### Could Higgs mechanism provide a description of p-adic particle massivation at QFT limit?

The most recent TGD based explanation of the observed Higgs like state with 125 GeV mass is as "half-Higgs" identified as "Euclidian pion". Euclidian pion would give the dominating contribution to the masses of gauge bosons but the contribution to fermion masses would be negligible and come from p-adic thermodynamics. This scenario saves from the hierarchy problem resulting from fermionic loops giving large contribution from heavy fermion masses and destabilizes Higgs mechanism. It is also known that for the observed mass of the Higgs like state Higgs vacuum is unstable.

What if the Higgs like state decays to fermions pairs with the rate predicted by standard form of Higgs mechanism? This is unpleasant question from TGD point of view. Could it mean that TGD is deadly wrong? Unpleasant questions are often the most useful ones so that it is perhaps time to boldly articulate also this question.

Is the recent TGD based view about Higgs like state as "Euclidian pion" as source of gauge boson masses and p-adic thermodynamics as a source of fermion masses exactly correct? p-Adic thermodynamics is based on very general assumptions like super-conformal invariance, the existence of string like objects of length of order CP_{2} length predicted by the modified Dirac equation, and the powerful number theoretic constraints coming from p-adic thermodynamics and p-adic length scale hypothesis. Could Higgs mechanism be only a QFT approximation for a microscopic description of massivation based on p-adic thermodynamics - as suggested for more than fifteen years ago - so that the two approaches would not be actually competitors?

**Microscopic description of massivation**

Consider first the microscopic description in more detail (see this).

- In the recent TGD description elementary particles correspond to loops carrying Kähler magnetic monopole flux and having two wormhole contacts with Euclidian signature of induced metric as ends at which magnetic flux flows between opposite light-like 3-D wormhole throats at different space-time sheets. In the case of fermions fermion number resides at wormhole throat at the either end of the loop. In the case of bosons fermion and antifermion number reside at the opposite throats of either wormhole contact. One can imagine variants of this picture since two wormhole contacts are involved: fermion number could be delocalized to both wormhole contacts and both wormhole throats, and bosons could have fermion and antifermion at the throats of different wormhole contacts. p-Adic mass calculations do not allow to distinguish between these options. The solutions of the modified Dirac equation assign to the flux loop closed string and this leads to a rich spectrum of topological quantum numbers and implies that elementary particles are also knots: unfortunately the predicted effects are extremely small.

- What does one actually mean with the expectation value of mass squared in p-adic thermodynamics (as a matter of fact, ZEO suggests that p-adic thermodynamics is replaced with its "complex square root". This has some non-trivial number theoretical implications in the case of fermions (see this). There are two options.

- Genuine mass squared is in question. The simplest possibility is that both throats of the wormhole carry light-like momentum. If the momenta are not parallel, this can give rise to stringy mass squared spectrum with string tension determined by CP
_{2}length. The role of string is connects the opposite throats of the wormhole contact. In the case of bosons the ends of the short string connecting the throats would carry fermion and antifermion. In the case of fermions second throat would carry purely bosonic excitations generated by the symplectic algebra of δ M^{4}_{+/-}× CP_{2}. One could also assign mass squared to the string but holography suggests that this mass squared is identifiable as total mass squared assignable to the ends.

- Longitudinal mass squared is in question in the case of wormhole throat. The option favored by ZEO and number theoretical arguments is that p-adic thermodynamics gives only longitudinal mass squared, that this the square of M
^{2}-projection of light-like fermion momentum, where M^{2}⊂ M^{4}characterizes given CD.

What happens in the case of contact? Could the transversal momenta of the throats cancel and give rise to a purely longitudinal contribution equal to the entire momentum so that longitudinal option would be equivalent with the first one?

Or could it be that the second wormhole throat does not contribute to the mass squared. The physical mass squared would be the average of longitudinal mass squared over various choices of M

^{2}⊂ M^{4}so that Lorentz invariance would be achieved. The propagators associated with massless twistor lines would be defined by the M^{2}projections of fermionic or bosonic momenta and would therefore be finite. Also gauge conditions would involve only the longitudinal projection. I have not been able to develop any killer argument against this option.

- Genuine mass squared is in question. The simplest possibility is that both throats of the wormhole carry light-like momentum. If the momenta are not parallel, this can give rise to stringy mass squared spectrum with string tension determined by CP
- According to the most recent view (see this), the dominating contribution to gauge boson masses would be due to their coupling to Higgs like Euclidian pion developing vacuum expectation associated with coherent state. But is this fundamental description or only effective description obtained at 8-D QFT limit? An alternative view discussed for a year or two ago is that gauge boson masses correspond to "stringy" contribution from the
*long*portion of the closed flux tube pair connecting the two wormhole contacts with a distance of order weak length scale associated with the gauge boson - the analog of Minkowskian meson. The contribution from the*short*part of the closed flux tube - the wormhole contact defining Euclidian pion - would dominate fermionic masses. In this case Higgs vacuum expectation could provide only a convenient effective description at QFT limit.

