Table VI photon-decay audit
Generated by checks/audit_table_vi_photon_decays.jl on 2026-10-07.
Coverage: 79/79 canonical rows (42 M1, 35 E1, 2 M2); no omitted rows.
Numerics: OscillatorSolver — nbasis = 24:8:80 adaptive, ΔE ≤ 0.1 MeV, beta in [0.25, 2.35] GeV (22 bracket points, refined to 0.002 GeV), 3 levels/channel.
Every radial state uses the shared fixed-channel solver, including the spin-dependent P waves. P1 pseudoscalar mixing contains 1nn/1ss/1cc/1bb and 2nn/2ss/2cc; the n=1 vector and tensor blocks contain all four flavors. The final MixedSpectrum owns each signed composition. Unlisted higher radial mixing and D/F partners are not introduced. Pure-flavor charges are composed exactly once: the old ground-state eta calculation counted the perfect-mixing 1/sqrt(2) factor a second time.
The paper's exponents 0.7/0.5 and Table III annihilation parameters are unchanged. Footnote c retains the E2 recoil correction; footnote g applies exp(-q²/(16β²)), β=0.40 GeV. Footnote a's additive +0.01 μN contribution to phi -> pi gamma is a paper-supplied pi0-eta mixing input. Parenthesized paper predictions are order-of-magnitude estimates, not precision targets. Approximately zero is preserved as a qualifier.
M1 values are μ/μN; E1/M2 values are MeV^(1/2), whose squares are widths in MeV. Signs are shown without row-dependent rephasing or adjustments. Mixed states retain a positive overlap with their assigned unmixed state, using the same ascending-mass assignment as Spectrum. This shared phase convention avoids reversing heavy states because of a tiny negative nn admixture. No per-row sign adjustment is made.
M1
Non-parenthesized targets: 28/31 signs; median |model/paper| 1.002.
| Decay | Computed | Paper | q MeV | q reference MeV | src |
|---|---|---|---|---|---|
| rho -> pi gamma | +0.688552 | +0.69 | 375.3 | 375.7 | PDG 2026 |
| rho -> eta gamma | +1.44545 | +1.53 | 194.0 | 194.5 | PDG 2026 |
| eta' -> rho gamma | +2.00574 | +1.85 | 165.1 | 164.7 | PDG 2026 |
| omega -> pi gamma | +2.06509 | +2.07 | 379.2 | 379.3 | PDG 2026 |
| omega -> eta gamma | +0.464316 | +0.50 | 199.6 | 199.7 | PDG 2026 |
| eta' -> omega gamma | +0.682791 | +0.63 | 159.1 | 159.0 | PDG 2026 |
| phi -> pi gamma | +0.0585345 | (+0.06) | 500.4 | 500.7 | PDG 2026 |
| phi -> eta gamma | +0.750264 | +0.71 | 362.5 | 362.8 | PDG 2026 |
| phi -> eta' gamma | -0.596911 | -0.66 | 59.8 | 60.1 | PDG 2026 |
| eta_r -> omega gamma | +0.0901472 | -0.18 | 410.1 | 507.1 | PDG 2026 |
| eta_r -> rho gamma | +0.306125 | +0.57 | 414.6 | 510.9 | PDG 2026 |
| eta_r -> phi gamma | +0.507345 | +0.37 | 245.2 | 358.7 | PDG 2026 |
| eta'_r -> omega gamma | -0.0698938 | +0.01 | NaN | 626.9 | experimental assignment unavailable |
| eta'_r -> rho gamma | -0.211788 | +0.008 | NaN | 630.3 | experimental assignment unavailable |
| eta'_r -> phi gamma | -0.0304954 | -0.29 | NaN | 495.9 | experimental assignment unavailable |
| K*+ -> K+ gamma | +0.912245 | +0.91 | 309.3 | — | PDG 2026 |
| K*0 -> K0 gamma | -1.20071 | -1.20 | 309.5 | — | PDG 2026 |
| D*+ -> D+ gamma | -0.352501 | -0.35 | 135.7 | — | PDG 2026 |
| D*0 -> D0 gamma | +1.77902 | +1.78 | 137.0 | — | PDG 2026 |
| F* -> F gamma | -0.134325 | -0.13 | 138.9 | — | PDG 2026 |
| B*- -> B- gamma | +1.3652 | +1.37 | 45.1 | — | PDG 2026 |
| B*0 -> B0 gamma | -0.775895 | -0.78 | 44.8 | — | PDG 2026 |
