Reading the paper
A map of S. Godfrey and N. Isgur, Phys. Rev. D 32, 189 (1985), doi:10.1103/PhysRevD.32.189, for readers who want to check the code against the article. The article is not distributed with this repository. Page numbers refer to the pages of the PDF.
Where things are
| PDF pages | content |
|---|---|
| 1–2 | introduction and motivation |
| 2–4 | the Hamiltonian: relativized kinetic term, potentials, smearing, running coupling, numerical procedure |
| 4 | the three-stage diagonalization; mixing by tensor and antisymmetric spin-orbit terms |
| 5 | Table II: model parameters |
| 5–6 | light nonstrange and strange mesons (Fig. 4, with strange mixing angles) |
| 7 | isoscalar mesons, Fig. 5 |
| 8 | charmonium and charmed mesons (Figs. 6–7, with charmed mixing angles) |
| 9 | bottomonium and |
| 11 | Table III: isoscalar mixing |
| Sec. IV | strong decays (Tables IV–V), radiative transitions (Table VI), annihilation and electromagnetic properties (Table VII) |
| 35–38 | Appendix A: smearing and the effective potentials |
| 37–38 onward | Appendices B–D: wavefunction conventions, helicity amplitudes, electromagnetic operators |
Appendix A in brief
Appendix A is where the relativization is made concrete. Its equations fall into three groups:
Smearing (A7)–(A9): a Gaussian smearing function, the smeared potential as a convolution, and the mass-dependent width
. Smeared central potentials (A10)–(A14): the pointwise
and , and closed forms for their smeared versions and , with Effective spin-dependent operators and the numerical method (A15)–(A17): contact, tensor and spin-orbit operators built from derivatives of
and with their momentum factors, and the factorization of matrix elements in an oscillator basis.
Equations (A1)–(A6) derive these operators from a scattering amplitude. They motivate the construction but are not used directly as formulas. Equations to code lists the implementation of each equation.
Reading with care
The article is typeset densely and some equations break across lines. Transcriptions of equations and table values in this repository were checked against the page images, not against text extraction.
Spectrum values in Figs. 4–9 are read from level diagrams. The digitized values in
GIPaper/data/carry an uncertainty of a few MeV.The paper works in the isospin limit:
and have the same mass, and / splittings of heavy-light mesons are outside its scope. The mixing angles quoted in the captions of Figs. 4, 7 and 9 are not consistent with the rest of the calculation; see Mixing angles: a paper erratum.