Data on cross-sections (relative reaction rates) for Higgs boson decay processes

Enrico Fermi suggested that when a neutron decays into a proton, electron, and antineutrino, the process is identical to a neutron and a neutrino scattering (a reaction with an effective cross-sectional target area or “cross-section”) with a change of charge and mass, so that a proton and an electron emerge. This enabled weak decay to be treated as a “simple” particle scattering interaction, with an effective cross-section. In 1967 the “electroweak theory” was developed which unified the weak strength of this weak reaction with the electromagnetic gauge theory force (which is far stronger at low energy) by inserting a massive (80 GeV) charged W vector boson into the weak interaction process, this mass being necessary to explain the observed weakness of the weak force relative to the electromagnetic force. The W boson with 80 GeV mass and other properties as predicted was discovered in 1983 at CERN, and now the “Higgs” particle which is postulated to give the 80 GeV mass to the W boson has supposedly been discovered, again at CERN:

“The only fly in the ointment is its decay rate to two photons. This is nearly twice as large as expected. The significance of the discrepancy with the standard model is about 2.5 sigma. It could be a fluke. We have learnt to show some healthy skepticism when it comes to observations of physics beyond the standard model. However it is also consistent with an enhancement due to the presence of another charged boson. If that boson exists it must have a mass at least a bit larger than the W otherwise the Higgs would decay to this particle in pairs and we would see the effect on the other decay rates. It can’t be too massive otherwise it would not enhance the diphoton rate enough.” – Dr Philip Gibbs

The latest data on the quantities of 125 GeV massive spin-0 bosons seen by the CMS and ATLAS detectors at CERN’s LHC can be compared to the Higgs boson cross-sections for different reactions (e.g. decay processes) predicted by the Standard Model of particle physics (the electroweak theory).  The results show that the ratios of observed/expected signals for different decays are:

1.0 for two neutral weak bosons (ZZ),

1.75 for two gamma rays, and

0.75 for two two charged weak bosons (WW).

Dr Woit comments: “The bottom line is that, within errors, everything is consistent with the SM predictions. The gamma-gamma channel is the one to watch, it is about 2 sigma high.”

A preprint issued yesterday by Pier Paolo Giardin and others, called “Is the resonance at 125 GeV the Higgs boson?”, states: “The recently discovered resonance at 125 GeV has properties remarkably close to those of the Standard Model Higgs boson.”

A comment today by Mohit Sinha on Woit’s blog discusses the discrepancies in decays, suggesting that the 2-sigma excess in the double gamma ray production (i.e. 2 statistical standard deviations in a Gaussian/normal dfistribution error curve; not to be confused with the observed/expected ratios) “could be pointing to another not-yet-discovered boson along with the Higgs-like boson just discovered”, while the underestimated double W production decay data may weaken the case for spin-0 and instead suggest that the new 125 GeV boson is a massive spin-2 vector boson (of relevance to quantum gravity gauge theories).  The detection of double gamma ray decay rules out spin-1, which would violate the conservation of momentum, since gamma rays are spin-1, but doesn’t rule out spin-0 or spin-2.  If the low WW production debunks spin-0, then that would leave spin-2 by elimination.  However, gravity itself is long-ranged and so its quanta can’t have rest mass, so if there is a spin-2 massive boson it’s not the graviton, although if quantum gravity is a gauge theory which connects into the Standard Model, you can expect some symmetry breaking boson (although conventional stringy ideas would suggest that the quantum gravity symmetry breaking scale would be near the immense Planck mass, far greater than the LHC can see).  But the most probable explanation is simply that the relatively small amount of data available on WW production in spin-0 decays has given an inaccurate result, which will improve when more data is accumulated.

One good example of a symmetry breaking massive pseudo-Goldstone boson which acts as a vector boson is the pion, which mediates the strong nuclear attractive force between nucleons (neutrons, protons) in the nucleus, keeping it bound together against the mutual electromagnetic repulsion from the protons.  The pion is a QCD symmetry breakdown pseudo-Goldstone boson, but acts as a vector boson.  Note that the pion is a composite particle, containing one quark and one anti-quark, each having spin-1/2.  The combination acts as an effective spin-1 boson, just in the same way that superconductivity arises from the Cooper pairs of electrons (fermions, each spin-1/2) coupling their spins together to form effective “bosons” of spin-1, which lose all electrical resistance and propagate like massive (slower than light) photons.  It’s possible that the spin-0 massive boson is a composite, by analogy to these examples.  The pion is not a fundamental particle, since it contains two fundamental particles, but nevertheless (1) it arises through symmetry breaking, and (2) it acts as a vector boson for the nuclei-scale strong force (gluons of course mediate the QCD force between individual quarks).  What concerns me, as my paper shows, is that the electroweak Z boson’s 91 GeV mass seems to be the building block of the masses of fundamental particles.

Another commentator today on Woit’s blog, “truth” (who seems to think like a string theorist) claims: “The Goldstone models couple to the W, Z bosons to give them mass and the vev gives mass to the fermions. None of that requires the extra degree of freedom which is the Higgs boson. The only reason we have to add this extra degree of freedom is to ensure the theory is unitary at high energies. So what the LHC has discovered is that unitarity is respected by nature. This is the real content of the discovery. It is quite interesting to me that unitarity is the guiding principle of string theory, i.e., string theory is the only known consistent theory of gravity that exactly respects unitarity. This is extremely interesting.”

This is just a circular argument or assertion of dogma.  The data available are no proof that the massive spin-0 boson detected is precise confirmation of the electroweak theory with Higgs mechanism, so interpreting the data this way and then asserting that this speculative assertion amounts to a proof of unitarity and string theory is absurd.

Another commentator on Woit’s blog, David Nataf, points out that there is a “4-sigma signal of a gamma-ray emission line (that could be a dark matter annihilation line) toward the Galactic center at an energy 130 GeV”, i.e. close in energy to the 125 GeV massive spin-0 LHC particle, in the paper, “A Tentative Gamma-Ray Line from Dark Matter Annihilation at the Fermi Large Area Telescope” by Christoph Weniger, and “Strong Evidence for Gamma-ray Line Emission from the Inner Galaxy” by Meng Su and Douglas P. Finkbeiner, Nataf states: “The first version of the abstract of the second paper comments on how the energy is very close to that of the Higgs, I think they suggest the dark matter particle might decay into the Higgs.” 

Peter Shor in the same comments section on Woit’s blog states: “you can easily add sterile heavy right-handed neutrinos to the Standard Model, and that these could both explain dark matter and the low mass of the left-handed neutrinos [using the see-saw mechanism], so maybe Occam’s razor actually predicts the Standard Model with added heavy sterile neutrinos.”  Massive (125 GeV) right-handed neutrinos could decay, but since they are fermions (with spin-1/2) it’s hard to see how they can decay into bosons (with integer spin), unless there is some mechanism for spin angular momentum to be conserved.  For example, to conserve spin angular momentum, a massive spin-0 boson could be emitted when a 125 GeV right-handed neutrino decayed into a left-handed, trivial-mass neutrino.


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