Goldberger-Treiman constraint criterion for hyperon coupling constants

Abstract

The generalized Goldberger-Treiman relation is combined with the Dashen-Weinstein sum rule to provide a constraint equation between the gKΣN and gKΛN coupling constants. A comprehensive examination of the published phenomenological and theoretical hyperon couplings has yielded a much smaller set of values, spanning the intervals 0.80 ≤ gKΣN / √ 4π ≤ 2.72 and −3.90 ≤ gKΛN / √ 4π ≤ −1.84, consistent with this criterion. The SUF (3) and Goldberger-Treiman hyperon couplings satisfy the constraint along with predictions from a Taylor series extrapolation using the same momentum variation as exhibited by gπNN .

K-Λ and K-Σ photo-production in a coupled channels framework

“…In particular the sign of g N KΛ , see Table I, deviates from the customary negative value [27]. In a calculation like ours and many of the ones cited in [27] this sign is undetermined.…”

“…In particular the sign of g N KΛ , see Table I, deviates from the customary negative value [27]. In a calculation like ours and many of the ones cited in [27] this sign is undetermined. Changing the sign of all coupling constants involving a single Λ-field leaves the calculated observables invariant since it corresponds to a sign redefinition of this field.…”

“…The SU (3) prediction for this coupling constant is very sensitive to the exact value of F/D and our extracted values can be seen as an argument to favor a somewhat smaller value for F/D. We should note that the relative sign of the g N ΣK and g N ΛK couplings is often taken to be negative [27]. It should be noted, however, that this sign cannot be determined from a calculation as presented in this work because it depends on an arbitrary sign in the definition of the Λ-baryonic field.…”

“…In weak-decay processes the sign of the vector v.s. axial vector can be determined, which only fixes the sign of the axial coupling if the vector coupling is assumed to be positive [27]. For the Baryon-Baryon-Vector (BBV , Table III, lower plane) sector the SU (3) predictions are based on the assumptions of the extreme quark model and vector meson universality [36], which requires S = 3F − D and D = 0.…”

“…axial-vector coupling does correspond to an observable. The magnitude of the couplings is within the broad range specified in [27]. [13].…”