257 research outputs found
Testing an approximation to large-Nc QCD with a toy model
We consider a simple model of large-Nc QCD defined by a spectrum consisting
of an infinite set of equally spaced zero-width vector resonances. This model
is an excellent theoretical laboratory for investigating certain approximation
schemes which have been used recently in calculations of hadronic parameters,
such as the Minimal Hadronic Approximation. We also comment on some of the
questions concerning issues of local duality versus global duality and
finite-energy sum rules.Comment: LateX file; 16 pages, 7 figure
Higher Order Evaluation of the Critical Temperature for Interacting Homogeneous Dilute Bose Gases
We use the nonperturbative linear \delta expansion method to evaluate
analytically the coefficients c_1 and c_2^{\prime \prime} which appear in the
expansion for the transition temperature for a dilute, homogeneous, three
dimensional Bose gas given by T_c= T_0 \{1 + c_1 a n^{1/3} + [ c_2^{\prime}
\ln(a n^{1/3}) +c_2^{\prime \prime} ] a^2 n^{2/3} + {\cal O} (a^3 n)\}, where
T_0 is the result for an ideal gas, a is the s-wave scattering length and n is
the number density. In a previous work the same method has been used to
evaluate c_1 to order-\delta^2 with the result c_1= 3.06. Here, we push the
calculation to the next two orders obtaining c_1=2.45 at order-\delta^3 and
c_1=1.48 at order-\delta^4. Analysing the topology of the graphs involved we
discuss how our results relate to other nonperturbative analytical methods such
as the self-consistent resummation and the 1/N approximations. At the same
orders we obtain c_2^{\prime\prime}=101.4, c_2^{\prime \prime}=98.2 and
c_2^{\prime \prime}=82.9. Our analytical results seem to support the recent
Monte Carlo estimates c_1=1.32 \pm 0.02 and c_2^{\prime \prime}= 75.7 \pm 0.4.Comment: 29 pages, 3 eps figures. Minor changes, one reference added. Version
in press Physical Review A (2002
Charge and mass effects on the evaporation of higher-dimensional rotating black holes
To study the dynamics of discharge of a brane black hole in TeV gravity
scenarios, we obtain the approximate electromagnetic field due to the charged
black hole, by solving Maxwell's equations perturbatively on the brane. In
addition, arguments are given for brane metric corrections due to backreaction.
We couple brane scalar and brane fermion fields with non-zero mass and charge
to the background, and study the Hawking radiation process using well known low
energy approximations as well as a WKB approximation in the high energy limit.
We argue that contrary to common claims, the initial evaporation is not
dominated by fast Schwinger discharge.Comment: Published version. Minor typos corrected. 29 pages, 5 figure
Asymptotically Improved Convergence of Optimized Perturbation Theory in the Bose-Einstein Condensation Problem
We investigate the convergence properties of optimized perturbation theory,
or linear expansion (LDE), within the context of finite temperature
phase transitions. Our results prove the reliability of these methods, recently
employed in the determination of the critical temperature T_c for a system of
weakly interacting homogeneous dilute Bose gas. We carry out the explicit LDE
optimized calculations and also the infrared analysis of the relevant
quantities involved in the determination of in the large-N limit, when
the relevant effective static action describing the system is extended to O(N)
symmetry. Then, using an efficient resummation method, we show how the LDE can
exactly reproduce the known large-N result for already at the first
non-trivial order. Next, we consider the finite N=2 case where, using similar
resummation techniques, we improve the analytical results for the
nonperturbative terms involved in the expression for the critical temperature
allowing comparison with recent Monte Carlo estimates of them. To illustrate
the method we have considered a simple geometric series showing how the
procedure as a whole works consistently in a general case.Comment: 38 pages, 3 eps figures, Revtex4. Final version in press Phys. Rev.
