New light on electromagnetic corrections to the scattering parameters obtained from experiments on pionium

We calculate the electromagnetic corrections needed to obtain isospin invariant hadronic pion-pion s-wave scattering lengths a^0, a^2 from the elements a_cc, a_0c of the s-wave scattering matrix for the (\pi^+ \pi^-, \pi^0 \pi^0) system at the \pi^+ \pi^- threshold. These elements can be extracted from experiments on pionium. Our calculation uses energy independent hadronic pion-pion potentials that satisfactorily reproduce the low-energy phase shifts given by two-loop chiral pertur- bation theory. We also take into account an important relativistic effect whose inclusion influences the corrections considerably.Comment: 14 pages including 3 figures. Uses elsart.cls. Some numbers have been updated and a few typos have been correcte

The extraction of hadronic parameters from experiments on pionium

Experimental values of the lifetime of the 1s level of pionium and of the difference between the energies of the 2s and 2p levels yield values of the a(0c) and a(cc) elements of the s-wave scattering matrix for the 2-channel (pi+ pi-, pi0 pi0) system at the pi+ pi- threshold. We develop a method for obtaining the isospin invariant quanties a20 - a00 and 2a00 + a20 from a(0c) and a(cc). We emphasize that the isospin invariant scattering lengths a00 and a20 universally used in the literature cannot be considered to be purely hadronic quantities.Comment: 17 pages, Revtex, 1 postscript figure, new version of figure which removes ghostscript problem

Analysis of the low-energy π−p\pi^- p charge-exchange data

We analyse the charge-exchange (CX) measurements $\pi^- p\rightarrow \pi^0 n$ below pion laboratory kinetic energy of 100 MeV. After the removal of five degrees of freedom from the initial database, we combine it with the truncated $\pi^+ p$ database of Ref. \cite{mrw1} and fit the ETH model \cite{glmbg} to the resulting data. The set of the parameter values of the ETH model, as well as the predictions derived on their basis for the hadronic phase shifts and for the low-energy $\pi N$ constants, are significantly different from the results obtained in the analysis of the truncated $\pi^\pm p$ elastic-scattering databases. The main difference in the hadronic phase shifts occurs in $\tilde{\delta}_{0+}^{1/2}$. We discuss the implications of these findings in terms of the violation of the isospin invariance in the hadronic part of the $\pi N$ interaction. The effect observed amounts to the level of $7-8$ in the CX scattering amplitude below 70 MeV. The results and conclusions of this study agree well with those obtained in the mid 1990s, when the isospin invariance was first tested by using $\pi N$ experimental data, and disagree with the predictions obtained within the framework of the heavy-baryon Chiral-Perturbation Theory

Comments on a monetarist approach to demand management

Monetary policy ; Macroeconomics

A comparative static analysis of some monetarist propositions

Monetary policy ; Fiscal policy

Views on deficits and interest rates

Interest rates ; Budget deficits

Editor's introduction

Monetary policy

A review of empirical studies of the money supply mechanism

Money supply

Identification of dynamic economic models from reduced form VECM structures: an application of covariance restrictions

This analysis is a straightforward implementation of both long-run and short-run identifying or overidentifying restrictions on a vector error correction model in the "structural VAR" framework. The framework utilizes covariance restrictions, long-run multiplier restrictions, error correction coefficient restrictions, and restrictions on slope coefficients of the stimultaneous interactions in the "economic model." The framework is general enough to incorporate restrictions on impact multipliers. Two examples are provided. The first example is a dynamic M2 demand specification with a comparison to previous results that are constructed using restrictions on distributed lag coefficients to achieve identification. The second example illustrates the identification of equilibrium short-term and long-term interest responses of money demand using error-correction coefficient restrictions when the individual coefficients are underidentified in the cointegrating vectors in the presence of stationary interest rate spreads.Econometric models ; Demand for money