This makes every builder of TOE humble! Of course, a new theory cannot achieve the precision of the predictions of the standard model. What is needed is understanding at a qualitative level and despite its marvellous accuracy, standard model cannot provide this understanding.
This anomaly suggests new massive particles. Also the earlier earthquakes, the CP breaking anomaly of B mesons and g-2 anomaly for muon, suggest new massive particles.
Using the language of quantum field theory (QFT), new particles should appear in self-energy loops of the W boson. Also the QFT limit of TGD uses this language although it is replaced with something much more elegant at the fundamental level (see this and this).
Can one understand these anomalies in the TGD framework.
- In the TGD framework, the family replication phenomenon for fermions (one has three quark and lepton generations) is explained topologically and the CKM mixing of fermions as induced by their topological mixing. This goes outside the standard model which just assumes CKM mixing without any attempt to understand it.
- Fermions would have 3 generations, which correspond to 3 topologies for a 2-D wormhole throat characterized by the number of handles: sphere, torus as sphere with one handle, and sphere with two handles.
For a higher number of handles, one would have analogs of many-particle states with handles regarded as particles moving around the sphere like free particles: mass spectrum would be continuous - one could talk about ur particles.
For the 3 lightest genera there is Z2 conformal symmetry irrespective of conformal moduli. This symmetry allows a bound state of 2-handles. One can assign a dynamically generated symmetry group SU(3)g to these 3 fermion states (electron, muon, tau + plus neutrinos and 3 quark generations). Fermions of these 3 generations form a triplet.
- Bosons would correspond to pairs of wormhole throats characterized by handle number and group theoretically to a tensor product 3× 3 of fermion triplets (see this and this). This would give a singlet and octet. Singlet would correspond to ordinary gauge bosons and gravitons. For singlet, ordinary gauge bosons, the couplings to fermions would be the same for all genera.
Octet would contain 2 states with vanishing SU(3)g quantum numbers plus 3+3=6 SU(3)g charged states. Let us refer to these 2 states as "2 exotics". The 2 exotics have vanishing SU(3)g quantum numbers and are analogs of neutral pion π
0 and η in good old hadron physics involving strong isospin and strangeness.
An intuitive guess is that the 3+3 SU(3)g "charged" states are heavy (analogous to kaon K and charged pions π+/- in the old-fashioned quark model). Thus 2+6 new states with the same standard model quantum numbers as the existing ones, are predicted, and the 2 exotics are expected to be light.
- Exotics could explain the anomalous CP violation for neutral B mesons. The couplings to fermions specified by SU(3)g charge matrices, which are orthogonal for the 3 generations and therefore cannot be the same for all generations. One would have a violation of universality and this is at the core of CP violation anomaly.
- The (2) exotics could also explain the anomaly of g-2 anomaly (yes: anomaly of anomaly!) of muon.
- Fermionic generations mix topologically. For instance, a sphere becomes a quantum superposition of several topologies containing mostly sphere and a little bit of torus and also a sphere with two handles. CKM mixing is essentially the difference of the topological mixings for U and D type quarks.
Could also gauge bosons with the same SU(3)g quantum numbers belonging to singlet and octet mix? A pair of spherical wormhole throats would get a small contribution from a pair of torus and g=2 wormholes.
- Could one find some support for the mixing idea existing hadron physics? Vector boson dominance of the good old hadron physics assumed that photons can mix with rho mesons. ρ mesons correspond to quark pairs completely analogous to the analog of the first SU(3)g singlet (analog of pion).
This mixing would be caused by the decay of photons to a quark pair in turn forming a ρ meson.
Exactly the same could happen for SU(3)g. An ordinary gauge boson would decay to a virtual quark pair, which would combine with a small amplitude also to an exotic gauge boson, which is actually a superposition of fermion pairs in TGD. This would be induced by the topological mixing.
- What about self energy corrections from the intermediate gauge boson pairs appearing in self-energy loops? They are certainly very small but in the TGD framework, they do not appear at the fundamental level in the lowest order.
The reason is that in the TGD Universe also gauge bosons are quark and lepton pairs: there are no fundamental bosons in the TGD Universe since bosons emerge from fermions as fermion-antifermion pairs (two pairs for gravitons).