Higgs versus Nambu-Goldstone bosons, supersymmetry and a neutrino condensate

In 1973, D.V. Volkov and V.P. Akulov published a paper entitled “Is the neutrino a goldstone particle?”, in Physics Letters B, Volume 46, Issue 1, Pages 109-110. A neutrino is a spin-1/2 fermion, not a boson. Suppose two massive neutrinos form a Bose-Einstein condensate, with effective spin-0 (analogous to Cooper pairs of electrons, an effective boson in superconductivity).

W+ + W + Z0 -> 2H0

80.4 + 80.4 + 91.2 = 2(126) GeV

where each boson is a condensate of a pair of spin-1/2 fermions.

To annoy Ed Witten and confuse the string theorists (who are in knots anyway), let’s name as “supersymmetry” the checkable theory that Standard Model bosons are Bose-Einstein condensates of Standard Model fermions. (This has nothing to do with the 1:1 mythical boson:fermion supersymmetry theory in string theory, which increases the number of parameters from 18 in the standard model to 125 without predicting any of their values, just to try to make couplings similar at the uncheckable Planck scale.) For a massive Nambu-Goldstone or Higgs boson, this ties up the loose ends in electroweak theory:

“Higgs did not resolve the dilemma between the Goldstone theorem and the Higgs mechanism. … I emphasize that the Nambu-Goldstone boson does exist in the electroweak theory. It is merely unobservable by the subsidary condition (Gupta condition). Indeed, without Nambu-Goldstone boson, the charged pion could not decay into muon and antineutrino (or antimuon and neutrino) because the decay through W-boson violates angular-momentum conservation. … I know that it is a common belief that pion is regarded as an “approximate” NG boson. But it is quite strange to regard pion as an almost massless particle. It is equivalent to regard nuclear force as an almost long-range force! The chiral invariance is broken in the electroweak theory. And as I stated above, the massless NG boson does exist.”

– Professor N. Nakanishi, Not Even Wrong blog comment, November 14, 2010 at 9:42 pm (See our diagram of this pion spin “anomaly”above.)

“Pion’s spin is zero, while W-boson’s spin is one. People usually understand that the pion decays into a muon and a neutrino through an intermediate state consisting of one W-boson. But this is forbidden by the angular-momentum conservation law in the rest frame of the pion.”

– Professor N. Nakanishi, Not Even Wrong blog comment, November 15, 2010 at 1:46 am.
Nakanishi states that despite the Higgs mechanism which produces massive weak bosons (Z and W massive particles), a massless Nambu-Goldstone boson is also required in electroweak theory, in order to permit the charged pion with spin-0 to decay without having to decay into a spin-1 massive weak boson. In other words, there must be a “hidden” massless alternative to weak bosons as intermediaries. This is explained clearly in our theory of SU(2).

The nature of neutrinos (Majorana or Dirac) is involved. Please see our paper for a discussion of the difference and its importance for chiral symmetry and dark matter: right-handed neutrinos don’t undergo weak interactions, so they would be dark matter. The fact that neutrinos change flavour in transit is evidence for a small mass and thus is indirect evidence for the existence of right-handed massive neutrinos. We discussed the recent CERN LHC evidence for a massive ~126 GeV Nambu-Goldstone boson in posts linked here and in the previous post here and here.

The Standard Model as it stands can’t predict the mass of the Higgs boson, and the Higgs mass mechanism ignores quantum gravity considerations (where mass is quantized gravitational charge). It’s not even proved (only surmised by groupthink dogma) that ~126 GeV is rest mass, since if you have a predictive mechanism in place of the Higgs mechanism, we showed a chiral SU(2) electromagnetic Yang-Mills theory where the chiral left-handedness of spin appears as Lenz’s law of the magnetic field curl helicity around the direction of motion of an electric charge. This fact comes from Maxwell’s electromagnetism treatise of 1873 and is defensible using Weyl’s 1929 chiral parity-breaking interpretation of Dirac’s spinor in 1929, which Pauli opposed, and is completely separate from the SU(2) left-handed spinor evidence which is incorporated in the Standard Model (by excluding right-handed neutrinos). Suppose electroweak symmetry breaking involves some kind of annihilation of the triplet of weak bosons to form a pair of spin-0 H-bosons (H standing preferably for Hypothetical, not Higgs):

W+ + W + Z0 -> 2H0

80.4 + 80.4 + 91.2 = 2(126) GeV

(Dharwadker and Khachatryan’s prediction from 2009. See also their guest post on Dr Dorigo’s blog. It seems that any abstract reasoning behind their formula is as physically impenetrable the Koide formula. However, like Rydberg’s empirical formula years later in the hands of Bohr, it may prove useful to developing physics.)

if the two spin-0 bosons have equal masses, each has a mass of 126 GeV. If one H-boson spinor is left-handed and one is right-handed, only the left-handed one is seen, because it is the only one which undergoes weak interactions. Notice an analogy between this simple H formula and one side of the Koide formula, summing lepton masses:

(MW+ + MW- + MZ0)/2 = MH

(Me + Mmuon + Mtauon)/2 = (Me1/2 + Mmuon1/2 + Mtauon1/2)2/3.

