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

Nucleons Properties at Finite Lattice Spacing in Chiral Perturbation Theory

Properties of the proton and neutron are studied in partially-quenched chiral perturbation theory at finite lattice spacing. Masses, magnetic moments, the matrix elements of isovector twist-2 operators and axial-vector currents are examined at the one-loop level in a double expansion in the light-quark masses and the lattice spacing. This work will be useful in extrapolating the results of simulations using Wilson valence and sea quarks, as well as simulations using Wilson sea quarks and Ginsparg-Wilson valence quarks, to the continuum.Comment: 16 pages LaTe

Periodic orbit effects on conductance peak heights in a chaotic quantum dot

We study the effects of short-time classical dynamics on the distribution of Coulomb blockade peak heights in a chaotic quantum dot. The location of one or both leads relative to the short unstable orbits, as well as relative to the symmetry lines, can have large effects on the moments and on the head and tail of the conductance distribution. We study these effects analytically as a function of the stability exponent of the orbits involved, and also numerically using the stadium billiard as a model. The predicted behavior is robust, depending only on the short-time behavior of the many-body quantum system, and consequently insensitive to moderate-sized perturbations.Comment: 14 pages, including 6 figure

Hadronic Electromagnetic Properties at Finite Lattice Spacing

Electromagnetic properties of the octet mesons as well as the octet and decuplet baryons are augmented in quenched and partially quenched chiral perturbation theory to include O(a) corrections due to lattice discretization. We present the results for the SU(3) flavor group in the isospin limit as well as the results for SU(2) flavor with non-degenerate quarks. These corrections will be useful for extrapolation of lattice calculations using Wilson valence and sea quarks, as well as calculations using Wilson sea quarks and Ginsparg-Wilson valence quarks.Comment: 19 pages, 0 figures, RevTeX

Chiral Dynamics of Low-Energy Kaon-Baryon Interactions with Explicit Resonance

The processes involving low energy $\bar{K}N$ and $Y\pi$ interactions (where $Y= \Sigma$ or $\Lambda$) are studied in the framework of heavy baryon chiral perturbation theory with the $\Lambda$(1405) resonance appearing as an independent field. The leading and next-to-leading terms in the chiral expansion are taken into account. We show that an approach which explicitly includes the $\Lambda$(1405) resonance as an elementary quantum field gives reasonable descriptions of both the threshold branching ratios and the energy dependence of total cross sections.Comment: 16 pages, 6 figure

On neutral pion electroproduction off deuterium

Threshold neutral pion electroproduction on the deuteron is studied in the framework of baryon chiral perturbation theory at next-to-leading order in the chiral expansion. To this order in small momenta, the amplitude is finite and a sum of two- and three-body interactions with no undetermined parameters. We calculate the S-wave multipoles for threshold production and the deuteron S-wave cross section as a function of the photon virtuality. We also discuss the sensitivity to the elementary neutron amplitudes.Comment: 6 pp, revtex, 3 figs, corrected version, to appear in Phys. Rev.

Neutrino-Deuteron Scattering in Effective Field Theory at Next-to-Next-to Leading Order

We study the four channels associated with neutrino-deuteron breakup reactions at next-to-next to leading order in effective field theory. We find that the total cross-section is indeed converging for neutrino energies up to 20 MeV, and thus our calculations can provide constraints on theoretical uncertainties for the Sudbury Neutrino Observatory. We stress the importance of a direct experimental measurement to high precision in at least one channel, in order to fix an axial two-body counterterm.Comment: 32 pages, 14 figures (eps

Two Nucleons on a Lattice

The two-nucleon sector is near an infrared fixed point of QCD and as a result the S-wave scattering lengths are unnaturally large compared to the effective ranges and shape parameters. It is usually assumed that a lattice QCD simulation of the two-nucleon sector will require a lattice that is much larger than the scattering lengths in order to extract quantitative information. In this paper we point out that this does not have to be the case: lattice QCD simulations on much smaller lattices will produce rigorous results for nuclear physics.Comment: 13 pages, 6 figure

Saxion Emission from SN1987A

We study the possibility of emission of the saxion, a superpartner of the axion, from SN1987A. The fact that the observed neutrino pulse from SN1987A is in excellent agreement with the current theory of supernovae places a strong bound on the energy loss into any non-standard model channel, therefore enabling bounds to be placed on the decay constant, f_a, of a light saxion. The low-energy coupling of the saxion, which couples at high energies to the QCD gauge field strength, is expected to be enhanced from QCD scaling, making it interesting to investigate if the saxion could place stronger bounds on f_a than the axion itself. Moreover, since the properties of the saxion are determined by f_a, a constraint on this parameter can be translated into a constraint on the supersymmetry breaking scale. We find that the bound on f_a from saxion emission is comparable with the one derived from axion emission due to a cancellation of leading-order terms in the soft-radiation expansion.Comment: 18 pages, 2 figures; minor changes, typos corrected, version to appear in JHE