revised figure reference to recent work adde

The Polarizability of the Deuteron

The scalar and tensor polarizabilities of the deuteron are calculated using the recently developed effective field theory that describes nucleon-nucleon interactions. Leading and next-to-leading order contributions in the perturbative expansion predict a scalar electric polarizability of 0.595 fm^3. The tensor electric polarizability receives contributions starting at next-to-leading order from the exchange of a single potential pion and is found to be -0.062 fm^3. We compute the leading contributions to the scalar and tensor magnetic polarizabilities, finding 0.067 fm^3 and 0.195 fm^3, respectively.Comment: 13 pages, 4 figures as 6 eps files, latex. References adde

Short-range interactions in an effective field theory approach for nucleon-nucleon scattering

We investigate in detail the effect of making the range of the ``contact'' interaction used in effective field theory (EFT) calculations of NN scattering finite. This is done in both an effective field theory with explicit pions, and one where the pions have been integrated out. In both cases we calculate NN scattering in the ${}^1 S_0$ channel using potentials which are second-order in the EFT expansion. The contact interactions present in the EFT Lagrangian are made finite by use of a square-well regulator. We find that there is an optimal radius for this regulator, at which second-order corrections to the EFT are identically zero; for radii near optimal these second-order corrections are small. The cutoff EFTs which result from this procedure appear to be valid for momenta up to about 100 MeV/c. We also find that the radius of the square well cannot be reduced to zero if the theory is to reproduce both the experimental scattering length and effective range. Indeed, we show that, if the NN potential is the sum of a one-pion exchange piece and a short-range interaction, then the short-range piece must extend out beyond 1.1 fm, regardless of its particular form.Comment: 15 pages, RevTeX, uses BoxedEPS.te