Table III Mixing Audit
Generated by julia GIPaper/checks/audit_table_iii_mixings.jl. 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), 6 levels/channel.
This audit compares the implemented literal pseudoscalar P1/P2 modes (Eq. 18a,b on HO radial wavefunctions) with the promoted Table III amplitude rows in data/transcription_mixings.csv. The basis is ordered as:
1 ns, 1 ss, 1 cc, 1 bb, 2 ns, 2 ss, 2 cc
Current Conclusion
All diagonal masses and Eq. (17) overlaps use the same native full fixed-channel oscillator wavefunctions. P1/P2 use seven flavor/radial entries; vector and tensor channels use the original four-flavor ground-state blocks. Every signed component is retained below, including small charm and bottom admixtures. State assignment and global signs maximize overlap with the reference vector; no component is adjusted to its paper value.
P1
| state | pole / column | mass GeV | target GeV | mass Δ MeV | Table Δ MeV | vector RMS | max | largest model components |
|---|---|---|---|---|---|---|---|---|
eta(548) | 1 | 0.531 | 0.520 | +11 | 370 | 0.023 | 0.045 | 1 ss=-0.772, 1 ns=+0.625, 2 ns=+0.111 |
eta_c(2980) | 5 | 2.965 | 2.970 | -5 | n/a | 0.000 | 0.001 | 1 cc=+1.000, 1 ns=-0.008, 1 ss=-0.004 |
eta_prime(958) | 2 | 1.000 | 0.960 | +40 | 810 | 0.053 | 0.121 | 2 ns=+0.591, 1 ns=+0.568, 1 ss=+0.553 |
eta_r(?) | 3 | 1.496 | 1.440 | +56 | n/a | 0.141 | 0.314 | 2 ss=-0.754, 2 ns=+0.586, 1 ns=-0.252 |
eta_r_prime(?) | 4 | 1.799 | 1.630 | +169 | n/a | 0.189 | 0.303 | 2 ss=+0.638, 2 ns=+0.543, 1 ns=-0.473 |
Complete signed components
| state | 1 ns model | 1 ns paper | 1 ss model | 1 ss paper | 1 cc model | 1 cc paper | 1 bb model | 1 bb paper | 2 ns model | 2 ns paper | 2 ss model | 2 ss paper | 2 cc model | 2 cc paper |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
eta(548) | +0.624859 | +0.67 | -0.77176 | -0.73 | +0.000914627 | +0.001 | +0.000149169 | +0.0002 | +0.110561 | +0.11 | +0.0414014 | +0.042 | -0.000414172 | -0.0005 |
eta_c(2980) | -0.00773413 | -0.008 | -0.00441472 | -0.005 | +0.999948 | +1 | +0.000207639 | +0.0002 | +0.00362998 | +0.004 | +0.00262967 | +0.003 | -0.00197757 | -0.002 |
eta_prime(958) | +0.567734 | +0.58 | +0.552502 | +0.62 | +0.0042809 | +0.004 | +0.00059307 | +0.0005 | +0.590926 | +0.47 | +0.152326 | +0.13 | -0.00184572 | -0.002 |
eta_r(?) | -0.251642 | -0.26 | -0.160242 | -0.17 | -0.00279668 | -0.003 | -0.000308596 | -0.0003 | +0.585848 | +0.79 | -0.753507 | -0.44 | +0.00111161 | +0.001 |
eta_r_prime(?) | -0.473113 | -0.17 | -0.270978 | -0.1 | -0.00850052 | -0.003 | -0.000773937 | -0.0003 | +0.543461 | +0.26 | +0.638203 | +0.86 | +0.00312732 | +0.001 |
Mean vector RMS for P1: 0.082; max vector RMS: 0.189. Mean abs mass residual for P1: 56 MeV against the paper-model targets.
