1,013 research outputs found
Precise numerical results for limit cycles in the quantum three-body problem
The study of the three-body problem with short-range attractive two-body
forces has a rich history going back to the 1930's. Recent applications of
effective field theory methods to atomic and nuclear physics have produced a
much improved understanding of this problem, and we elucidate some of the
issues using renormalization group ideas applied to precise nonperturbative
calculations. These calculations provide 11-12 digits of precision for the
binding energies in the infinite cutoff limit. The method starts with this
limit as an approximation to an effective theory and allows cutoff dependence
to be systematically computed as an expansion in powers of inverse cutoffs and
logarithms of the cutoff. Renormalization of three-body bound states requires a
short range three-body interaction, with a coupling that is governed by a
precisely mapped limit cycle of the renormalization group. Additional
three-body irrelevant interactions must be determined to control subleading
dependence on the cutoff and this control is essential for an effective field
theory since the continuum limit is not likely to match physical systems ({\it
e.g.}, few-nucleon bound and scattering states at low energy). Leading order
calculations precise to 11-12 digits allow clear identification of subleading
corrections, but these corrections have not been computed.Comment: 37 pages, 8 figures, LaTeX, uses graphic
Perturbative Effective Field Theory at Finite Density
An accurate description of nuclear matter starting from free-space nuclear
forces has been an elusive goal. The complexity of the system makes
approximations inevitable, so the challenge is to find a consistent truncation
scheme with controlled errors. Nonperturbative effective field theories could
be well suited for the task. Perturbative matching in a model calculation is
used to explore some of the issues encountered in extending effective field
theory techniques to many-body calculations.Comment: 21 pages, 5 figure
Middle pleistocene glaciation in Patagonia dated by cosmogenic-nuclide measurements on outwash gravels
The well-preserved glacial record in Argentine Patagonia offers a ~ 1 Ma archive of terrestrial climate extremes in southern South America. These glacial deposits remain largely undated beyond the range of radiocarbon dating at ca. 40 ka. Dating old glacial deposits (> several 105 a) by cosmogenic surface exposure methods is problematic because of the uncertainty in moraine degradation and boulder erosion rates. Here, we show that cobbles on outwash terraces can reliably date âoldâ glacial deposits in the Lago PueyrredĂłn valley, 47.5° S, Argentina. Favorable environmental conditions (e.g., aridity and strong winds) have enabled continuous surface exposure of cobbles and preservation of outwash terraces. The data demonstrate that nuclide inheritance is negligible and we therefore use the oldest surface cobbles to date the deposit. 10Be concentrations in outwash cobbles reveal a major glacial advance at ca. 260 ka, concurrent with Marine Isotope Stage 8 (MIS 8) and dust peaks in Antarctic ice cores. A 10Be concentration depth-profile in the outwash terrace supports the age and suggests a low terrace erosion rate of ca. 0.5 mm kaâ 1. We compare these data to exposure ages obtained from associated moraines and find that surface boulders underestimate the age of the glaciation by ~ 100 ka; thus the oldest boulders in this area do not date closely moraine deposition. The 10Be concentration in moraine cobbles help to constrain moraine degradation rates. These data together with constraints from measured 26Al/10Be ratios suggest that all moraine boulders were likely exhumed after original deposition. We determine the local Last Glacial Maximum (LGM) occurred at ~ 27â25 ka, consistent with the maximum LGM in other parts of Patagonia
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
Decoupling heavy particles simultaneously
The renormalization group is extended to cases where several heavy particles
are decoupled at the same time. This involves large logarithms which are
scale-invariant and so cannot be eliminated by a change of renormalization
scheme. A set of scale-invariant running couplings, one for each heavy
particle, is constructed without reference to intermediate thresholds. The
entire heavy-quark correction to the axial charge of the weak neutral current
is derived to next-to-leading order, and checked in leading order by evaluating
diagrams explicitly. The mechanism for cancelling contributions from the top
and bottom quarks in the equal-mass limit is surprisingly non-trivial.Comment: 6 pages, 4 figures. Talk presented at the "QCD Down Under" Workshop,
Barossa Valley and Adelaide, Australia, 10-19 March 2004, with ref 8 now
linked to hep-ph/050727
Running couplings for the simultaneous decoupling of heavy quarks
Scale-invariant running couplings are constructed for several quarks being
decoupled together, without reference to intermediate thresholds.