K -> pi pi and a light scalar meson
We explore the Delta-I= 1/2 rule and epsilon'/epsilon in K -> pi pi
transitions using a Dyson-Schwinger equation model. Exploiting the feature that
QCD penguin operators direct K^0_S transitions through 0^{++} intermediate
states, we find an explanation of the enhancement of I=0 K -> pi pi transitions
in the contribution of a light sigma-meson. This mechanism also affects
epsilon'/epsilon.Comment: 7 pages, REVTE
Survey of nucleon electromagnetic form factors
A dressed-quark core contribution to nucleon electromagnetic form factors is
calculated. It is defined by the solution of a Poincare' covariant Faddeev
equation in which dressed-quarks provide the elementary degree of freedom and
correlations between them are expressed via diquarks. The nucleon-photon vertex
involves a single parameter; i.e., a diquark charge radius. It is argued to be
commensurate with the pion's charge radius. A comprehensive analysis and
explanation of the form factors is built upon this foundation. A particular
feature of the study is a separation of form factor contributions into those
from different diagram types and correlation sectors, and subsequently a
flavour separation for each of these. Amongst the extensive body of results
that one could highlight are: r_1^{n,u}>r_1^{n,d}, owing to the presence of
axial-vector quark-quark correlations; and for both the neutron and proton the
ratio of Sachs electric and magnetic form factors possesses a zero.Comment: 43 pages, 17 figures, 12 tables, 5 appendice
Mesons as qbar-q Bound States from Euclidean 2-Point Correlators in the Bethe-Salpeter Approach
We investigate the 2-point correlation function for the vector current. The
gluons provide dressings for both the quark self energy as well as the vector
vertex function, which are described consistently by the rainbow
Dyson-Schwinger equation and the inhomogeneous ladder Bethe-Salpeter equation.
The form of the gluon propagator at low momenta is modeled by a 2-parameter
ansatz fitting the weak pion decay constant. The quarks are confined in the
sense that the quark propagator does not have a pole at timelike momenta. We
determine the ground state mass in the vector channel from the Euclidean time
Fourier transform of the correlator, which has an exponential falloff at large
times. The ground state mass lies around 590 MeV and is almost independent of
the model form for the gluon propagator. This method allows us to stay in
Euclidean space and to avoid analytic continuation of the quark or gluon
propagators into the timelike region.Comment: 21 pages (REVTEX), 8 Postscript figure
Self-Similar Factor Approximants
The problem of reconstructing functions from their asymptotic expansions in
powers of a small variable is addressed by deriving a novel type of
approximants. The derivation is based on the self-similar approximation theory,
which presents the passage from one approximant to another as the motion
realized by a dynamical system with the property of group self-similarity. The
derived approximants, because of their form, are named the self-similar factor
approximants. These complement the obtained earlier self-similar exponential
approximants and self-similar root approximants. The specific feature of the
self-similar factor approximants is that their control functions, providing
convergence of the computational algorithm, are completely defined from the
accuracy-through-order conditions. These approximants contain the Pade
approximants as a particular case, and in some limit they can be reduced to the
self-similar exponential approximants previously introduced by two of us. It is
proved that the self-similar factor approximants are able to reproduce exactly
a wide class of functions which include a variety of transcendental functions.
For other functions, not pertaining to this exactly reproducible class, the
factor approximants provide very accurate approximations, whose accuracy
surpasses significantly that of the most accurate Pade approximants. This is
illustrated by a number of examples showing the generality and accuracy of the
factor approximants even when conventional techniques meet serious
difficulties.Comment: 22 pages + 11 ps figure
Masses of ground and excited-state hadrons
We present the first Dyson-Schwinger equation calculation of the light hadron
spectrum that simultaneously correlates the masses of meson and baryon ground-
and excited-states within a single framework. At the core of our analysis is a
symmetry-preserving treatment of a vector-vector contact interaction. In
comparison with relevant quantities the
root-mean-square-relative-error/degree-of freedom is 13%. Notable amongst our
results is agreement between the computed baryon masses and the bare masses
employed in modern dynamical coupled-channels models of pion-nucleon reactions.
Our analysis provides insight into numerous aspects of baryon structure; e.g.,
relationships between the nucleon and Delta masses and those of the
dressed-quark and diquark correlations they contain.Comment: 25 pages, 7 figures, 4 table
Mass Spectra of Supersymmetric Yang-Mills Theories in 1+1 Dimensions
Physical mass spectra of supersymmetric Yang-Mills theories in 1+1 dimensions
are evaluated in the light-cone gauge with a compact spatial dimension. The
supercharges are constructed and the infrared regularization is unambiguously
prescribed for supercharges, instead of the light-cone Hamiltonian. This
provides a manifestly supersymmetric infrared regularization for the
discretized light-cone approach. By an exact diagonalization of the supercharge
matrix between up to several hundred color singlet bound states, we find a
rapidly increasing density of states as mass increases.Comment: LaTeX file, 32 page, 7 eps figure
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