P2
| state | pole / column | mass GeV | target GeV | mass Δ MeV | Table Δ MeV | vector RMS | max | largest model components |
|---|---|---|---|---|---|---|---|---|
eta(548) | 1 | 0.490 | 0.490 | -0 | 340 | 0.015 | 0.031 | 1 ss=-0.753, 1 ns=+0.649, 2 ns=+0.095 |
eta_c(2980) | 5 | 2.965 | 2.970 | -5 | n/a | 0.000 | 0.000 | 1 cc=+1.000, 2 cc=-0.002, 1 ns=-0.002 |
eta_prime(958) | 2 | 0.973 | 0.930 | +43 | 780 | 0.047 | 0.107 | 1 ss=+0.723, 1 ns=+0.498, 2 ns=+0.447 |
eta_r(?) | 3 | 1.262 | 1.270 | -8 | n/a | 0.003 | 0.007 | 2 ns=+0.992, 1 ss=+0.080, 1 ns=+0.077 |
eta_r_prime(?) | 4 | 1.550 | 1.550 | -0 | n/a | 0.011 | 0.016 | 2 ss=+0.984, 2 ns=-0.144, 1 ns=+0.077 |
Complete signed components
| state | 1 ns model | 1 ns paper | 1 ss model | 1 ss paper | 1 cc model | 1 cc paper | 1 bb model | 1 bb paper | 2 ns model | 2 ns paper | 2 ss model | 2 ss paper | 2 cc model | 2 cc paper |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
eta(548) | +0.649053 | +0.68 | -0.752999 | -0.73 | -0.00507325 | -0.005 | +0.000285987 | +0.0003 | +0.0954169 | +0.09 | +0.0508505 | +0.051 | +0.00252896 | +0.002 |
eta_c(2980) | -0.00189327 | -0.002 | -0.00142442 | -0.001 | +0.999993 | +1 | +0.000310875 | +0.0002 | +0.00110039 | +0.001 | +0.0010541 | +0.001 | -0.00228765 | -0.002 |
eta_prime(958) | +0.498411 | +0.48 | +0.723387 | +0.78 | -0.00953964 | -0.008 | +0.00106514 | +0.0009 | +0.446585 | +0.34 | +0.169551 | +0.14 | +0.00452487 | +0.004 |
eta_r(?) | +0.0765792 | +0.07 | +0.0796832 | +0.08 | -0.00473571 | -0.005 | -0.000271271 | -0.0002 | +0.991527 | +0.99 | +0.0680748 | +0.07 | +0.00215578 | +0.002 |
eta_r_prime(?) | +0.0767279 | +0.09 | +0.0678194 | +0.08 | -0.00575936 | -0.006 | -0.00010074 | -0.0001 | -0.143618 | -0.16 | +0.984301 | +0.97 | +0.00248118 | +0.003 |
Mean vector RMS for P2: 0.015; max vector RMS: 0.047. Mean abs mass residual for P2: 11 MeV against the paper-model targets.
Non-Pseudoscalar Rows
1 3S1 — Eq. (16), four flavors
Radial n=2 entries are not part of these original Table III blocks; they are not zero predictions.
| state | mass GeV | 1 ns model | 1 ns paper | 1 ss model | 1 ss paper | 1 cc model | 1 cc paper | 1 bb model | 1 bb paper |
|---|---|---|---|---|---|---|---|---|---|
omega(783) | 0.778867 | +0.999725 | +0.999 | -0.0234443 | -0.02 | -0.000903615 | -0.001 | -0.00012346 | -0.0001 |
phi(1019) | 1.019406 | +0.0234437 | +0.02 | +0.999725 | +0.999 | -0.000598872 | -0.0006 | -7.54019e-05 | -7e-05 |
J/psi(3097) | 3.091823 | +0.000917402 | +0.0009 | +0.00057752 | +0.0006 | +0.999999 | +1 | -3.62771e-05 | -3e-05 |
1 3P2 — Eq. (16), four flavors
Radial n=2 entries are not part of these original Table III blocks; they are not zero predictions.
| state | mass GeV | 1 ns model | 1 ns paper | 1 ss model | 1 ss paper | 1 cc model | 1 cc paper | 1 bb model | 1 bb paper |
|---|---|---|---|---|---|---|---|---|---|
f2(1270) | 1.275819 | +0.997973 | +0.997 | +0.0635923 | +0.06 | +0.00256941 | +0.007 | +0.0002341 | +0.0009 |
f2_prime(1515) | 1.531624 | -0.063596 | -0.07 | +0.997975 | +0.997 | +0.00135105 | +0.004 | +0.000112579 | +0.0004 |