The Pion nucleon coupling constant and the Goldberger-Treiman relation

Dec, 2003

15 pages

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Abstract:

The latest

\pi N

elastic scattering data are re-analysed to determine the coupling constant

g_c

of the charged pion, using the dispersion relation for the invariant amplitude

B^{(+)}

. Depending on the choice of data-base, values

g^2_c/4\pi = 13.80

to 13.65 are obtained with errors of

\pm 0.12

. We re-examine the well known discrepancy with the Goldberger-Treiman relation. After allowing for the mass dependence of the pion decay constant

f_\pi

, a (2-3)% discrepancy is predicted, hence

g^2_c/4\pi = 13.74 \pm 0.10

in the prior case. The mass difference between charge states of

\Delta (1232)

is

M^0 -M^{++} = 2.0 \pm 0.4

MeV, close to twice the mass difference between neutron and proton. The difference in widths on resonance is

\Gamma ^0 - \Gamma ^{++} =3.8 \pm 1.0

MeV. One may account for a width difference of 4.5 MeV from phase space for decays and the extra channel

\Delta ^0 \to \gamma n

.

Note:

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