2,287 research outputs found
Analytic structure in the coupling constant plane in perturbative QCD
We investigate the analytic structure of the Borel-summed perturbative QCD
amplitudes in the complex plane of the coupling constant. Using the method of
inverse Mellin transform, we show that the prescription dependent Borel-Laplace
integral can be cast, under some conditions, into the form of a dispersion
relation in the a-plane. We also discuss some recent works relating resummation
prescriptions, renormalons and nonperturbative effects, and show that a method
proposed recently for obtaining QCD nonperturbative condensates from
perturbation theory is based on special assumptions about the analytic
structure in the coupling plane that are not valid in QCD.Comment: 14 pages, revtex4, 1 eps-figur
CMB temperature anisotropy at large scales induced by a causal primordial magnetic field
We present an analytical derivation of the Sachs Wolfe effect sourced by a
primordial magnetic field. In order to consistently specify the initial
conditions, we assume that the magnetic field is generated by a causal process,
namely a first order phase transition in the early universe. As for the
topological defects case, we apply the general relativistic junction conditions
to match the perturbation variables before and after the phase transition which
generates the magnetic field, in such a way that the total energy momentum
tensor is conserved across the transition and Einstein's equations are
satisfied. We further solve the evolution equations for the metric and fluid
perturbations at large scales analytically including neutrinos, and derive the
magnetic Sachs Wolfe effect. We find that the relevant contribution to the
magnetic Sachs Wolfe effect comes from the metric perturbations at
next-to-leading order in the large scale limit. The leading order term is in
fact strongly suppressed due to the presence of free-streaming neutrinos. We
derive the neutrino compensation effect dynamically and confirm that the
magnetic Sachs Wolfe spectrum from a causal magnetic field behaves as
l(l+1)C_l^B \propto l^2 as found in the latest numerical analyses.Comment: 31 pages, 2 figures, minor changes, matches published versio
Convergence of the expansion of the Laplace-Borel integral in perturbative QCD improved by conformal mapping
The optimal conformal mapping of the Borel plane was recently used to
accelerate the convergence of the perturbation expansions in QCD. In this work
we discuss the relevance of the method for the calculation of the Laplace-Borel
integral expressing formally the QCD Green functions. We define an optimal
expansion of the Laplace-Borel integral in the principal value prescription and
establish conditions under which the expansion is convergent.Comment: 10 pages, no figure
from decays: contour-improved versus fixed-order summation in a new QCD perturbation expansion
We consider the determination of from hadronic decays, by
investigating the contour-improved (CI) and the fixed-order (FO)
renormalization group summations in the frame of a new perturbation expansion
of QCD, which incorporates in a systematic way the available information about
the divergent character of the series. The new expansion functions, which
replace the powers of the coupling, are defined by the analytic continuation in
the Borel complex plane, achieved through an optimal conformal mapping. Using a
physical model recently discussed by Beneke and Jamin, we show that the new
CIPT approaches the true results with great precision when the perturbative
order is increased, while the new FOPT gives a less accurate description in the
regions where the imaginary logarithms present in the expansion of the running
coupling are large. With the new expansions, the discrepancy of 0.024 in
between the standard CI and FO summations is reduced to
only 0.009. From the new CIPT we predict , which practically coincides with the result of the
standard FOPT, but has a more solid theoretical basis
Theory of unitarity bounds and low energy form factors
We present a general formalism for deriving bounds on the shape parameters of
the weak and electromagnetic form factors using as input correlators calculated
from perturbative QCD, and exploiting analyticity and unitarity. The values
resulting from the symmetries of QCD at low energies or from lattice
calculations at special points inside the analyticity domain can beincluded in
an exact way. We write down the general solution of the corresponding Meiman
problem for an arbitrary number of interior constraints and the integral
equations that allow one to include the phase of the form factor along a part
of the unitarity cut. A formalism that includes the phase and some information
on the modulus along a part of the cut is also given. For illustration we
present constraints on the slope and curvature of the K_l3 scalar form factor
and discuss our findings in some detail. The techniques are useful for checking
the consistency of various inputs and for controlling the parameterizations of
the form factors entering precision predictions in flavor physics.Comment: 11 pages latex using EPJ style files, 5 figures; v2 is version
accepted by EPJA in Tools section; sentences and figures improve
Gravitational waves from stochastic relativistic sources: primordial turbulence and magnetic fields
The power spectrum of a homogeneous and isotropic stochastic variable,
characterized by a finite correlation length, does in general not vanish on
scales larger than the correlation scale. If the variable is a divergence free
vector field, we demonstrate that its power spectrum is blue on large scales.
Accounting for this fact, we compute the gravitational waves induced by an
incompressible turbulent fluid and by a causal magnetic field present in the
early universe. The gravitational wave power spectra show common features: they
are both blue on large scales, and peak at the correlation scale. However, the
magnetic field can be treated as a coherent source and it is active for a long
time. This results in a very effective conversion of magnetic energy in
gravitational wave energy at horizon crossing. Turbulence instead acts as a
source for gravitational waves over a time interval much shorter than a Hubble
time, and the conversion into gravitational wave energy is much less effective.
We also derive a strong constraint on the amplitude of a primordial magnetic
field when the correlation length is much smaller than the horizon.Comment: Replaced with revised version accepted for publication in Phys Rev
Stringent constraints on the scalar K pi form factor from analyticity, unitarity and low-energy theorems
We investigate the scalar K pi form factor at low energies by the method of
unitarity bounds adapted so as to include information on the phase and modulus
along the elastic region of the unitarity cut. Using at input the values of the
form factor at t=0 and the Callan-Treiman point, we obtain stringent
constraints on the slope and curvature parameters of the Taylor expansion at
the origin. Also, we predict a quite narrow range for the higher order ChPT
corrections at the second Callan-Treiman point.Comment: 5 pages latex, uses EPJ style files, 3 figures, replaced with version
accepted by EPJ
Detection of gravitational waves from the QCD phase transition with pulsar timing arrays
If the cosmological QCD phase transition is strongly first order and lasts
sufficiently long, it generates a background of gravitational waves which may
be detected via pulsar timing experiments. We estimate the amplitude and the
spectral shape of such a background and we discuss its detectability prospects.Comment: 7 pages, 5 figs. Version accepted by PR
Finding the sigma pole by analytic extrapolation of scattering data
We investigate the determination of the pole from
scattering data below the threshold, including the new precise
results obtained from decay by NA48/2 Collaboration. We discuss also
the experimental status of the threshold parameters and and the
phase shift . In order to reduce the theoretical bias, we use a
large class of analytic parametrizations of the isoscalar -wave, based on
expansions in powers of conformal variables. The pole obtained with
this method is consistent with the prediction based on ChPT and Roy equations.
However, the theoretical uncertainties are now larger, reflecting the
sensitivity of the pole position to the specific parametrizations valid in the
physical region. We conclude that Roy equations offer the most precise method
for the determination of the pole from elastic scattering
- …