** Next:** Electromagnetic corrections.
** Up:** Strong interaction
** Previous:** Scattering length
** Contents**

###

coupling constant

Another motivation for a better direct determination of the pion-nucleon scattering
lengths is connected to the coupling constant . The Goldberger-Miyazawa-Oehme
(GMO) sum rule [18], which is obtained from a forward dispersion relation
for the isospin-odd scattering amplitude, provides a relation between
the scattering length and the coupling constant :

Here and are the incident pion momentum and energy, and
is the isospin-odd total cross section. The integral (5) is known with
an accuracy of the order of 1% (see [36,37,38] and references therein).
Therefore the determination of the width
with one percent
accuracy offers the possibility to determine the pion-nucleon coupling with
an accuracy of better than 1%. An immediate application is an evaluation of
the Goldberger-Treiman discrepancy [39,40] which accounts for a small
correction to the Goldberger-Treiman relation

where is the axial-vector coupling constant and is the weak
pion decay constant.

** Next:** Electromagnetic corrections.
** Up:** Strong interaction
** Previous:** Scattering length
** Contents**
*Pionic Hydrogen Collaboration*

*1998*