Scope and limitations

This page lists what GIModel covers and what it deliberately leaves out. The purpose is to make clear which questions the package can answer.

Covered

• The complete 1985 spectrum algorithm: the fixed-sector Hamiltonian with all Appendix A operators, spectroscopic mixing, and isoscalar annihilation mixing, solved in the paper's oscillator basis with automatic convergence.

• An independent solver: finite differences, as a cross-check.

• Physical states: masses, contributions, and signed components through every mixing stage, with solver-native wavefunctions in position and momentum space.

• All observables of the paper's Tables III–VII, computed from the solved states: isoscalar mixing, strong decays in the paper's reduction, radiative transitions, and leptonic, two-photon and gluonic widths, and charge radii.

• Beyond the paper: the Eq. (19) emission operator evaluated on the solved wavefunctions rather than a common Gaussian, with all partial waves and coherent mixing (see Strong decays beyond the paper).

Not covered

• Other decay models. There is no quark-pair-creation () model. Decays that need a new quark pair (for example  ), emission of mesons other than pseudoscalars, and hadronic or semileptonic weak transitions are not implemented.

• Coupled channels. Mass shifts and mixing induced by decay channels (threshold effects, pole dressing) are not included. This matters for states near or above open-flavor thresholds, such as the .

• Isospin breaking. As in the paper, and are degenerate.

• Baryons and exotics. Only mesons.

• Top quarks. The 1985 parameter set has no top mass; toponium rows of the paper are not computed.

Things to keep in mind

• Mixing depends on the requested basis. Only requested levels enter a mixing block (Computing a spectrum). Include every level that can mix with the state you study.

• Convergence is certified for energies. Wavefunction-sensitive quantities (widths, values at the origin, cancellation-prone overlaps) should be checked separately (Solvers and convergence).

• Kinematics use model masses. Decay momenta follow from the masses of the solved states. Use mass_correction_factor to compare at measured masses.

• Couplings of the emission operator are inputs. and are not predicted and must be calibrated.

• Known reference discrepancies. The mixing angles in the 1985 figure captions (Mixing angles: a paper erratum) and the amplitudes of transitions from radially excited states (Results at a glance) differ from the paper for reasons that are documented, not hidden.