3,580 research outputs found
Baryons in QCD_{AS} at Large N_c: A Roundabout Approach
QCD_{AS}, a variant of large N_c QCD in which quarks transform under the
color two-index antisymmetric representation, reduces to standard QCD at N_c =
3 and provides an alternative to the usual large N_c extrapolation that uses
fundamental representation quarks. Previous strong plausibility arguments
assert that the QCD_{AS} baryon mass scales as N_c^2; however, the complicated
combinatoric problem associated with quarks carrying two color indices impeded
a complete demonstration. We develop a diagrammatic technique to solve this
problem. The key ingredient is the introduction of an effective multi-gluon
vertex: a "traffic circle" or "roundabout" diagram. We show that arbitrarily
complicated diagrams can be reduced to simple ones with the same leading N_c
scaling using this device, and that the leading contribution to baryon mass
does, in fact, scale as N_c^2.Comment: 9 pages, 9 pdf figures, ReVTeX with pdflate
Pion-Nucleon Scattering Relations at Next-to-Leading Order in 1/N_c
We obtain relations between partial-wave amplitudes for pi-N-->pi-N and
pi-N-->pi-Delta directly from large N_c QCD. While linear relations among
certain amplitudes holding at leading order (LO) in 1/N_c were derived in the
context of chiral soliton models two decades ago, the present work employs a
fully model-independent framework based on consistency with the large N_c
expansion. At LO we reproduce the soliton model results; however, this method
allows for systematic corrections. At next-to-leading order (NLO), most
relations require additional unknown functions beyond those appearing at
leading order (LO) and thus have little additional predictive power. However,
three NLO relations for the pi-N-->pi-Delta reaction are independent of unknown
functions and make predictions accurate at this order. The amplitudes relevant
to two of these relations were previously extracted from experiment. These
relations describe experiment dramatically better than their LO counterparts.Comment: 8 pages, 2 figures; references adde
Statistical mechanics of Floquet systems: the pervasive problem of near degeneracies
The statistical mechanics of periodically driven ("Floquet") systems in
contact with a heat bath exhibits some radical differences from the traditional
statistical mechanics of undriven systems. In Floquet systems all quasienergies
can be placed in a finite frequency interval, and the number of near
degeneracies in this interval grows without limit as the dimension N of the
Hilbert space increases. This leads to pathologies, including drastic changes
in the Floquet states, as N increases. In earlier work these difficulties were
put aside by fixing N, while taking the coupling to the bath to be smaller than
any quasienergy difference. This led to a simple explicit theory for the
reduced density matrix, but with some major differences from the usual time
independent statistical mechanics. We show that, for weak but finite coupling
between system and heat bath, the accuracy of a calculation within the
truncated Hilbert space spanned by the N lowest energy eigenstates of the
undriven system is limited, as N increases indefinitely, only by the usual
neglect of bath memory effects within the Born and Markov approximations. As we
seek higher accuracy by increasing N, we inevitably encounter quasienergy
differences smaller than the system-bath coupling. We therefore derive the
steady state reduced density matrix without restriction on the size of
quasienergy splittings. In general, it is no longer diagonal in the Floquet
states. We analyze, in particular, the behavior near a weakly avoided crossing,
where quasienergy near degeneracies routinely appear. The explicit form of our
results for the denisty matrix gives a consistent prescription for the
statistical mechanics for many periodically driven systems with N infinite, in
spite of the Floquet state pathologies.Comment: 31 pages, 3 figure
Non-perturbative regularization and renormalization: simple examples from non-relativistic quantum mechanics
We examine several zero-range potentials in non-relativistic quantum
mechanics. The study of such potentials requires regularization and
renormalization. We contrast physical results obtained using dimensional
regularization and cutoff schemes and show explicitly that in certain cases
dimensional regularization fails to reproduce the results obtained using cutoff
regularization. First we consider a delta-function potential in arbitrary space
dimensions. Using cutoff regularization we show that for the
renormalized scattering amplitude is trivial. In contrast, dimensional
regularization can yield a nontrivial scattering amplitude for odd dimensions
greater than or equal to five. We also consider a potential consisting of a
delta function plus the derivative-squared of a delta function in three
dimensions. We show that the renormalized scattering amplitudes obtained using
the two regularization schemes are different. Moreover we find that in the
cutoff-regulated calculation the effective range is necessarily negative in the
limit that the cutoff is taken to infinity. In contrast, in dimensional
regularization the effective range is unconstrained. We discuss how these
discrepancies arise from the dimensional regularization prescription that all
power-law divergences vanish. We argue that these results demonstrate that
dimensional regularization can fail in a non-perturbative setting.Comment: 19 pages, LaTeX, uses epsf.te
Nucleon-Nucleon Scattering under Spin-Isospin Reversal in Large-N_c QCD
The spin-flavor structure of certain nucleon-nucleon scattering observables
derived from the large N_c limit of QCD in the kinematical regime where
time-dependent mean-field theory is valid is discussed. In previous work, this
regime was taken to be where the external momentum was of order N_c which
precluded the study of differential cross sections in elastic scattering. Here
it is shown that the regime extends down to order N_c^{1/2} which includes the
higher end of the elastic regime. The prediction is that in the large N_c
limit, observables describable via mean-field theory are unchanged when the
spin and isospin of either nucleon are both flipped. This prediction is tested
for proton-proton and neutron-proton elastic scattering data and found to fail
badly. We argue that this failure can be traced to a lack of a clear separation
of scales between momentum of order N_c^{1/2} and N_c^1 when N_c is as small as
three. The situation is compounded by an anomalously low particle production
threshold due to approximate chiral symmetry.Comment: 5 pages, 1 figur
Is strong CP invariance due to a massless up quark?
