## Friday, April 08, 2022

### Is Standard Model tumbling down?: W boson mass is .1 per cent higher than predicted!

Particle physicists have found a new anomaly (see this). The  measured mass of the W boson is by .1 per cent higher than predicted by high precision calculation! For a layman .1 per cent does not sound like an earthquake but, in the accuracies achieved, it is. Weak interactions are indeed weak, this kind of accuracy is possible. Physics has become incredibly precise!

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.

1. 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.

The new physics prediction is that also the gauge bosons and graviton have the analog of family replication (see this and this).

2. 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.

3. 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 π0 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.

The  exotics appear in  various loop corrections at the QFT limit of TGD.
1. 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.
2. The (2) exotics could also explain the anomaly of g-2 anomaly (yes: anomaly of anomaly!) of muon.
Could the  exotics also explain  the W mass anomaly?  Could a mixing  between ordinary gauge bosons and  (2)  exotics give a positive  contribution to the  self-energy loops of W and increase the mass slightly?  If  the mass changes in this manner, it must increase. This is encouraging.
1. 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.

2. 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.

3. 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).

Also leptons,  could emerge from quarks but that is another story (see  this). The  fundamental particle physics  reduces to that for quarks (see  thisthis).

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