The Goldberger- Treiman Discrepancy

The GolbergerTreiman discrepancy ∆GT = 1 − mNgA fπGπN is related to the asymptotic behaviour of the pionic form factor of the nucleon obtained from baryonic QCD sum rules. The result is .015 . ∆GT . .022. The Goldberger-Treiman relation (GTR) [1] mNgA = fπGπN (1) which relates the nucleon mass mN , the axial-vector renormalization constant in β − decay gA, the πdecay constant fπ and the π − N coupling constant GπN is one of the most remarkable relations of hadronic physics. Explicit chiral symmetry breaking by the quark masses leads to small corrections to the GTR, the Goldberger -Treiman discrepancy (GTD) [2] ∆GT = 1− mNgA fπGπN (2) which arises from the coupling of the divergence of the axial vector current to the J = 0 continuum. The evaluation of ∆GT has been addressed recently in the framework of baryon chiral perturbation theory [3]. On the experimental side gA = 1.267± .004 and fπ = 92.42MeV are known to enough precision and most of the uncertainty in ∆GT results from the uncertainty in GπN . The most recent determination of GπN from NN, NN̄ and πN data is by the Nijmegen group [4] GπN = 13.05± .08 which corresponds to ∆GT = .014± .009 (3) Similar results are obtained by the VPI group [5]. Larger values are given by Bugg and Machleidt [6] and by Loiseau et al. [7] GπN = 13.65± .30 which corresponds to ∆GT = .056± .02 (4) e-mail: [email protected]