Large-momentum scales can also be included. The result is a multi-scale
generalization of the renormalization group applicable to any order.
Inconsistencies in the usual decoupling procedure with a single running
coupling can then be avoided, e.g. when cancelling anomalous corrections from
t,b quarks to the axial charge of the proton.Comment: 12 pages, 1 figure, version to appear in PLB. Pages 8-11 and Fig. 1
are new, with consequent changes to the abstract, page 2, and the references.
We show that our multi-scale renormalization group is needed to achieve
anomaly cancellation in t,b decoupling from the weak neutral current, and
extend it to include large moment
Relativistic Point-Coupling Models as Effective Theories of Nuclei
Recent studies have shown that concepts of effective field theory such as
naturalness can be profitably applied to relativistic mean-field models of
nuclei. Here the analysis by Friar, Madland, and Lynn of naturalness in a
relativistic point-coupling model is extended. Fits to experimental nuclear
data support naive dimensional analysis as a useful principle and imply a
mean-field expansion analogous to that found for mean-field meson models.Comment: 26 pages, REVTeX 3.0 with epsf.sty, plus 5 figure
Coupled-channel effective field theory and proton-Li scattering
We apply the renormalisation group (RG) to analyse scattering by short-range
forces in systems with coupled channels. For two S-wave channels, we find three
fixed points, corresponding to systems with zero, one or two bound or virtual
states at threshold. We use the RG to determine the power countings for the
resulting effective field theories. In the case of a single low-energy state,
the resulting theory takes the form of an effective-range expansion in the
strongly interacting channel. We also extend the analysis to include the
effects of the Coulomb interaction between charged particles. The approach is
then applied to the coupled Li and Be channels which couple to
a state of Be very close to the Be threshold. At
next-to-leading order, we are able to get a good description of the Li
phase shift and the Be(n,p)Li cross section using four parameters.
Fits at one order higher are similarly good but the available data are not
sufficient to determine all five parameters uniquely.Comment: 22 pages, 2 figures, RevTeX4, typos corrected, accepted for
publication in European Physical Journal
Effective Field Theory for Dilute Fermions with Pairing
Effective field theory (EFT) methods for a uniform system of fermions with
short-range, natural interactions are extended to include pairing correlations,
as part of a program to develop a systematic Kohn-Sham density functional
theory (DFT) for medium and heavy nuclei. An effective action formalism for
local composite operators leads to a free-energy functional that includes
pairing by applying an inversion method order by order in the EFT expansion. A
consistent renormalization scheme is demonstrated for the uniform system
through next-to-leading order, which includes induced-interaction corrections
to pairing.Comment: 31 pages, 10 figures, affiliation updated, paper unchange
The Strong CP Problem and Axions
I describe how the QCD vacuum structure, necessary to resolve the
problem, predicts the presence of a P, T and CP violating term proportional to
the vacuum angle . To agree with experimental bounds, however,
this parameter must be very small ). After briefly
discussing some possible other solutions to this, so-called, strong CP problem,
I concentrate on the chiral solution proposed by Peccei and Quinn which has
associated with it a light pseudoscalar particle, the axion. I discuss in
detail the properties and dynamics of axions, focusing particularly on
invisible axion models where axions are very light, very weakly coupled and
very long-lived. Astrophysical and cosmological bounds on invisible axions are
also briefly touched upon.Comment: 14 pages, to appear in the Lecture Notes in Physics volume on Axions,
(Springer Verlag
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