- This picture leads naturally to generalized Feynman diagrams suggesting strongly twistor Grassmannian description since even the virtual wormhole throats are light-like. This description in turn would lead to QFT description when wormhole contacts are approximated by points of M
^{4}× CP_{2}or even M^{4}.

p-Adic mass calculations give universal results but the drawback clearly is that they cannot fix the details of the model of elementary particles.

**Does Higgs mechanism emerge at the QFT limit as effective description?**

The above description is definitely not QFT description. Does QFT description exist at all - say as a limit of twistorial description? It the QFT limit exists in some sense, what can one conclude about it? In the possibly existing QFT description one must idealize flux loops with point-like particles. Even if p-adic thermodynamics predicts fermion masses by assigning them to short Euclidian strings and gauge boson masses by assigning them to long Minkowskian strings in the closed flux tube, the only manner to describe this at QFT limit might be based on the use of vacuum expectation of Higgs like field and coupling to Higgs field. One could even argue that p-adic thermodynamics is equivalent to Higgs mechanism at QFT limit.

Even if both fermionic and bosonic particle massivation were due to to p-adic thermodynamics at the fundamental level, one is forced to describe it at QFT limit by taking mass as given thermal mass. This could be achieved by using coupling to the vacuum expectation of the Higgs like state (Euclidian pion) and by choosing the dimensionless coupling so that a correct value of mass results.

If the fermions couple also to the quantum part of Higgs field as bosons would certainly do, one obtains standard model prediction but encounters the hierarchy problem and vacuum stability problem. M_{89} hadron physics for which the bump at mass about 130 GeV suggested by the results of Fermi laboratory serves as evidence, might solve these problems. A more plausible option is that the badly broken supersymmetry generated by the second quantized modes of induced spinor field labelled by conformal weight - essentially conformal supersymmetry - guarantees the cancellation of loop contributions at high energies. Note that the modes associated with right-handed neutrino are delocalized at the entire 4-surface, and do not seem plausible candidates for the needed SUSY (see this. One would end up with a description in which Higgs effectively gives rise to the masses of fermions. The outcome would be however an artifact of the QFT approximation.

One can consider QFT limits in H=M^{4}× CP_{2} and M^{4} respectively.

- The 8-dimensional QFT limit treats fermions using H-spinors with quarks and leptons having different H-chiralities. In this case it is impossible to describe mass as in M
^{4}since it would give rise to a coupling between quarks and leptons and break separate conservation of baryon and lepton numbers. One must introduce instead of scalar mass a vector in CP_{2}tangent space analogous to polarization vector.

- At quantum level Higgs vacuum expectation value defines a vector in CP
_{2}tangent space expressible in terms of complexified gamma matrices having dimension 1/length so that is natural for the phenomenological description of mass generated by p-adic thermodynamics. In this description the counterpart of Higgs vacuum expectation would be the quantity H^{k}γ_{k}=H^{A}γ_{A}, where H^{A}is a vector in CP_{2}tangent space assignable to braid end at the partonic 2-surface (end or wormhole throat orbit at the boundary of CD). H^{A}has dimensions of 1/length just as Higgs like field. The length squared of this vector would define the mass squared.

- Can one identify H
^{A}in terms of induced geometry? The CP_{2}part of second fundamental form vanishing for minimal surfaces (analogous to massless particles) is such a vector field. Only the value of H^{A}at braid end is needed so that H^{A}would be effectively constant. Quantum classical correspondence suggests that H^{A}corresponds to vacuum expectation of Higgs field.

- At quantum level Higgs vacuum expectation value defines a vector in CP
- M
^{4}QFT limit would define even stronger approximation, which must be however consistent with 8-D QFT limit. Now one must use 4-D spinors and describe the coupling in terms of scalar mass coupling different M^{4}chiralities. There are two options for the coupling g;Ψbar; ΨΦ and (g/m_{0})Ψbar; γ^{μ}Ψ D_{μ}Φ. The latter option gives automatically effective coupling gm/m_{0}and Higgs couplings are therefore proportional to fermion masses. Fermion masses can be reproduced by the standard form of Higgs mechanism and also now the illusion that Higgs gives rise to fermion masses is created.

For a summary of the evolution of TGD inspired ideas about particle massivation see the chapter Higgs or something else? of "p-Adic length scale hierarchy and hierarchy of Planck constants". See also the short article Is it really Higgs?.

## 2 Comments:

Well,

Something to say to the readers of this blog.

These ideas are a bit unconventional, but still not as mad as most internet physicists. The education shows in commandment of math and understanding the basic concepts.

Here in University of Helsinki the madness of this guy official, however. It is advised for nobody to read these before having at least a M.Sc. in theoretical physics.

To Anonymous and Readers:

Interesting that the powerholders of Helsinki University are not anymore able to hide their fears that young students might find TGD. Hitherto the silence has been complete.

I have been without basic academic human rights for 35 years because of jealousy of certain professors and still the situation is the same: after having developed a successful unification of fundamental interactions with applications ranging to biology and theory of consciousness.

To all readers of this blog: I feel deep shame for the University of Helsinki. Not only for the powerholders but also for the personnel who should have had the moral integrity to do something for the situation during these years: intellectual dishonesty and cowardice have however prevented this.

Helsinki University should have been a place for doing fundamental research but has degenerated to a place populated by sillies like this miserable Anonymous who does not have even courage to use his own name.

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