1,026 research outputs found
Determination of the chiral pion-pion scattering parameters: a proposal
An explicitly crossing-symmetric decomposition of the pion-pion scattering
amplitudes into low- and high-energy components is established. The high-energy
components are entirely determined by absorptive parts at high energies. With
the exception of the two leading-order parameters, all the parameters appearing
in the one- and two-loop chiral amplitudes are determined by the high-energy
components of the exact amplitudes.Comment: 14 pages plain latex, 2 figures, uuencoded, tarred and compresse
Chiral two-loop pion-pion scattering parameters from crossing-symmetric constraints
Constraints on the parameters in the one- and two-loop pion-pion scattering
amplitudes of standard chiral perturbation theory are obtained from explicitly
crossing-symmetric sum rules. These constraints are based on a matching of the
chiral amplitudes and the physical amplitudes at the symmetry point of the
Mandelstam plane. The integrals over absorptive parts appearing in the sum
rules are decomposed into crossing-symmetric low- and high-energy components
and the chiral parameters are finally related to high-energy absorptive parts.
A first application uses a simple model of these absorptive parts. The
sensitivity of the results to the choice of the energy separating high and low
energies is examined with care. Weak dependence on this energy is obtained as
long as it stays below ~560 MeV. Reliable predictions are obtained for three
two-loop parameters.Comment: 23 pages, 4 figures in .eps files, Latex (RevTex), our version of
RevTex runs under Latex2.09, submitted to Phys. Rev. D,minor typographical
corrections including the number at the end of the abstract, two sentences
added at the end of Section 5 in answer to a referee's remar
One-channel Roy equations revisited
The Roy equation in the single channel case is a nonlinear, singular integral
equation for the phase shift in the low-energy region. We first investigate the
infinitesimal neighborhood of a given solution, and then present explicit
expressions for amplitudes that satisfy the nonlinear equation exactly. These
amplitudes contain free parameters that render the non-uniqueness of the
solution manifest. They display, however, an unphysical singularity at the
upper end of the interval considered. This singularity disappears and
uniqueness is achieved if one uses analyticity properties of the amplitudes
that are not encoded in the Roy equation.Comment: 36 pages (LaTex), 9 figures embedded with epsfig.st
Determination of SU(2) Chiral Perturbation Theory low energy constants from a precise description of pion-pion scattering threshold parameters
We determine the values of the one- and two-loop low energy constants
appearing in the SU(2) Chiral Perturbation Theory calculation of pion-pion
scattering. For this we use a recent and precise sum rule determination of some
scattering lengths and slopes that appear in the effective range expansion. In
addition we provide sum rules for these coefficients up to third order in the
expansion. Our results when using only the scattering lengths and slopes of the
S, P, D and F waves are consistent with previous determinations, but seem to
require higher order contributions if they are to accommodate the third order
coefficients of the effective range expansion.Comment: 16 pages. Version published in Phys. Rev. D. Enlarged discussions in
several sections, appendices and many references added. Results and
conclusions unchange
Magnetic Confinement, MHD Waves, and Smooth Line Profiles in AGN
In this paper, we show that if the broad line region clouds are in
approximate energy equipartition between the magnetic field and gravity, as
hypothesized by Rees, there will be a significant effect on the shape and
smoothness of broad emission line profiles in active galactic nuclei. Line
widths of contributing clouds or flow elements are much wider than their
thermal widths, due to the presence of non-dissipative MHD waves, and their
collective contribution produce emission line profiles broader and smoother
than would be expected if a magnetic field were not present. As an
illustration, a simple model of isotropically emitting clouds, normally
distributed in velocity, is used to show that smoothness can be achieved for
less than 80,000 clouds and may even be as low as a few hundred. We conclude
that magnetic confinement has far reaching consequences for observing and
modeling active galactic nuclei.Comment: to appear in MNRA
On the precision of the theoretical predictions for pi pi scattering
In a recent paper, Pelaez and Yndurain evaluate some of the low energy
observables of pi pi scattering and obtain flat disagreement with our earlier
results. The authors work with unsubtracted dispersion relations, so that their
results are very sensitive to the poorly known high energy behaviour of the
scattering amplitude. They claim that the asymptotic representation we used is
incorrect and propose an alternative one. We repeat their calculations on the
basis of the standard, subtracted fixed-t dispersion relations, using their
asymptotics. The outcome fully confirms our earlier findings. Moreover, we show
that the Regge parametrization proposed by these authors for the region above
1.4 GeV violates crossing symmetry: Their ansatz is not consistent with the
behaviour observed at low energies.Comment: Added more material, mostly in Sects. 7, 8 and 9, in support of the
same conclusions. Latex, 28 pages, 3 figure
Testing the Rule with Exclusive Semi-Leptonic Kaon Decays
We consider the possibility of violations of the selection rule at an appreciable level in {\it exclusive} semi-leptonic decays of
Kaons. At -Factories, intense Kaon beams will be available and will probe
among others, the semi-leptonic decays and in addition
to and could provide novel testing grounds for the
rule. In particular, the branching ratio of is non-negligible
and could be used to probe new phenomena associated with the violation of this
selection rule. Furthermore, we modify certain di-lepton event rate ratios and
asymmetries and time asymmetries that have been constructed by Dass and Sarma
for di-lepton events from Beon decays to test the at the
, to the Kaon system at the . We find that the large
width of the relative to that of plays an important role in
enhancing some of the time asymmetries.Comment: 10 pages, Plain Latex, To be run twice
The Low Energy Expansion for Pion-Pion Scattering and Crossing Symmetry in Dispersion Relations
We show that a suitable setting for comparison of the low-energy
representation for pion-pion scattering amplitudes, with dispersive
representation for these amplitudes, is provided by certain manifestly crossing
symmetric dispersion relations. We begin with a discussion of fixed-t
dispersion relations and discuss the origin of crossing constraints that arise
in this context when we consider resonance saturation with certain
states. We demonstrate that the approach advocated here does not require us to
enforce such constraints. Our results are contrasted with those from fixed-t
dispersion relations. We finally discuss the numerical import of our results.Comment: 24 pages plain LaTeX, to be run twic
The pro-active resource management departments of constituent entities of the tourism cluster
The proposed approach to the pro-active resource management departments of constituent entities of the tourism cluster, in particular of housekeeping service of the hotel. The developed methodology of the pro-active resource management of housekeeping service of the hotel was described
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