g-2 two anomaly of muon's magnetic moment in the TGD framework

g-2 anomaly for muons magnetic moment is a possible indication of new physics. There are two approaches to the estimation of the g-2 in the existing physics.

1. The first one is based on the experimental input from hadron physics and the second one is based on QCD lattice calculations and relies on quarks and gluons (see this. The QCD prediction conforms with the most recent experimental result (2025).
2. The calculation using empirical data from hadronic vacuum polarization, which predicts that the anomalous magnetic moment of muon is larger than the standard model prediction by factor of order 10^-9. TGD supports this approach.

The TGD view of hadrons differs from the QCD view since the TGD view of color is very different. The basic predictions are as follows and follow from Dirac equation for free fermions in H=M⁴×CP₂. The two H-chiralities correspond to quarks and leptons and the different couplings to CP₂ Kähler predict correctly the charge spectrum and electroweak couplings.

1. The Dirac equation in H=M⁴×CP₂ has two variants. First variant assumes just the usual M⁴ geometry without Kähler form whereas the second option assumes that M⁴ has self-dual Kähler form strongly suggested by twistorialization. 8-D masslessness predicts that the mass squared spectra (eigenvalues of the Dirac operator squared) for M⁴ and CP₂ must be same. Mass squared contains scalar d’Alembertian contribution depending on the color partial wave and spin term which does not depend on color partial wave. The d’Alembertian contribution is multiple of 3 for both quarks but the spin contribution is equal to 3 of for leptons but equal to 1 for quarks.
2. Without M⁴ Kähler form 8-D masslessness this gives no additional conditions and one obtains infinite number of color partial waves with mass scale given by CP₂ mass of about 10^-4 Planck masses except for right-handed neutrino which is massless.
3. If Kähler form is assumed, the mass squared spectra for leptons having H chirality +1 as product of M⁴ and CP₂ chiralities is still integer valued for both M⁴ and CP₂ and it is possible to satisfy 8-D masslessness since leptons couple to 3-multiple of both Kahler form of CP₂ and M⁴.

   For quarks the chirality is -1 and now it is possible to obtain integer valued spin term only if the number of quarks is a multiple of 3. Baryons are obtained as the simplest hadrons. Mesons cannot correspond to quarks pairs but to baryon-antibaryon pairs.

4. The masses are huge: mass scale is CP₂ mass equal to about 10^-4 Planck masses. The proposed mechanism has been that there must be negative contributions to mass squared identifiable as conformal weight which can be used to reduce the mass squared to zero. p-Adic thermodynamics would give the light masses as thermodynamic mass squared. This is possible.

The solutions of M⁴ Dirac equation allow also negative integer values M⁴ mass squared but 8-D massless does not allow them. One can however construct massless lepton states and 3n-quark states by using pairs of left and right handed neutrinos to screen the electroweak quantum numbers above weak scale and make leptons color singlets and quarks color triplets. If either neutrino or both of them are tachyonic, one can obtain zero mass states. Entire hierarchy hadron physics is obtained since the number of color partial waves is infinite.

5. The basic prediction following from mere Dirac equations in H with M⁴ Kähler form is that baryons and mesons as baryon-antibaryon pairs are the basic dynamical units. This has a direct relevance for the understanding of muon’s anomalous g-2 anomaly. This means that the g-2 must be calculated by using baryons as basic units and therefore hadronic data. p-Adic length scale hypothesis and also the infinite number of color partial waves predicts a hierarchy of scaled up hadron physics and electroweak physics. If TGD is right, the g-2 anomaly can be seen as a support for new physics. The scaled up hadron physics and possible scaled variants of weak bosons could give rise to the g-2 anomaly but TGD does not have the machinery to estimate it precisely enough. In any case, the situation is extremely interesting from the TGD point of view.

See the article About Dirac equation in H=M⁴×CP₂ assuming Kähler structure for M⁴ or the chapter with the same title.

For a summary of earlier postings see Latest progress in TGD.

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.