In his book "The Trouble With Physics", Lee Smolin writes that he is still stunned by the falsification of the $SU(5)$ Georgi-Glashow model by the null results of proton decay experiments.

I should like a *simple* but, if possible, quantitative explanation of how $SU(5)$ is falsified by the null results of attempts like Super-Kamiokande to witness proton decay? Obviously this theory foretells proton decay and we haven't seen it, but have we waited long enough or looked hard enough to say at a reasonable confidence that the null result falsifies the theory?

I am not a particle physicist, and you might see my outsiders answer to "What is the significance of Lie groups SO(3) and SU(2) to particle physics?" to gauge my level of competence.

Here is my reasoning so far, so, unless it is wrong (if so, please correct me), please use the following to help structure an answer.

The Georgi-Glashow model postulates that the theory of the primordial universe was a gauge theory with $SU(5)$ structure group. So this symmetry of physical laws is exact in the absence of some symmetry breaking mechanism which has taken hold today. I would like to know if there is a succinct summary of what this symmetry breaking mechanism might be.

So, at high enough energies - much greater than the potential drop that physical systems today get from "falling down the potential hill" begotten by the symmetry breaking mechanism in (1) - particles of the standard model should behave according the ancient $SU(5)$-symmetric laws.

Quarks and leptons would show themselves not to be fundamental but to be superpositions of the particles of the $SU(5)$ theory.

So, quarks and leptons are indeed coupled and, at today's everyday energy levels, there should be a tiny, but nonzero rate of "jumping over the unification energy barrier" - quantum tunnelling - so that protons should slowly spontaneously become other superpositions of $SU(5)$ model particles - i.e. protons should "decay".

So, the rate of decay is related to the size of the unification energy.

Presumably, if $SU(5)$ can be deemed falsified, we have a reasonable confidence in an **upper** bound to the unification energy such that the very slow proton decay rates ($<10^{-34} \mathrm{year}^{-1}$) consistent with the Super-Kamiokande null result imply a unification energy well above this upper bound. Usually quantum tunnelling rates are exponentially dependent on barrier sizes, so that small errors in energy barriers mean huge errors in tunnelling rates, so I'd be intrigued to see an analysis of the sensitivity of results to observational uncertainties.

**So, in summary, here are my questions:**

How in detail are unification energies related to implied decay rates?

How do we know what the unification energies are, or plausibly could be? How can we be sure that the bounds on these energies imply we should be seeing proton decay?

Conversely, what could be the symmetry breaking mechanism for $SU(5)$?

Since these things are probably well known to the relevant people, references instead of detailed answers would certianly be acceptable to me.

This post imported from StackExchange Physics at 2014-03-30 15:14 (UCT), posted by SE-user WetSavannaAnimal aka Rod Vance