"Unification of gravity, gauge fields, and Higgs bosons", A. Garrett Lisi, Lee Smolin, and Simone Speziale (April 28, 2010)
We consider a diffeomorphism invariant theory of a gauge field valued in a Lie algebra that breaks spontaneously to the direct sum of the spacetime Lorentz algebra, a Yang-Mills algebra, and their complement. Beginning with a fully gauge invariant action – an extension of the Plebanski action for general relativity – we recover the action for gravity, Yang-Mills, and Higgs fields. The low-energy coupling constants, obtained after symmetry breaking, are all functions of the single parameter present in the initial action and the vacuum expectation value of the Higgs. . . .
All physical constants – including Newton’s constant, the cosmological constant, the Yang-Mills coupling and Higgs parameters – derive solely from g and the Higgs vev [vacuum expectation value].
In the theory, "g" is a number related in a simple way to the the Yang-Mills coupling constant, which is the constant that governs the strength of interactions in the strong force. There is one problem. The predictions of the equations "are clearly far from observed values[.]"
The result is all too typical in its rough elegance but ultimate failure. But, nevertheless, it is worth noting that physicists are getting better and better at creating equations that have all of the mathematical features necessary to replicate all of the laws of nature in a quantum mechanical way (including dark energy), even if they are struggling to get some of the details right.
* The nuclear strong force that holds atomic nuclei together is in theory perfectly explained by quantum chromodynamics (QCD). But, the math is too hard to make predictions that are as accurate as the experimental results that we observe. Two particular problems in calculating with QCD: "Chiral symmetry breaking and confinement." Neuberger from Rutgers briefly sums up the state of QCD at a technical level.
Confinement refers to the fact that the the strong interaction forces go from being weaker than electro-magnetic forces at short distances to being confining at long distances. As a result of confinement, given time to act, quarks always come in twos or threes, bound by the strong force (the top quark, which is the heaviest of the quarks, decays into a lighter quark, almost always the bottom quark, before it has time to bond with other quarks).
In addition to making it hard to understand the strong force, our lack of understanding of them adds uncertainty to calculations at particle accelerators in experiments designed to discover new particles and figure out the nature of the time symmetry violations that we observe in certain weak force (i.e. beta decay) events. Understanding chirality in this context is important, because we need to know how much of the left handed particle, right handed particle asymmetries that we observe coming out of these giant atom smashers is due to the strong force, which we thing we fully understand in theory, and how much is coming from the weak force, where there are still some mysteries.
* The noose continues to narrow around the possible characteristics of the Higgs boson, which is the highest priority for researchers at our atom smashers to identify. It is the only fundamental particle in standard model of particle physics that has not yet been discovered, and it is critical, because it imparts mass to everything else.
Experiments conducted to date have been narrowing in on how much a standard model Higgs boson could weight (almost all of its other characteristics are already determined by the theory). If it exists, these experiments show that it is very likely that its mass is in the region 114-157 GeV. Experiements have largely ruled out lighter Higgs bosons and heavier ones if the standard model is correct. It should be possible to determine if there is a Higgs boson of this mass by about 2013 if experiments in the works proceed as planned.
If it isn't found in this range, than theories dependent upon a standard model Higgs particle or something similar need to be refurbished to find some other way to give particles mass.
* In the less flashy, but vaguely reassuring department, Dutch physicist Th. M. Nieuwenhuize is making the case from careful observation of dark matter profiles in one of the best understood galaxies that observed dark matter (which is inferred from astronomical observations that show that gravity according to general relativity does not accurately describe the motion of celestial objects if only visible matter exists), could simply be a bunch of fast moving neutrinos of a mass of about 1.5 eV which is close to the theoretical prediction from other sources. This is called a "hot dark matter" theory (because the particles are moving at fast, although not relativistic speeds), which its proponent recognizes is controversial:
[These] predictions pose a firm confrontation to conclusions based on more intricate cosmological theories, such as the cold-dark-matter model with cosmological constant (ΛCDM model, concordance model). Indeed, our findings are in sharp contradiction with present cosmological understanding, where neutrinos are believed to be ruled out as major dark-matter source. Studies like WMAP5 arrive at bounds of the type mνe +mνμ +mντ 0.5 eV. They start from the CDM paradigm, or from a mixture of CDM and neutrinos, the reason for this being indirect, namely that without CDM the CMB peaks have found no explanation. But the CDM particle has not been detected, so other paradigms, such as neutrino dark matter, cannot be dismissed at forehand. The CDM assumption has already questioned and it is also concluded that WIMP dark matter has an eV mass.
A neutrino explanation of dark matter would also have the effect of throwing cold water on various extensions of the standard model that call for new stable particles, and on modified gravity regimes that would explain dark matter phenomena, because they would no longer be needed to explain physical phenomena.