A brief history of the pion-nucleon coupling constant

Abstract

This work provides a brief history of determinations of the pion-nucleon (πN ) coupling constant from πN and N N data. From robust analyses of twenty reported values of the charged-pion coupling constant, exhibiting sizeable fluctuation, the result f 2 c = 762.9 +6.5 −6.2 • 10 −4 is obtained. Similar values are extracted for the other two πN coupling constants, f 2 0 and f 2 p , from fewer data. The average values of the various πN coupling constants, extracted in this work, suggest no splitting, in agreement with the thesis of the Nijmegen group. Additional analysis of the f 2 c and f 2 0 values, both reported in four studies, turned to be inconclusive: one of these studies suggests that f 0 < f c , whereas another slightly favours f 0 > f c ; no significant splitting effects are observed in the other two studies. The analysis of the low-energy πN data with the ETH model indicates significant splitting and, under certain conditions, it implies that f 0 > f c . Also discussed in the paper are the electromagnetic corrections, which need to be applied to the strong shift and to the total decay width of the ground state of pionic hydrogen in order that estimates for the hadronic s-wave πN scattering lengths be obtained; this is a relevant subject as f 2 c may be extracted from the isovector scattering length by use of the Goldberger-Miyazawa-Oehme sum rule. Regarding the removal of the electromagnetic effects in the πN system at threshold, my opinion is that Theory must find a way to provide reliable and accurate corrections, matching the level of accuracy of the experimental results.

Determination of the masses and decay widths of the scalar-isoscalar and vector-isovector mesons below $2$ GeV

“…This method of providing estimates for the quantities y and δ y was applied in Ref. [7] to results exhibiting sizeable variability. Given an input dataset (y i , δy i : i = 1, 2, .…”

“…(The scale factors, reported in the PDG compilation, are not always the Birge factors of this work, i.e., values obtained via Eq. (7). In the Section 'Procedures' in the Chapter 'Introduction' of the PDG compilation one reads: "When combining data with widely varying errors, we modify this procedure [i.e., the determination of the scale factor via Eq.…”

“…, N) by one constant, Ref. [7] applied seven continuous soft-weight robust methods to a dataset which is known to contain outliers. Each of these methods features a tuning parameter k ∈ R * + .…”

XYZ spectroscopy at electron-hadron facilities: Exclusive processes

“…with g 2 πN N /(4π) 13.81 ± 0.12 [20]. Away from the pole, the residue β(t) is unconstrained in Regge theory and accounts for the suppression at large t visible in data.…”

Relativistic levels of mesic atoms

“…Hence the difference between the measured transition energies from excited states to the fundamental one and the corresponding energies calculated by pure QED are essentially the same as the shift of the fundamental level. A history of the determination of the pion-nucleon coupling constant can be found in [11]. Up to the most recent papers [12,13], the mass of the π meson has been evaluated by matching the measured values of the photon energy emitted in the transitions between two rather high level of pionic atoms.…”