# How does the Super-Kamiokande experiment falsify SU(5)?

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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.

1. 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.

2. 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.

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

4. 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:

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

2. 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?

3. 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
Excellent questions! I don't really have time for an answer now, but may come back to one. In the meantime check out this relevant Q&A. PDG review on GUTs is here (pdf). See especially the sections on gauge coupling unification starting on pg. 4, Figure 15.1 (which is already enough to rule out the classic SU(5)) and nucleon decay starting pg. 9. Zee has nice introductory chapters in his QFT book. And there are many other reviews out there...

This post imported from StackExchange Physics at 2014-03-30 15:14 (UCT), posted by SE-user Michael Brown
@DImension10AbhimanyuPS Why, do you think he's a bit loopy?!! Actually I liked the book from the autobiographical perspective, and at least Smolin seems to be one of the few criticizing string theory (which I have no grasp of BTW) from a standpoint of having gotten the expertise in the field himself. I thought he kind of gainsaid himself on one of the main themes - the supposed lack of falsifiability of ST - because he also seems to say do not underestimate the craft of the astronomers and experimentalists who come up with ingenious and unforeseen ways to test the seemingly untestable...

This post imported from StackExchange Physics at 2014-03-30 15:14 (UCT), posted by SE-user WetSavannaAnimal aka Rod Vance
@DImension10AbhimanyuPS ... all the time. So, whilst the lack of falsifiability so far seems to be a problem, it would seem a bit too soon to say there never will be one - that's from an outsider's point of view. That experimental discovery slows down relative to the work put in is not surprising. Another experimentalist who seems to know her stuff on this site also seems to be of the view that the string theorists will turn some symmetry up that will further "organizes" the experimental results.

This post imported from StackExchange Physics at 2014-03-30 15:14 (UCT), posted by SE-user WetSavannaAnimal aka Rod Vance
@MichaelBrown Thanks muchly for the PDG review, I've only just become aware (two days ago) of the PDG's expositions so I need to get more in the habit of checking them out. My main "teacher" on this stuff has so far been John Baez.

This post imported from StackExchange Physics at 2014-03-30 15:14 (UCT), posted by SE-user WetSavannaAnimal aka Rod Vance
@DImension10AbhimanyuPS Smolin is a deliberate provocateur with a minority viewpoint, and so gets put on the banned list for a certain kind of person. But any time there is a dominating theoretical program without any direct experimental support it is helpful to have such different, non-crackpotty, voices around. Of course take what he says with a healthy grain of salt and verify everything you can for yourself, but that applies for every author. ;) ...

This post imported from StackExchange Physics at 2014-03-30 15:14 (UCT), posted by SE-user Michael Brown
... I liked Smolin's autobiographical reflections as well, but I find he wanders into philosophy and sociology too often when I feel he ought to be writing about physics. Anyway, PDG reviews are pretty good for what they are: mostly terse data dumps. For good pedagogy you ought to go elsewhere, like Baez.

This post imported from StackExchange Physics at 2014-03-30 15:14 (UCT), posted by SE-user Michael Brown
Some comments on your points 1-4. 1. The simplest way to break the SU(5) symmetry is with a second Higgs field, in addition to the one which subsequently breaks SU(2)xU(1) to U(1). 2. Yes. 3. Quarks and leptons would still be fundamental, but they are classified into larger and fewer multiplets (5- and 10-dimensional reps of SU(5)) than in the SM. 4. The new ingredient is that a quark can become a lepton (or vice versa), thanks to the extra SU(5) bosons (X and Y particles, or leptoquark bosons). It's rare because they are heavy. The proton disintegrates e.g. into a pion and a lepton.

This post imported from StackExchange Physics at 2014-03-30 15:14 (UCT), posted by SE-user Mitchell Porter
@MitchellPorter Thanks for the further insights. "It's rare because they are heavy." Is this part of the answer? The rest masses of the X and Y are part of the energy hurdle that must "rarely" be tunneled through?

This post imported from StackExchange Physics at 2014-03-30 15:14 (UCT), posted by SE-user WetSavannaAnimal aka Rod Vance
@DImension10AbhimanyuPS I actually think, reading between the lines of Smolin, that if push came to shove and people seriously talked about forsaking ST altogether, he would be thoroughly horrified. He's being polemical of course. He's just saying that maybe theory is too blinkered and that maybe too many resources are put torwards ST - he's also clearly someone who has had high expectations of what his generation ought to have been able to do, yet didn't, and that is the source of his worry. Comparing himself to the after WWII generation (when things could be experimentally tested at much ...

This post imported from StackExchange Physics at 2014-03-30 15:14 (UCT), posted by SE-user WetSavannaAnimal aka Rod Vance
@DImension10AbhimanyuPS ...lower energies) maybe leads him to be too harsh on himself and his peers. As he says, experimentalists come up with dazzlingly unforeseen, clever ways of testing stuff all the time, so maybe science just has to wait a bit longer than science thought it would be waiting.

This post imported from StackExchange Physics at 2014-03-30 15:14 (UCT), posted by SE-user WetSavannaAnimal aka Rod Vance
@WetSavannaAnimalakaRodVance Have you successfully resolved this question yet? If you haven't, I think you should consider putting a small bounty. If you have, please do write an answer.

This post imported from StackExchange Physics at 2014-03-30 15:14 (UCT), posted by SE-user dj_mummy
@dj_mummy No, still hoping to answer it myself sometime, but the bounty might be a good idea.

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

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