11 research outputs found
Electromagnetic corrections for the analysis of low energy pi-p scattering data
We calculate the electromagnetic corrections to the isospin invariant mixing
angle and to the two eigenphases for the s and p-waves for low energy pi-p
elastic and charge exchange scattering. These corrections have to be applied to
the nuclear quantities obtained from phase shift analyses of the experimental
data in order to obtain the hadronic phases. We compare our results with
earlier calculations and estimate the uncertainties in the corrections.Comment: 19 pages, 5 figures. Uses elsart.cls Accepted for publication in
Nuclear Physics
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
Phase-shift analysis of low-energy elastic-scattering data
Using electromagnetic corrections previously calculated by means of a
potential model, we have made a phase-shift analysis of the
elastic-scattering data up to a pion laboratory kinetic energy of 100 MeV. The
hadronic interaction was assumed to be isospin invariant. We found that it was
possible to obtain self-consistent databases by removing very few measurements.
A pion-nucleon model was fitted to the elastic-scattering database obtained
after the removal of the outliers. The model-parameter values showed an
impressive stability when the database was subjected to different criteria for
the rejection of experiments. Our result for the pseudovector
coupling constant (in the standard form) is . The six
hadronic phase shifts up to 100 MeV are given in tabulated form. We also give
the values of the s-wave scattering lengths and the p-wave scattering volumes.
Big differences in the s-wave part of the interaction were observed when
comparing our hadronic phase shifts with those of the current GWU solution. We
demonstrate that the hadronic phase shifts obtained from the analysis of the
elastic-scattering data cannot reproduce the measurements of the
charge-exchange reaction, thus corroborating past evidence that the hadronic
interaction violates isospin invariance. Assuming the validity of the result
obtained within the framework of chiral perturbation theory, that the mass
difference between the - and the -quark has only a very small effect on
the isospin invariance of the purely hadronic interaction, the
isospin-invariance violation revealed by the data must arise from the fact that
we are dealing with a hadronic interaction which still contains residual
effects of electromagnetic origin.Comment: 43 pages, 6 figure