### Errata

Feynman has said that the life of scientist is the state of endless confusion. This is due to the skeptic attitude which means that every statement is always more or less plausible, never absolutely true. It would be so easy to just believe but this luxury is not for scientists.

In my own case the endless confusion is also due to my remarkable ability to make blunders. This ability must be unique to me since I have heard not a single scientist telling about possession of this gift, and many of them insist that I am not a scientist at all;-). The mechanism leading to the perception of the big blunder is always the same. Some days of depressive mood without any obvious reason. Then a sudden realization - almost as a rule during my daily walk - that I have done something horribly stupid. The discovery is followed by a deep feeling of shame. Probably something similar to that felt by all those innumerable discoverers of perpetuum mobiles who are told in detail how energy conservation and second law explain why their construct did not work in this demo and will never do so. Have I lived for vain? Has any-one read the article or chapter containing the blunder? How many people have discovered how stupid an error I have made? Or could I hope that no-one actually reads my scribblings? And if some-one does, could it be that this some-one understands nothing!

The long and tortuous task related to the understanding of Higgs mechanism and SUSY in TGD framework have been a rich source of blunders and erratic interpretations and I collected these Odysseia to two chapters (see this and this) which reveal all the miserable details of this journeys in theory landscape and at least show how to not to do it;-). I can of course console my self by saying that this is not solely due to my stupidity. In TGD all the particles follow as predictions of the theory: no fields are put in by hand as in the usual quantum field theory approach, where one can write Feynman rules immediately. It is obvious that if one starts just from the idea that space-times are 4-D surfaces in certain 8-D space, it takes some time and some blunders to deduce the particle spectrum and Feynman rules.

The latest electrifying experience during my daily walk was related to Higgs mechanism. In the previous shock for a month or so ago I had understood that 125 GeV particle identified usually as Higgs like boson very probably is not M_{89} pion as I had believed originally although it could be pion-like state. I had already earlier realized that TGD predicts two kinds of mesonlike states. Minkowskian mesons are counterparts of ordinary mesons assignable to long flux tubes with Minkowskian signature of the induced metric connecting different wormhole contacts at distance define by hadron size in question. For M_{89} hadrons it would be weak length scale. Euclidian mesons correspond to very short flux tubes connecting opposite throats of wormhole contacts. The latter are natural candidates for Higgs like bosons and can in principle be scalars or pseudoscalars. I assumed pseudoscalar but it does not actually affect the basic predictions.

There is a beautiful connection with color symmetry and strong u(2) identifiable as weak u(2). Color algebra decomposes to u(2) subalgebra and its complement transforming like 3+1 and 2+ 2bar respectively under u(2) having interpretation as imbedding of the electroweak u(2) acting as holonomies of CP_{2}. One can construct fermionic bilinears transforming according to both representations and 2+2bar is the natural candidate for Euclidian pion identified as Higgs like boson. 3+1 - as a matter fact 3 alone (for a reason which can be understood is a natural candidate for the Minkowskian pion.

I of course identified Higgs like boson in terms of 2+2bar Euclidian pion. I had to construct the TGD counterpart of Higgs mechanism generating vacuum expectation of Euclidian pion giving domination contributions to weak boson masses and providing them their longitudinal polarizations. Here I made incredibly stupid mistake: for some mysterious reason I treated the Euclidian pion as 3+1 rather than 2+2bar! Certainly, a cognitive remnant from the original identification of 125 GeV boson as Minkowskian pion. I did not even notice that 3+1 gives rise to a modification of Higgs mechanism in which both photon and Z boson would remain massless. Amusingly, I have proposed for years ago that a phase in which both photon and Z are massless in cellular length scales exists and is highly relevant for the physics of cell membrane. Maybe this 3+1 Higgs is there and characterizes different phase.

After discovering the error it took one day to develop a correct - or better to say "more correct" - view about Higgs mechanism. Within few hours I felt myself happy. Truth is a marvelous healer.

- The final solution (I hope so!) came from the observation that TGD predicts two kinds of meson like states corresponding to Kähler magnetic flux tubes connecting wormhole throats of separate wormhole contacts and to throats of same wormhole contact. The first meson like states are "long" and have Minkowskian signature. Second meson like states are very "short" and have Euclidian signature. It would be Euclidian pions which take the role of Higgs like state. It is essential that these states transform as 2+2bar under u(2) subset su(3). In the first approximation Higgs potential is exactly the same as in standard model and the massivation of gauge bosons proceeds in the same manner as in standard model. Hierarchy problem due to the instability of the tachyonic mass term for Higgs like particle is avoided since the direct couplings to fermions proportional to fermion masses are not needed because p-adic thermodynamics makes fermions massive. Also the predictions for the decay rates remain the same as for standard model Higgs if tachyonic mass squared is taken as a non-dynamical parameter.

- What is new is that one can also find a microscopic description for the tachyonic mass term in terms of a bilinear coupling to a superposition a×YM+ b× I of YM action density and instanton term most naturally restricted to the induced Kähler form. This term also predicts that - besides the ordinary decays to electroweak gauge boson pairs mediated by same action as in the case of the ordinary Higgs - there are also decays mediated by linear perturbative couplings to a×YM+ b× I. Instanton density brings in also CP breaking possibly related to the poorly understood CP breaking in hadronic physics. The quantitative estimate gives a result consistent with experimental data for reasonable magnitude of parameters. Also a connection with the dark matter researches reporting signal at 130 GeV and possibly also at 110 GeV suggests itself: maybe also these signals also correspond to Minkowskian and Euclidian pion-like states.

_{89}pions.

For the details of the Odysseia see the new chapter Higgs or something else? of "p-Adic length scale hypothesis and dark matter hierarchy", and for the latest vision about Higgs the article Is it really Higgs?.