Higgs without Higgs?

(Before It's News)

HCP2012 conference (Hadron Collider Physics Symposium) at Kyoto will provide new data about Higgs candidate at next Wednesday. Resonaances has summarized the basic problem related to the interpretation as standard model Higgs: two high yield of gamma pairs and too low yield of tau- τ-τbar and and b-bbar pairs. It is of course possible that higher statistics changes the situation.

Two options concerning the interpretation of Higgs like particle in TGD framework

Theoretically the situation quite intricate. The basic starting point is that the original p-adic mass calculations provided excellent predictions for fermion masses. For the gauge bosons the situation was different: a natural prediction for the W/Z mass ratio in terms of Weinberg angle is the fundamental prediction of Higgs mechanism and this prediction did not follow automatically from the p-adic mass calculation in the original form. For this and some other reasons the evolution of ideas about TGD counterpart of Higgs mechanism has been full of twists and turns. This summary is warmly recommended for a seriously interested reader.

p-Adic mass calculations and the results from LHC leave two options under consideration.

The recent view about particles as Kähler magnetic loops carrying monopole flux is forced by the assumption that the corresponding partonic 2-surfaces are Kähler magnetic monopoles (implied by the weak form of electric-magnetic duality). The loop proceeds from wormhole throat to another one, then traverses along wormhole contact to another space-time sheet and returns back and eventually is transferred to the first sheet via wormhole contact. The mass squared assignable to this flux loop could give the contribution usually assigned to Higgs vacuum expectation. If this picture is correct, then the reduction of the W/Z mass ratio to Weinberg angle might be much easier to understand. As a matter fact, I have proposed that the flux loop gives rise to a stringy spectrum of states with string tension determined by p-adic length scale associated with M₈₉.

My sincere hope is that the results of HCP2012 would allow to distinguish between these two options.

Trying to understand the QFT limit of TGD

Under the experimental pressures from LHC (there have been also rather harsh social pressures from Helsinki University ) it has become gradually clear that the understanding of whether TGD has M⁴ QFT limit or not, and how this limit can be defined, is essential for understanding also the role of Higgs. In the following a first attempt to understand this limit is made. I find it somewhat surprising that I am making this attempt only now but the understanding of the proper role of the classical gauge potentials has been quite a challenge.

1. If one believes that M⁴ QFT is a good approximation to TGD at low energy limit then the standard description of Higgs mechanism seems to be the only possibility: this just on purely mathematical grounds. The interpretation would however be that the masses of the particles determine Higgs vacuum expectation value rather than vice versa. This would of course be nothing unheard in the history of physics: the emergence of a microscopic theory – in the recent case p-adic thermodynamics – would force to change the direction of the causal arrow in “Higgs makes particles massive” to that in “Higgs expectation is determined by particle masses”.

2. The existence of M⁴ QFT limit is an intricate issue. In TGD Universe baryon and lepton number correspond to different chiralities of H=M⁴× CP₂ spinors and this means that Higgs like state cannot be H scalar (it would be lepto-quark in this case). Rather, Higgs like state must be a vector in CP₂ tangent space degrees of freedom. One can indeed construct a candidate for a Higgs like state as an Euclidian pion or its scalar counterpart: both are are favored and one can even consider the mixture of them. The H-counterpart is therefore CP₂ axial vector or CP₂ vector or mixture of them. Euclidian pion or scalar carries fermion and antifermion at opposite throats. It is easy to imagine that a coherent state of Euclidian pseudo-scalars or scalars or their mixture having Higgs expectation as M⁴ QFT correlate is formed.
3. The popular statement “gauge bosons eat almost all Higgs components” makes sense at the M⁴ QFT limit.: just a transition to the unitary gauge effectively eliminates all but one of the components of the Higgs like state and gauge bosons get third polarization. This means gauge boson massivation but for option II it would take place already in p-adic thermodynamics in ZEO (zero energy ontology).

The couplings of Higgs like states to gauge bosons should be consistent with QFT description. But is the counterpart of Higgs potential needed in the microscopic description if p-adic mass thermodynamics gives the masses or does it emerge only at M⁴ QFT limit? Does it even make sense to speak about Higgs part of the action at microscopic level. Could the counterpart of YM action be enough? How could one derive the standard model action in M⁴ from the microscopic theory?