| Fb* -> Fb gamma | -0.552079 | -0.55 | 48.3 | — | PDG 2026 |
| psi -> eta_c gamma | +0.68781 | +0.69 | 110.8 | 114.8 | PDG 2026 |
| psi' -> eta'_c gamma | +0.684319 | +0.68 | 48.0 | — | PDG 2026 |
| psi' -> eta_c gamma | -0.0580167 | -0.056 | 635.2 | 638.4 | PDG 2026 |
| Upsilon -> eta_b gamma | -0.121106 | -0.13 | 61.5 | 59.8 | PDG 2026 |
| Upsilon' -> eta'_b gamma | -0.121129 | -0.12 | 24.4 | 42.9 | PDG 2026 |
| Upsilon' -> eta_b gamma | +0.00769234 | +0.007 | 605.2 | 603.6 | PDG 2026 |
| Upsilon'' -> eta''_b gamma | -0.120756 | -0.12 | NaN | 15.0 | experimental assignment unavailable |
| Upsilon'' -> eta'_b gamma | +0.00713663 | +0.007 | 350.0 | 368.2 | PDG 2026 |
| Upsilon'' -> eta_b gamma | -0.00373866 | -0.004 | 912.2 | 911.0 | PDG 2026 |
| psi -> eta gamma | +0.00143968 | (+0.001) | 1500.0 | 1500.0 | PDG 2026 |
| psi -> eta' gamma | +0.0029533 | (+0.003) | 1400.3 | 1400.3 | PDG 2026 |
| psi -> pi0 gamma | +0.000744799 | (+0.0007) | 1545.5 | 1545.6 | PDG 2026 |
| psi -> eta_r gamma | -0.00138598 | (-0.002) | 1278.2 | 1213.7 | PDG 2026 |
| psi -> eta'_r gamma | -0.00549436 | (-0.002) | NaN | 1119.6 | experimental assignment unavailable |
| Upsilon -> eta gamma | +9.56384e-05 | (+8e-5) | 4714.3 | 4714.1 | PDG 2026 |
| Upsilon -> eta' gamma | -3.25933e-05 | (+3e-6) | 4681.7 | 4681.5 | PDG 2026 |
| Upsilon -> pi0 gamma | +4.14351e-08 | (~0) | 4729.2 | 4729.0 | PDG 2026 |
| Upsilon -> eta_r gamma | +8.65799e-05 | (-9e-5) | 4641.7 | 4620.4 | PDG 2026 |
| Upsilon -> eta'_r gamma | +8.2539e-05 | (+3e-4) | NaN | 4589.6 | experimental assignment unavailable |
E1
Non-parenthesized targets: 28/29 signs; median |model/paper| 1.010.
| Decay | Computed | Paper | q MeV | q reference MeV | src |
|---|---|---|---|---|---|
| A2 -> rho gamma | +0.15143 | +0.15 | 431.1 | 430.6 | PDG 2026 |
| f' -> phi gamma | -0.303033 | -0.31 | 416.2 | 421.4 | PDG 2026 |
| A2_0 -> omega gamma | +0.447278 | +0.44 | 426.8 | 426.4 | PDG 2026 |
| A1 -> pi gamma | +0.435227 | +0.56 | 607.3 | 630.0 | PDG 2026 |
| B -> pi gamma | +0.148949 | +0.63 | 607.0 | 607.8 | PDG 2026 |
| chi_2c -> psi gamma | +0.522107 | +0.50 | 429.6 | 429.4 | PDG 2026 |
| chi_1c -> psi gamma | +0.453983 | +0.44 | 389.4 | 388.7 | PDG 2026 |
| chi_0c -> psi gamma | +0.31202 | +0.30 | 303.7 | 303.2 | PDG 2026 |
| psi' -> chi_2c gamma | +0.145085 | +0.14 | 127.6 | 127.7 | PDG 2026 |
| psi' -> chi_1c gamma | +0.156488 | +0.15 | 171.3 | 171.8 | PDG 2026 |
| psi' -> chi_0c gamma | +0.146904 | +0.14 | 260.7 | 261.0 | PDG 2026 |
| chi_2b -> Upsilon gamma | -0.176853 | -0.18 | 441.5 | 442.6 | PDG 2026 |
| chi_1b -> Upsilon gamma | -0.167547 | -0.17 | 422.9 | 422.6 | PDG 2026 |
| chi_0b -> Upsilon gamma | -0.150233 | -0.16 | 391.0 | 391.9 | PDG 2026 |
| Upsilon' -> chi_2b gamma | -0.0425846 | -0.040 | 110.6 | 109.4 | PDG 2026 |
| Upsilon' -> chi_1b gamma | -0.0396098 | -0.038 | 129.8 | 130.1 | PDG 2026 |
| Upsilon' -> chi_0b gamma | -0.0296249 | -0.025 | 162.6 | 161.7 | PDG 2026 |
| chi'_2b -> Upsilon' gamma | -0.117979 | -0.12 | 242.3 | 234.3 | PDG 2026 |
| chi'_2b -> Upsilon gamma | +0.0858098 | +0.09 | 776.4 | 768.8 | PDG 2026 |
| chi'_1b -> Upsilon' gamma | -0.113882 | -0.11 | 229.4 | 224.5 | PDG 2026 |
| chi'_1b -> Upsilon gamma | +0.0683635 | +0.069 | 764.2 | 759.6 | PDG 2026 |
| chi'_0b -> Upsilon' gamma | -0.102612 | -0.10 | 207.0 | 204.9 | PDG 2026 |
