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

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

The footprint of E7 in amplitudes of N=8 supergravity

We study the low energy theorems associated with the non-linearly realized continuous E7 symmetry of the on-shell N=8 supergravity. For Nambu-Goldstone bosons we evaluate the one-soft-scalar-bosonemission amplitudes by computing the E7 current matrix element on the one-particle external lines. We use the explicit form of the conserved E7 Noether current and prove that all such matrix elements vanish in the soft momentum limit,assuming the SU(8) symmetry of the S-matrix.This implies that all tree amplitudes vanish in the one-soft-boson limit. We also discuss the implications of unbroken E7 symmetry for higher-order amplitudes.Comment: 18 p., 2 figure

Strongly Interacting W's and Z's and the Existence of a Heavy Fourth Generation of Fermions

By employing the dictum that axiomatic principles are devoid of predictive power, we find that the elastic unitarity constraint, applied to strong W$_L$W$_L$ scattering, does not alter the assumed spectrum of intermediate states. We consider intermediate states involving a heavy Higgs and heavy fermions of a hypothetical fourth generation doublet. In contrast to recent studies, we find no p-wave resonance, and therefore no violation of the S parameter upper bound. We conclude that the elastic unitarity constraint sheds no light on the existence of a heavy fourth generation.Comment: 8 pages including 4 uuencoded, tarred, and compressed postscript figures, CPP-93-0

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

Partially quenched chiral perturbation theory without Φ0\Phi_0

This paper completes the argument that lattice simulations of partially quenched QCD can provide quantitative information about QCD itself, with the aid of partially quenched chiral perturbation theory. A barrier to doing this has been the inclusion of $\Phi_0$, the partially quenched generalization of the $\eta'$, in previous calculations in the partially quenched effective theory. This invalidates the low energy perturbative expansion, gives rise to many new unknown parameters, and makes it impossible to reliably calculate the relation between the partially quenched theory and low energy QCD. We show that it is straightforward and natural to formulate partially quenched chiral perturbation theory without $\Phi_0$, and that the resulting theory contains the effective theory for QCD without the $\eta'$. We also show that previous results, obtained including $\Phi_0$, can be reinterpreted as applying to the theory without $\Phi_0$. We contrast the situation with that in the quenched effective theory, where we explain why it is necessary to include $\Phi_0$. We also compare the derivation of chiral perturbation theory in partially quenched QCD with the standard derivation in unquenched QCD. We find that the former cannot be justified as rigorously as the latter, because of the absence of a physical Hilbert space. Finally, we present an encouraging result: unphysical double poles in certain correlation functions in partially quenched chiral perturbation theory can be shown to be a property of the underlying theory, given only the symmetries and some plausible assumptions.Comment: 45 pages, no figure

Simulations with different lattice Dirac operators for valence and sea quarks

We discuss simulations with different lattice Dirac operators for sea and valence quarks. A goal of such a "mixed" action approach is to probe deeper the chiral regime of QCD by enabling simulations with light valence quarks. This is achieved by using chiral fermions as valence quarks while computationally inexpensive fermions are used in the sea sector. Specifically, we consider Wilson sea quarks and Ginsparg-Wilson valence quarks. The local Symanzik action for this mixed theory is derived to O(a), and the appropriate low energy chiral effective Lagrangian is constructed, including the leading O(a) contributions. Using this Lagrangian one can calculate expressions for physical observables and determine the Gasser-Leutwyler coefficients by fitting them to the lattice data.Comment: 17 pages, 1 ps figure (2 clarification paragraphs added

More on the infrared renormalization group limit cycle in QCD

We present a detailed study of the recently conjectured infrared renormalization group limit cycle in QCD using chiral effective field theory. It was conjectured that small increases in the up and down quark masses can move QCD to the critical trajectory for an infrared limit cycle in the three-nucleon system. At the critical quark masses, the binding energies of the deuteron and its spin-singlet partner are tuned to zero and the triton has infinitely many excited states with an accumulation point at the three-nucleon threshold. We exemplify three parameter sets where this effect occurs at next-to-leading order in the chiral counting. For one of them, we study the structure of the three-nucleon system in detail using both chiral and contact effective field theories. Furthermore, we investigate the matching of the chiral and contact theories in the critical region and calculate the influence of the limit cycle on three-nucleon scattering observables.Comment: 17 pages, 7 figures, discussion improved, results unchanged, version to appear in EPJ

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.

How good is the quenched approximation of QCD?

The quenched approximation for QCD is, at present and in the foreseeable future, unavoidable in lattice calculations with realistic choices of the lattice spacing, volume and quark masses. In this talk, I review an analytic study of the effects of quenching based on chiral perturbation theory. Quenched chiral perturbation theory leads to quantitative insight on the difference between quenched and unquenched QCD, and reveals clearly some of the diseases which are expected to plague quenched QCD. Uses jnl.tex and epsf.tex for figure 3. Figures 1 and 2 not included, sorry. Available as hardcopy on request.Comment: 22 pages, Wash. U. HEP/94-62 (Forgotten set of macros now included, sorry.