The Long and Short of Nuclear Effective Field Theory Expansions

Nonperturbative effective field theory calculations for NN scattering seem to break down at rather low momenta. By examining several toy models, we clarify how effective field theory expansions can in general be used to properly separate long- and short-range effects. We find that one-pion exchange has a large effect on the scattering phase shift near poles in the amplitude, but otherwise can be treated perturbatively. Analysis of a toy model that reproduces 1S0 NN scattering data rather well suggests that failures of effective field theories for momenta above the pion mass can be due to short-range physics rather than the treatment of pion exchange. We discuss the implications this has for extending the applicability of effective field theories.Comment: 22 pages, 9 figures, references corrected, minor modification

Resolving the Large-N Nuclear Potential Puzzle

The large $N_c$ nuclear potential puzzle arose because three- and higher-meson exchange contributions to the nucleon-nucleon potential did not automatically yield cancellations that make these contributions consistent with the general large $N_c$ scaling rules for the potential. Here it is proposed that the resolution to this puzzle is that the scaling rules only apply for energy-independent potentials while all of the cases with apparent inconsistencies were for energy-dependent potentials. It is shown explicitly how energy-dependent potentials can have radically different large N behavior than an equivalent energy-independent one. One class of three-meson graphs is computed in which the contribution to the energy-independent potential is consistent with the general large N rules even though the energy-dependent potential is not.Comment: Corrections to the toy mode

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

Renormalization schemes and the range of two-nucleon effective field theory

The OS and PDS renormalization schemes for the effective field theory with nucleons and pions are investigated. We explain in detail how the renormalization is implemented using local counterterms. Fits to the NN scattering data are performed in the 1S0 and 3S1 channels for different values of mu_R. An error analysis indicates that the range of the theory with perturbative pions is consistent with 500 MeV.Comment: 40 pages, typos corrected, journal version. Discussion of the range in section VII clarified, conclusions unchange

The large-N(c) nuclear potential puzzle

An analysis of the baryon-baryon potential from the point of view of large-N(c) QCD is performed. A comparison is made between the N(c)-scaling behavior directly obtained from an analysis at the quark-gluon level to the N(c)-scaling of the potential for a generic hadronic field theory in which it arises via meson exchanges and for which the parameters of the theory are given by their canonical large-N(c) scaling behavior. The purpose of this comparison is to use large-N(c) consistency to test the widespread view that the interaction between nuclei arises from QCD through the exchange of mesons. Although at the one- and two-meson exchange level the scaling rules for the potential derived from the hadronic theory matches the quark-gluon level prediction, at the three- and higher-meson exchange level a generic hadronic theory yields a potential which scales with N(c) faster than that of the quark-gluon theory.Comment: 17 pages, LaTeX, 5 figure

Scheming in Dimensional Regularization

We consider the most general loop integral that appears in non-relativistic effective field theories with no light particles. The divergences of this integral are in correspondence with simple poles in the space of complex space-time dimensions. Integrals related to the original integral by subtraction of one or more poles in dimensions other than D=4 lead to nonminimal subtraction schemes. Subtraction of all poles in correspondence with ultraviolet divergences of the loop integral leads naturally to a regularization scheme which is precisely equivalent to cutoff regularization. We therefore recover cutoff regularization from dimensional regularization with a nonminimal subtraction scheme. We then discuss the power-counting for non-relativistic effective field theories which arises in these alternative schemes.Comment: 12 pages, additional text in opening section, version to be published in J. Phys.

The NN scattering 3S1-3D1 mixing angle at NNLO

The 3S1-3D1 mixing angle for nucleon-nucleon scattering, epsilon_1, is calculated to next-to-next-to-leading order in an effective field theory with perturbative pions. Without pions, the low energy theory fits the observed epsilon_1 well for momenta less than $\sim 50$ MeV. Including pions perturbatively significantly improves the agreement with data for momenta up to $\sim 150$ MeV with one less parameter. Furthermore, for these momenta the accuracy of our calculation is similar to an effective field theory calculation in which the pion is treated non-perturbatively. This gives phenomenological support for a perturbative treatment of pions in low energy two-nucleon processes. We explain why it is necessary to perform spin and isospin traces in d dimensions when regulating divergences with dimensional regularization in higher partial wave amplitudes.Comment: 17 pages, journal versio

Unitarity And Anomalous Top-Quark Yukawa Couplings

Unitarity constraints on anomalous top-Higgs couplings are examined. We also compare the unitarity constraints with the constraints from electroweak baryogenesis and electric dipole moments derived earlier.Comment: Iowa State University Preprint, AMES-HET 94-11, (Tex file) 10 pages, one Figure available by reques

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

Hyperfine Spectroscopy of Optically Trapped Atoms

We perform spectroscopy on the hyperfine splitting of $^{85}$Rb atoms trapped in far-off-resonance optical traps. The existence of a spatially dependent shift in the energy levels is shown to induce an inherent dephasing effect, which causes a broadening of the spectroscopic line and hence an inhomogeneous loss of atomic coherence at a much faster rate than the homogeneous one caused by spontaneous photon scattering. We present here a number of approaches for reducing this inhomogeneous broadening, based on trap geometry, additional laser fields, and novel microwave pulse sequences. We then show how hyperfine spectroscopy can be used to study quantum dynamics of optically trapped atoms.Comment: Review/Tutoria