GIModel.jlMesons from the Godfrey–Isgur quark model

Masses, wavefunctions and decays of quark–antiquark mesons, from the relativized Hamiltonian of Phys. Rev. D 32, 189 (1985), in Julia.

Charmonium 1¹D₂ wavefunction drawn as a cloud of points

Masses

Every n ²ˢ⁺¹L_J level of any u, d, s, c, b pair, with its mass split into central, contact, spin-orbit and tensor parts, and the mixing between levels.

Wavefunctions

Position- and momentum-space wavefunctions for every state, including the signed flavor and spin components of mixed states.

Transitions

Radiative E1, M1 and M2, strong pseudoscalar emission, γγ, gg and ggg annihilation, and leptonic widths, all from the solved wavefunctions.

Checked against the paper

Spectra of all seven flavor sectors within a few MeV, and every table of the 1985 paper reproduced, with each difference documented.

Masses

One call solves the relativized Hamiltonian for a quark–antiquark pair and returns every requested level, with the paper's harmonic-oscillator method and an automatic convergence check. Here, the spectrum of the B_c mesons:

julia

using GIModel
params, mq = load_parameters_and_quark_masses(default_parameters_path())
Bc = compute_spectrum(params, Meson(mq, :b, :c);
    levels = spectrum_levels(2), solver = OscillatorSolver())
spectrum_state(Bc, "1^3S_1").mass_GeV     # 6.333

The two J^P = 1⁺ states are superpositions of the spin singlet and triplet, because the quark masses differ. Computing a spectrum →

The B_c meson spectrum computed with GIModel

Wavefunctions

The cloud at the top of this page is the charmonium 1¹D₂ state: points drawn from |ψ(r)|², coloured by the sign of ψ. Every state carries its radial wavefunction in position and momentum space, and mixed states expose each signed component.

Wavefunctions →

julia

spec = compute_spectrum(params, Meson(mq, :c, :c);
    levels = spectrum_levels(2), solver = OscillatorSolver())
wave = radial_wave(spec, "1^1D_2")
sample_wave(wave, range(0, 12; length = 241))   # u(r) on a grid
physical_components(spec, "1^3S_1")             # J/ψ: 1S with a small D admixture

Transitions

julia

using GIModel.QuarkModelTransitions
psi, eta_c = physical_state(spec, "1^3S_1"), physical_state(spec, "1^1S_0")
decay_width(matrix_element(eta_c, PhotonEmission(mq), psi))       # M1, MeV
decay_width(MasslessLeptonPair(), LeptonicCurrent(:electromagnetic, mq), psi)

Decay amplitudes use the same solved states, so mixing and radial structure enter coherently: photon emission (E1, M1, M2), pseudoscalar emission with all partial waves, annihilation into γγ, gg and ggg, and leptonic decays. Transitions and decays →

Get it

julia

using Pkg
Pkg.add(url = "https://github.com/mmikhasenko/GIModel.jl")

Then follow Getting started. If you use GIModel in published work, please cite S. Godfrey and N. Isgur, Phys. Rev. D 32, 189 (1985), and this repository.