1. Classical Higgs field does not seem to have any natural counterpart in the geometry of space-time surface (the trace of the second fundamental form does not work since it vanishes for preferred extremals which are also minimal surfaces).

2. Rather radical but very natural idea is that the classical gauge potentials obtained as components of induced spinor connection are identifiable as microscopic counterparts of Higgs vacuum expectation value. The space-time projection of the CP₂ vector valued Higgs would project to classical gauge fields! In fact, quantum Higgs could be the Euclidian pion in unitary gauge and it would give an additional CP₂ contribution to the quantum gauge potentials which are M⁴ vectors. This contribution would be present only in the Euclidian regions where one can apply CP₂ coordinates because CP₂ projection is 4-D. No Higgs part would be needed in the action at the microscopic level! Paraphrasing Wheeler, one could say that one has “Higgs without Higgs”! Here one must be however cautious: both M⁴ and CP₂ parts of 8-D gauge potential in principle have non-vanishing M⁴ and CP₂ projections. This does not however change the basic conclusion.

How to define the QFT limit M⁴ and does it give rise to Higgs potential?

1. One could think QFT limit at space-time sheets with Minkowskian signature and Minkowski coordinates rather than in M⁴. This would mean standard model in background gauge fields defined by the induced gauge potentials. Integration over them would guarantee Poincare invariance, and would correspond to a functional integral over “world of classical worlds” (WCW) – in other words over preferred extremals of Kähler action. Classical gauge potential have dimension 1/length so that the outcome of the functional integral could give as effective action YM action containing also Higgs action with potential depending on dimensional parameters.

2. More precisely: to obtain the counterpart of the standard model YM action one can apply the standard procedure leading to effective action – that is consider states, which contain besides the vacuum functional an interaction.
   1. The first guess would the exponential of the standard current-gauge potential interaction term in which classical electroweak gauge currents and color gauge currents couple to the gauge potentials, which are sums of two terms: quantum gauge potential plus the classical gauge potential. In Euclidian regions this term would be real and in Minkowskian regions imaginary.

   2. The are however two problems. The classical gauge current contains second order derivatives and tends to vanish for the most known extremals. The functional integral using Kähler action for a preferred extremals reducing to Kähler function in Euclidian regions and to imaginary Morse function in Minkowskian regions would define the effective action as a functional of quantum gauge fields. For preferred extremals Kähler action reduces to Chern-Simons terms for preferred extremals restricted to wormhole throats in accordance with holography and almost topological QFT property of quantum TGD. The first guess for the interaction term would however break the almost TQFT property since it is genuinely 4-dimensional unless it vanishes.

For these reasons a natural guess is that the interaction term is – or reduces to – a sum of electroweak and color Chern-Simons terms coming from Minkowskian and Euclidian regions giving imaginary and real contributions. There would be no dependence on the induced metric except through the boundary conditions stating weak electric-magnetic duality. This is enough to give rise to mass terms in the effective action.

Rather remarkably, this would give also the Higgs part of the action. The dominant contribution to the Higgs part of the action would naturally emerge from the quantum part of the induced gauge potentials in the Euclidian space-time regions whereas the dominant contribution gauge part would come from the Minkowskian regions. This conforms with the idea that Higgs is Euclidian M⁴ scalar.

To sum up, for option II the parameters for the counterpart of Higgs action emerging at QFT limit must be determined by the p-adic mass calculations in TGD framework and the flux tube structure of particles would in the case of gauge bosons give the standard contribution to gauge boson masses. For option one fermionic masses would emerge as mass parameters. The presence of Euclidian regions of space-time having interpretation as lines of generalized Feynman diagrams is absolutely crucial in making possible Higgs without Higgs. One must however emphasize that at this stage both options must be considered.

There is even a little piece of evidence for this picture. It is probably not an accident that Higgs vacuum expectation value corresponds to the minimum mass for p=M₈₉ if the p-adic counterpart of Higgs expectation squared is of order O(p) in other words one has μ²/m_CP2²= p=M₈₉.

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