14 research outputs found
Complete analysis of pion-nucleon scattering in chiral perturbation theory to third order
We consider pion-nucleon scattering in heavy-baryon chiral perturbation
theory to third order. All electromagnetic corrections appearing to this order
are included. We thus have a consistent description of strong and
electromagnetic effects, which allows us to isolate the strong part of the
interaction in an unambiguous way. We give pion-nucleon phase shifts up to pion
laboratory momenta of 100 MeV and find sizeable differences for the S-waves of
the elastic channels compared to previous phase shift analyses. The precise
description of the scattering process also allows us to address the question of
isospin violation in the strong interaction. For the usually employed triangle
relation we find an isospin breaking effect of -0.7% in the S-wave, whereas the
P-waves show an effect of -1.5% and -4 to -2.5%, respectively, for pion
laboratory momenta between 25 and 100 MeV.Comment: 17 pp, 7 fig
Pion-nucleon scattering in chiral perturbation theory II: Fourth order calculation
We analyse elastic-pion nucleon scattering to fourth order in heavy baryon
chiral perturbation theory, extending the third order study published in Nucl.
Phys. A640 (1998) 199. We use various partial wave analyses to pin down the
low-energy constants from data in the physical region. The S-wave scattering
lengths are consistent with recent determinations from pionic hydrogen and
deuterium. We find an improved description of the P-waves. We also discuss the
pion-nucleon sigma term and problems related to the prediction of the
subthreshold parameters.Comment: 28 pp, LaTeX2e, uses epsf, 6 figs, better discussion of the
convergence issues, accepted for publication in Nuclear Physics
Pion-nucleon scattering in an effective chiral field theory with explicit spin-3/2 fields
We analyze elastic-pion nucleon scattering to third order in the so-called
small scale expansion. It is based on an effective Lagrangian including pions,
nucleons and deltas as active degrees of freedom and counting external momenta,
the pion mass and the nucleon-delta mass splitting as small parameters. The
fermion fields are considered as very heavy. We present results for phase
shifts, threshold parameters and the sigma term. We discuss the convergence of
the approach. A detailed comparison with results obtained in heavy baryon
chiral perturbation theory to third and fourth order is also given.Comment: 44 pp, LaTeX2e, uses epsf, 6 fig
The chiral effective pion-nucleon Lagrangian of order p^4
We construct the minimal effective chiral pion-nucleon SU(2) Lagrangian at
fourth order in the chiral expansion. The Lagrangian contains 118 in principle
measurable terms. We develop both the relativistic as well as the heavy baryon
formulation of the effective field theory. For the latter, we also work out
explicitly all 1/m corrections at fourth order. We display all relevant
relations needed to find the linearly independent terms.Comment: 30 pp, LaTeX2e, coefficients of three third order 1/m^2 corrections
proportional to F_{\mu\nu}^+ corrected in eq.(3.8) and table
On the size of isospin violation in low-energy pion-nucleon scattering
We present an analysis of isospin-breaking effects in threshold pion-nucleon
scattering due to the light quark mass difference and the dominant virtual
photon effects. We discuss the deviation from various relations, which are
exact in the isospin limit. The size of the isospin-violating effects in the
relations involving the isovector amplitudes is typically of the order
of one percent. We also find a new remarkably large effect in an
isoscalar triangle relation connecting the charged and neutral pion scattering
off protons.Comment: 10 pp, LaTeX, uses epsf, 2 fig
Towards an understanding of isospin violation in pion-nucleon scattering
We investigate isospin breaking in low-energy pion-nucleon scattering in the
framework of chiral perturbation theory. This work extends the systematic
analysis of [1] to the energy range above threshold. Various relations, which
identically vanish in the limit of isospin symmetry, are used to quantify
isospin breaking effects. We study the energy dependence of the S- and P-wave
projections of these ratios and find dramatic effects in the S-waves of those
two relations which are given in terms of isoscalar quantities only. This
effect drops rather quickly with growing center-of-mass energy.Comment: 12 pp, REVTeX, 8 figs, FZJ-IKP(TH)-2000-2
One-loop analysis of the reaction pi N to pi pi N
Single pion production off nucleons is studied in the framework of heavy
baryon chiral perturbation theory to third order in the chiral expansion. Using
total and some older differential cross section data to pin down the low-energy
constants, most of the recent differential cross sections and angular
correlation functions can be described as well as total cross sections at
higher energies. We show that the contributions from the one loop graphs are
essentially negligible and that the dominant terms at second and third order
are related to pion-nucleon scattering graphs with one pion added. We also
discuss the possibility of extracting the pion-pion S-wave scattering lengths
from the unpolarized data.Comment: 57 pp, LaTeX file, 13 figures (uses epsf
Pion-nucleon scattering in chiral perturbation theory I: Isospin-symmetric case
We construct the complete effective chiral pion-nucleon Lagrangian to third
order in small momenta based on relativistic chiral perturbation theory. We
then perform the so-called heavy baryon limit and construct all terms
up-to-and-including order with fixed and free coefficients. As an
application, we discuss in detail pion-nucleon scattering. In particular, we
show that the expansion of the Born graphs calculated relativistically
can be recovered exactly in the heavy baryon approach without any additional
momentum-dependent wave function renormalization. We fit various empirical
phase shifts for pion laboratory momenta between 50 and 100 MeV. This leads to
a satisfactory description of the phase shifts up to momenta of about 200 MeV.
We also predict the threshold parameters, which turn out to be in good
agreement with the dispersive analysis. In particular, we can sharpen the
prediction for the isovector S-wave scattering length, . We also consider the subthreshold parameters
and give a short comparison to other calculations of scattering in
chiral perturbation theory or modifications thereof.Comment: 38 pp, LaTeX, uses epsf, 7 figs, additional remarks, one figure
added, version to be published in Nucl.Phys.
Pion-nucleon physics in chiral pertubation theory
In the present work, we study pion-nucleon physics in chiral perturbation theory.We show how to construct the most general effective Lagrangian including nucleons,pions, and external sources. The theoretical framework once set, we proceed to thedescription of physical processes. Elastic pion-nucleon scattering is shown to be describedto high accuracy in the limit of isospin symmetry. We construct the chiralamplitude to full one-loop order and discuss the convergence of the chiral series. Weexplicitly add the delta resonance to the theory, thus making a detailed comparisonbetween the chiral expansion and the so-called small-scale expansion possible. Theinclusion of isospin breaking effects into the theory allows us to quantify isospin symmetryviolation in elastic pion-nucleon scattering reactions. As a second applicationwe study single-pion production off nucleons. We particularly focus on questionsrelated to convergence, and show that the contributions from chiral loops are fairlysmall