A standing mystery in the Standard Model is the unnatural smallness of the
strong CP violating phase. A massless up quark has long been proposed as one
potential solution. A lattice calculation of the constants of the chiral
Lagrangian essential for the determination of the up quark mass, 2 alpha_8 -
alpha_5, is presented. We find 2 alpha_8 - alpha_5 = 0.29 +/- 0.18, which
corresponds to m_u / m_d = 0.410 +/- 0.036. This is the first such calculation
using a physical number of dynamical light quarks, N_f = 3.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Lett., corrected small
normalization error in f_pi (conclusions were unaffected), improved lattice
spacing analysis, improved finite volume analysi
Gasser-Leutwyler coefficients: A progress report
Last year, we reported our first results on the determination of
Gasser-Leutwyler coefficients using partially quenched lattice QCD with three
flavors of dynamical staggered quarks. We give an update on our progress in
determining two of these coefficients, including an exhaustive effort to
estimate all sources of systematic error. At this conference, we have heard
about algorithmic techniques to reduce staggered flavor symmetry breaking and a
method to incorporate staggered flavor breaking into the partially quenched
chiral Lagrangian. We comment on our plans to integrate these developments into
our ongoing program.Comment: 3 pages, 2 figures, Lattice2002(spectrum
Chiral Corrections to Lattice Calculations of Charge Radii
Logarithmic divergences in pion and proton charge radii associated with
chiral loops are investigated to assess systematic uncertainties in current
lattice determinations of charge radii. The chiral corrections offer a possible
solution to the long standing problem of why present lattice calculations yield
proton and pion radii which are similar in size.Comment: PostScript file only. Ten pages. Figures included. U. of MD Preprint
#92-19
Semi-Classical Description of Antiproton Capture on Atomic Helium
A semi-classical, many-body atomic model incorporating a momentum-dependent
Heisenberg core to stabilize atomic electrons is used to study antiproton
capture on Helium. Details of the antiproton collisions leading to eventual
capture are presented, including the energy and angular momentum states of
incident antiprotons which result in capture via single or double electron
ionization, i.e. into [He or He], and the
distribution of energy and angular momentum states following the Auger cascade.
These final states are discussed in light of recently reported, anomalously
long-lived antiproton states observed in liquid He.Comment: 15 pages, 9 figures may be obtained from authors, Revte
The economic implications of HLA matching in cadaveric renal transplantation.
Abstract
Background: The potential economic effects of the allocation of cadaveric kidneys on the basis of tissue-matching criteria are controversial. We analyzed the economic costs associated with the transplantation of cadaveric kidneys with various numbers of HLA mismatches and examined the potential economic benefits of a local, as compared with a national, system designed to minimize HLA mismatches between donor and recipient in first cadaveric renal transplantations. Methods: All data were supplied by the U.S. Renal Data System. Data on all payments made by Medicare from 1991 through 1997 for the care of recipients of a first cadaveric renal transplant were analyzed according to the number of HLA-A, B, and DR mismatches between donor and recipient and the duration of cold ischemia before transplantation. Results: Average Medicare payments for renal-transplant recipients in the three years after transplantation increased from 80,807 for kidneys with six HLA mismatches between donor and recipient, a difference of 34 percent (P\u3c0.001). By three years after transplantation, the average Medicare payments were 74,997 for those with more than 36 hours (P\u3c0.001). In simulations, the assignment of cadaveric kidneys to recipients by a method that minimized HLA mismatching within a local geographic area (i.e., within one of the approximately 50 organ-procurement organizations, which cover widely varying geographic areas) produced the largest cost savings ($4,290 per patient over a period of three years) and the largest improvements in the graft-survival rate (2.3 percent) when the potential costs of longer cold-ischemia time were considered. Conclusions: Transplantation of better-matched cadaveric kidneys could have substantial economic advantages. In our simulations, HLA-based allocation of kidneys at the local level produced the largest estimated cost savings, when the duration of cold ischemia was taken into account. No additional savings were estimated to result from a national allocation program, because the additional costs of longer cold-ischemia time were greater than the advantages of optimizing HLA matching
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