2,832 research outputs found
CORE and the Haldane Conjecture
The Contractor Renormalization group formalism (CORE) is a real-space
renormalization group method which is the Hamiltonian analogue of the Wilson
exact renormalization group equations. In an earlier paper\cite{QGAF} I showed
that the Contractor Renormalization group (CORE) method could be used to map a
theory of free quarks, and quarks interacting with gluons, into a generalized
frustrated Heisenberg antiferromagnet (HAF) and proposed using CORE methods to
study these theories. Since generalizations of HAF's exhibit all sorts of
subtle behavior which, from a continuum point of view, are related to
topological properties of the theory, it is important to know that CORE can be
used to extract this physics. In this paper I show that despite the folklore
which asserts that all real-space renormalization group schemes are necessarily
inaccurate, simple Contractor Renormalization group (CORE) computations can
give highly accurate results even if one only keeps a small number of states
per block and a few terms in the cluster expansion. In addition I argue that
even very simple CORE computations give a much better qualitative understanding
of the physics than naive renormalization group methods. In particular I show
that the simplest CORE computation yields a first principles understanding of
how the famous Haldane conjecture works for the case of the spin-1/2 and spin-1
HAF.Comment: 36 pages, 4 figures, 5 tables, latex; extensive additions to conten
Status of Spin Physics - Experimental Summary
The current status of spin physics experiments, based on talks presented at
the Third Circum-Pan-Pacific Symposium on High Energy Spin Physics held in
Beijing, 2001, is summarized in this article. Highlights of recent experimental
results at SLAC, JLab, and DESY, as well as future plans at these facilities
and at RHIC-spin are discussed.Comment: 18 pages, 7 figures, Invited talk presented at the Third
Circum-Pan-Pacific Symposium on High Energy Spin Physics held in Beijing,
October, 200
Type Ia Supernovae, Evolution, and the Cosmological Constant
We explore the possible role of evolution in the analysis of data on SNe Ia
at cosmological distances. First, using a variety of simple sleuthing
techniques, we find evidence that the properties of the high and low redshift
SNe Ia observed so far differ from one another. Next, we examine the effects of
including simple phenomenological models for evolution in the analysis. The
result is that cosmological models and evolution are highly degenerate with one
another, so that the incorporation of even very simple models for evolution
makes it virtually impossible to pin down the values of and
, the density parameters for nonrelativistic matter and for the
cosmological constant, respectively. Moreover, we show that if SNe Ia evolve
with time, but evolution is neglected in analyzing data, then, given enough SNe
Ia, the analysis hones in on values of and which
are incorrect. Using Bayesian methods, we show that the probability that the
cosmological constant is nonzero (rather than zero) is unchanged by the SNe Ia
data when one accounts for the possibility of evolution, provided that we do
not discriminate among open, closed and flat cosmologies a priori. The case for
nonzero cosmological constant is stronger if the Universe is presumed to be
flat, but still depends sensitively on the degree to which the peak
luminosities of SNe Ia evolve as a function of redshift. The estimated value of
, however, is only negligibly affected by accounting for possible
evolution.Comment: 45 pages, 15 figures; accepted for publication in The Astrophysical
Journal. Minor revisions and clarifications made including addition of recent
reference
Extrapolation of K to \pi\pi decay amplitude
We examine the uncertainties involved in the off-mass-shell extrapolation of
the decay amplitude with emphasis on those aspects that
have so far been overlooked or ignored. Among them are initial-state
interactions, choice of the extrapolated kaon field, and the relation between
the asymptotic behavior and the zeros of the decay amplitude. In the inelastic
region the phase of the decay amplitude cannot be determined by strong
interaction alone and even its asymptotic value cannot be deduced from
experiment. More a fundamental issue is intrinsic nonuniqueness of off-shell
values of hadronic matrix elements in general. Though we are hampered with
complexity of intermediate-energy meson interactions, we attempt to obtain a
quantitative idea of the uncertainties due to the inelastic region and find
that they can be much larger than more optimistic views portray.Comment: 16 pages with 5 eps figures in REVTE
Threshold corrections to rapidity distributions of Z and W^\pm bosons beyond N^2 LO at hadron colliders
Threshold enhanced perturbative QCD corrections to rapidity distributions of
and bosons at hadron colliders are presented using the Sudakov
resummed cross sections at NLO level. We have used renormalisation group
invariance and the mass factorisation theorem that these hard scattering cross
sections satisfy to construct the QCD amplitudes. We show that these higher
order threshold QCD corrections stabilise the theoretical predictions for
vector boson production at the LHC under variations of both renormalisation and
factorisation scales.Comment: 17 pages, 8 eps figures. This paper is dedicated to the memory of
W.L.G.A.M. van Neerve
The Nucleon Spin Polarizability at Order ) in Chiral Perturbation Theory
We calculate the forward spin-dependent photon-nucleon Compton amplitude as a
function of photon energy at the next-to-leading () order in
chiral perturbation theory, from which we extract the contribution to nucleon
spin polarizability. The result shows a large correction to the leading order
contribution.Comment: 7 pages, latex, 2 figures included as .eps file
A Derivative of the Gerasimov-Drell-Hearn Sum Rule
We derive a sum rule which establishes a linear relation between a particle's
anomalous magnetic moment and a quantity connected to the photoabsorption
cross-section. This quantity cannot be measured directly. However, it can be
computed within a given theory. As an example, we demonstrate validity of the
sum rule in QED at tree level--the renowned Schwinger's correction to the
anomalous magnetic moment is readily reproduced. In the case of the strong
interactions, we also consider the calculation of the nucleon magnetic moment
within chiral theories.Comment: 11 pages, 5 figures, minor corrections, published versio
Scaling laws in hadronic processes and string theory
We propose a possible scheme for getting the known QCD scaling laws within
string theory. In particular, we consider amplitudes for exclusive scattering
of hadrons at large momentum transfer, hadronic form factors and distribution
functions.Comment: 13 pages, 2 figures, a comment and a reference added, a final version
to appear in Physical Review
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