146 research outputs found
A one parameter representation for the Isgur-Wise function
We use a lattice QCD heavy-light wavefunction to generate a single
parameter, model independent description of the Isgur-Wise function. Using
recent data we find the zero-recoil slope to be , while
the second derivative turns out to be .Comment: Latex (uses epsf macro), 7 pages of text, 2 postscript figures
included
Sensitivity analysis of reactive ecological dynamics
Author Posting. © Springer, 2008. This is the author's version of the work. It is posted here by permission of Springer for personal use, not for redistribution. The definitive version was published in Bulletin of Mathematical Biology 70 (2008): 1634-1659, doi:10.1007/s11538-008-9312-7.Ecological systems with asymptotically stable equilibria may exhibit significant transient
dynamics following perturbations. In some cases, these transient dynamics include
the possibility of excursions away from the equilibrium before the eventual return; systems
that exhibit such amplification of perturbations are called reactive. Reactivity is
a common property of ecological systems, and the amplification can be large and long-lasting.
The transient response of a reactive ecosystem depends on the parameters of
the underlying model. To investigate this dependence, we develop sensitivity analyses
for indices of transient dynamics (reactivity, the amplification envelope, and the optimal
perturbation) in both continuous- and discrete-time models written in matrix form.
The sensitivity calculations require expressions, some of them new, for the derivatives
of equilibria, eigenvalues, singular values, and singular vectors, obtained using matrix
calculus. Sensitivity analysis provides a quantitative framework for investigating the
mechanisms leading to transient growth. We apply the methodology to a predator-prey
model and a size-structured food web model. The results suggest predator-driven and
prey-driven mechanisms for transient amplification resulting from multispecies interactions.Financial support provided by NSF grant DEB-0343820, NOAA grant NA03-NMF4720491,
the Ocean Life Institute of the Woods Hole Oceanographic Institution, and the Academic
Programs Office of the MIT-WHOI Joint Program in Oceanography
Modelling form factors in HQET
We present a simple and straightforward method for relating the form factors
in HQET, as defined by the covariant trace formalism, to the overlaps of the
rest frame wave functions of the light degrees of freedom. We also point out
several inconsistencies present in recent calculations of the radiative rare
decays, and also show how these can be fixed even within the framework of
the non-relativistic quark model.Comment: Latex, 16 pages of tex
The anomalous threshold, confinement, and an essential singularity in the heavy-light form factor
The analytic behavior of the heavy-light meson form factor is investigated
using several relativistic examples including unconfined, weakly confined, and
strongly confined mesons. It is observed that confinement erases the anomalous
threshold singularity and also induces an essential singularity at the normal
annihilation threshold. In the weak confinement limit, the "would be" anomalous
threshold contribution is identical to that of the real singularity on its
space-like side.Comment: Latex 2.09 with epsf.sty. 24 pages of text and 8 postscript figures.
Postscript version of complete paper will also be available soon at
http://phenom.physics.wisc.edu/pub/preprints/1997/madph-97-983 or at
ftp://phenom.physics.wisc.edu/pub/preprints/1997/madph-97-98
On the bounds for the curvature and higher derivatives of the Isgur-Wise function
We discuss constraints imposed on the zero-recoil curvature and higher
derivatives of the Isgur-Wise function by a general quark model. These
constraints are expressed as bounds for a given slope parameter, and compared
with those based upon analyticity properties of QCD spectral functions. Our
results also indicate that in the analysis of the experimental data for
semileptonic B\rar D^{(*)} decays it may be important to include at least the
third term in the form factor expansion about the zero recoil point.Comment: 14 pages, latex, uses epsf macro, 5 postscript figures include
Semileptonic form factors - a model-independent approach
We demonstrate that the B->D(*) l nu form factors can be accurately predicted
given the slope parameter rho^2 of the Isgur-Wise function. Only weak
assumptions, consistent with lattice results, on the wavefunction for the light
degrees of freedom are required to establish this result. We observe that the
QCD and 1/m_Q corrections can be systematically represented by an effective
Isgur-Wise function of shifted slope. This greatly simplifies the analysis of
semileptonic B decay. We also investigate what the available semileptonic data
can tell us about lattice QCD and Heavy Quark Effective Theory. A rigorous
identity relating the form factor slope difference rho_D^2-rho_A1^2 to a
combination of form factor intercepts is found. The identity provides a means
of checking theoretically evaluated intercepts with experiment.Comment: 18 pages, Revtex, 4 postscript figures, uses epsfig.st
S to P wave form factors in semi-leptonic B decays
We apply HQET to semi-leptonic and meson decays into the observed
charmed wave states. In order to examine the sensitivity of the results to
the choice of a specific model, we perform all calculations using several
different meson models, and find that uncertainty introduced by the choice of a
particular model is about 30\%. Specifically, assuming and
, we obtain branching ratios of and for B\rar D_{1}l\bar{\nu}_{l} and B\rar D_{2}^{*}l\bar{\nu}_{l}
decays, respectively.Comment: Latex (uses epsf macro), 36 pages of text, 11 postscript figures
include
Perturbative QCD Analysis of Meson Decays
Resummation of large QCD radiative corrections, including leading and
next-to-leading logarithms, in pion electromagnetic form factor is reviewed.
Similar formalism is applied to exclusive processes involving heavy mesons, and
leads to Sudakov suppression for the semi-leptonic decay . It is
found that, with the inclusion of Sudakov effects, perturbative QCD analysis of
this decay is possible for the energy fraction of the pion above 0.3. By
combining predictions from the soft pion theorems, we estimate that the upper
limit of the KM matrix element is roughly 0.003.Comment: 26 pages in latex, figures are available for reques
Ecological Invasion, Roughened Fronts, and a Competitor's Extreme Advance: Integrating Stochastic Spatial-Growth Models
Both community ecology and conservation biology seek further understanding of
factors governing the advance of an invasive species. We model biological
invasion as an individual-based, stochastic process on a two-dimensional
landscape. An ecologically superior invader and a resident species compete for
space preemptively. Our general model includes the basic contact process and a
variant of the Eden model as special cases. We employ the concept of a
"roughened" front to quantify effects of discreteness and stochasticity on
invasion; we emphasize the probability distribution of the front-runner's
relative position. That is, we analyze the location of the most advanced
invader as the extreme deviation about the front's mean position. We find that
a class of models with different assumptions about neighborhood interactions
exhibit universal characteristics. That is, key features of the invasion
dynamics span a class of models, independently of locally detailed demographic
rules. Our results integrate theories of invasive spatial growth and generate
novel hypotheses linking habitat or landscape size (length of the invading
front) to invasion velocity, and to the relative position of the most advanced
invader.Comment: The original publication is available at
www.springerlink.com/content/8528v8563r7u2742
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