| chi'_0b -> Upsilon gamma | +0.0451212 | +0.047 | 743.0 | 741.0 | PDG 2026 |
| Upsilon'' -> chi'_2b gamma | -0.046837 | -0.044 | 86.1 | 94.6 | PDG 2026 |
| Upsilon'' -> chi_2b gamma | -0.0200216 | -0.020 | 433.4 | 432.6 | PDG 2026 |
| Upsilon'' -> chi'_1b gamma | -0.0426439 | -0.043 | 99.2 | 104.5 | PDG 2026 |
| Upsilon'' -> chi_1b gamma | -0.00727053 | -0.008 | 452.0 | 452.6 | PDG 2026 |
| Upsilon'' -> chi'_0b gamma | -0.031295 | -0.030 | 121.9 | 124.2 | PDG 2026 |
| Upsilon'' -> chi_0b gamma | +0.00197288 | -0.002 | 483.8 | 483.2 | PDG 2026 |
| psi -> A2 gamma | +0.00271128 | (+0.002) | 1267.9 | 1268.0 | PDG 2026 |
| psi -> f gamma | +0.00980963 | (+0.024) | 1285.8 | 1288.1 | PDG 2026 |
| psi -> f' gamma | +0.00300425 | (+0.010) | 1176.8 | 1173.0 | PDG 2026 |
| Upsilon -> A2 gamma | +0.002585 | (+0.002) | 4638.4 | 4638.2 | PDG 2026 |
| Upsilon -> f gamma | -0.00102654 | (-0.006) | 4644.2 | 4644.8 | PDG 2026 |
| Upsilon -> f' gamma | -0.00196242 | (-0.002) | 4608.5 | 4607.1 | PDG 2026 |
M2
Non-parenthesized targets: 2/2 signs; median |model/paper| 0.759.
| Decay | Computed | Paper | q MeV | q reference MeV | src |
|---|---|---|---|---|---|
| A2 -> pi gamma | +0.396363 | +0.55 | 651.9 | 651.8 | PDG 2026 |
| K*(1420) -> K gamma | +0.382584 | +0.48 | 628.2 | 626.9 | PDG 2026 |
Largest magnitude residuals
eta'_r -> rho gamma: |model/paper| 26.474.
eta'_r -> omega gamma: |model/paper| 6.989.
eta'_r -> phi gamma: |model/paper| 0.105.
B -> pi gamma: |model/paper| 0.236.
eta_r -> omega gamma: |model/paper| 0.501.
eta_r -> rho gamma: |model/paper| 0.537.
eta_r -> phi gamma: |model/paper| 1.371.
A2 -> pi gamma: |model/paper| 0.721.
Kinematics provenance
All operator and displayed momenta use the same PDG 2026 registry. No model eigenvalue is used for kinematics. Historical reference q values are reconstructed from legacy audit inputs, some of which were GI model estimates; they are not printed GI momenta. Missing experimental assignments leave q and q-dependent amplitudes unavailable. Momentum-independent M1 moments remain calculable.
Encoding corrections
The 3S -> 1S bottomonium target is -0.004; +0.007 belongs to 3S -> 2S. The A2 -> pi M2 denominator is sqrt(60) m_u, not sqrt(60 m_u). A1 -> pi is spin-flip E1, not M2: J=1 -> J=0 allows a dipole photon. Canonical identities, rather than CSV row positions, select every target.
Paper inconsistency
B -> pi gamma is printed as sqrt(2) q/3 E1^u(pi,B), and the printed +0.63 uses it. The equivalent A2 -> rho gamma row (same 1P -> 1S n nbar overlap and isovector charge) is printed as q/9. E1 does not act on spin, so 1P1 -> 1S0 carries the same 1/3 angular factor as 3PJ -> 3S1. The model uses 1/3, so this row sits a factor 3sqrt(2) below the paper (18 in the rate).
The spin-flip rows (A2 -> pi gamma, A1 -> pi gamma, K_(1420) -> K gamma) are printed with denominators sqrt(60) m and 6m. The magnetization current of Eq. (22) gives sqrt(120) m and sqrt(72) m: the paper's amplitudes are sqrt(2) too large. This is verified with MultipolePhotonEmission, which reproduces the standard M1 and E1 widths and the Karl-Meshkov-Rosner M2/E1 ratios of chi_cJ -> J/psi gamma with the same operator. K_(1420) -> K gamma also carries the centre-of-mass emitter weights 2 m_other/(m_u+m_s), which the paper omits. A2 -> pi gamma is the row the paper used to fit the 0.5 m/E exponent of E_n, so that fit absorbed the factor sqrt(2).