Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1995-07-26
Nucl.Phys. B457 (1995) 147-174
Physics
High Energy Physics
High Energy Physics - Phenomenology
30 pp, LaTeX file, uses epsf, 6 figures (appended), corrections in sections 5 and 6, conclusions unchanged
Scientific paper
10.1016/0550-3213(95)00526-9
In the framework of heavy baryon chiral perturbation theory, we give thIn the framework of heavy baryon chiral perturbation theory, we give the chiral expansion for the $\pi N \to \pi \pi N$ threshold amplitudes $D_1$ and $D_2$ to quadratic order in the pion mass. The theoretical results agree within one standard deviation with the empirical values. We also derive a relation between the two threshold amplitudes of the reaction $\pi N \to \pi \pi N$ and the $\pi \pi$ S--wave scattering lengths, $a_0^0$ and $a_0^2$, respectively, to order ${\cal O}(M_\pi^2)$. We show that there are uncertainties mostly related to resonance excitation which make an accurate determination of the $\pi \pi$ scattering length $a_0^0$ from the $\pi \pi N$ threshold amplitudes at present very difficult. The situation is different in the $\pi \pi$ isospin two final state. Here, the chiral series converges and one finds $a_0^2 = -0.031 \pm 0.007$ consistent with the one--loop chiral perturbation theory prediction.
Bernard Véronique
Kaiser Nicholas
Meißner Ulf-G.
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