Bochum 1998 – scientific programme

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HK: Hadronen und Kerne

HK 20: Structure of Baryons, Mesons III, Theory

HK 20.2: Talk

Monday, March 16, 1998, 17:30–17:45, H

Pion-nucleon coupling constant and sigma term — •R.G.E. Timmermans — KVI, University of Groningen, The Netherlands

Two important measures of chiral symmetry breaking due to nonzero quark masses are the Goldberger-Treiman discrepancy, obtained from the pion-nucleon coupling constant f_NNπ², and the pion-nucleon sigma term σ_{π N}. In recent years, both quantities have been subject to debate and revision. In this contribution, I review the present status [1].

Accurate new values for f_NNπ² have been obtained from the pp, np, pp→nn, and π p scattering data. These determinations, by different groups, agree on a “low” coupling constant f_NNπ²=0.075(1), superseding previously accepted values by Bugg, Kroll, and Koch and Pietarinen. As a result, the Goldberger-Treiman discrepancy has become significantly smaller, viz. Δ_πN = 1.9(5)%.

According to the Cheng-Dashen theorem, the pion-nucleon “sigma term” σ_{π N}=(m_u+m_d)⟨ p| uu+dd|p⟩/2 can be obtained from a specific π N scattering amplitude Σ at the unphysical point s=u=M², t=2m_π². In 1982, Koch obtained Σ=64(8) MeV, using the amplitudes of the 1980 Karlsruhe-Helsinki π N analysis of Höhler and collaborators. A recent analysis of modern meson-factory data, however, gives Σ=42(5)(5) MeV. This novel value implies σ_{π N}≃ 30 MeV, with important repercussions for the strangeness content of the nucleon.

[1] R.G.E. Timmermans, Proc. of the XVth Int. Conf. on Few-Body Problems in Physics, Nucl. Phys. A, in press, and references therein.