608 research outputs found
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 and interactions (where
or ) are studied in the framework of heavy baryon chiral
perturbation theory with the (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 (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
WW 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
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 , the partially quenched generalization of
the , 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 , and that the resulting theory contains
the effective theory for QCD without the . We also show that previous
results, obtained including , can be reinterpreted as applying to the
theory without . We contrast the situation with that in the quenched
effective theory, where we explain why it is necessary to include .
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.
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