Does the H-boson have 126 GeV rest mass or not? Not necessarily! Many assume that it a H-boson is converted into four leptons or two gamma rays, in the LHC ATLAS and CMS detectors, it is a massive 126 GeV spin-0 particle decaying. However, a massless boson like a gamma ray can undergo pair-production in a strong field (the LHC collisions create strong fields!), despite having no rest mass. The fact that you always see 126 GeV as total energy of the spin-0 boson interaction doesn’t prove that it is a particle of 126 GeV rest mass which is decaying due to its mass. A gamma ray can undergo pair-production to form a pair of particles only if the gamma ray has a total energy of 1.022 MeV or more, because pair-production is only possible when the gamma ray energy exceeds the rest mass of the particles it forms. (Pair-production is a non-reversible process, because when an electron and positron annihilate, the conservation of momentum shows you get a pair of gamma rays coming off in opposite directions, each being the recoil momentum of the other. You can argue that there is symmetry if a gamma ray interacts with a virtual photon which behaves like a gamma ray to cause pair production in strong fields, although here the virtual photon is off-shell, not onshell like a gamma ray.) So you could be fooled by this false pair production logic when considering the case of H-boson “decay” into four leptons or two gamma rays, and you could claim that gamma rays have a rest mass of 1.022 MeV, or that the H-boson has a “rest mass” of 126 GeV. Both claims would be correct. Higgs electroweak interactions are new territory, since electroweak mixing in the Standard Model is empirically checked, but electroweak symmetry breaking details are not yet fully established. You cannot confuse speculative theoretical conjecture with facts.

A spin-0 Nambu-Goldstone boson therefore doesn’t have to have rest mass or “decay” in order to produce 126 GeV four-lepton or two-gamma ray products. Like a massless gamma ray which always produces fermion pairs with an energy of 1.022 MeV or more, the spin-0 Nambu-Goldstone boson could be massless, and carries energy without rest mass. The 126 GeV energy (confused for the Higgs boson rest mass) is then a result of the interaction above, half the sum of the weak boson masses. The electroweak symmetry breaking boson only has rest mass if there is explicit symmetry breaking in U(1) X SU(2), such as occurs in the standard electroweak theory where electromagnetism is treated as a U(1) parity-conserving interaction and SU(2) as a parity-breaking (left handed spinor) interaction. If electrodynamics and weak interactions both have the same chiral properties, there is no explicit symmetry breaking, but only spontaneous symmetry breaking.


Standard model electroweak theory: requires massive spin-0 Higgs boson because of explicit electroweak symmetry breaking, since U(1) conserves parity but SU(2) doesn’t conserve parity (it is left-handed).

Alternative electroweak theory: spontaneous symmetry breaking produces a massless (not massless) spin-0 boson. Both electrodynamics and weak interactions are derived from SU(2); massless SU(2) bosons give electromagnetic interaction, massive SU(2) bosons give weak interaction. Both electromagnetism and weak interactions are chiral, the chiral handedness of the electromagnetic interaction is seen in the handedness of the magnetic field helicity around the path of a moving charge. Magnetic fields wouldn’t exist according to Maxwell’s theory of the mechanism for magnetism (gauge boson spin handedness) if the electromagnetic interaction obeyed parity conservation, so it doesn’t.

Copy of a comment submitted to http://snarxivblog.blogspot.com/2012/01/dharwadker-and-khachatryans-prediction.html:

There is an illustration here.

2W + Z -> 2H

2(80.4) + 91.2 = 2(126) GeV.

Note that 2W -> H is one Standard Model Higgs production interaction, while

truth quark + anti-truth quark -> H

is another Standard Model Higgs production interaction. If we treat this second example as equivalent to a Bose-Einstein condensate (each quark being one fermion in the condensate boson), the Z boson is in some sense equivalent to a spin-1 version of the H spin-0 boson, so

2W + Z -> 2H

is feasible, although only one H boson has the spin-0 observed, and the other is spin-1 (right-handed spinor, if it doesn’t participate in weak interactions, thus remaining invisible to ATLAS and CMS).

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