How far ahead are we in Grand Unified Theory? Are we still searching for proton decay?
Moderator's note: Moved to Beyond the Standard Model forum.
I see papers on experimental bounds on proton decay every few years or so. The last experimental result I blogged on it was in August of 2015, where I summarized the finding stating with a link to my source that:
The latter research results were restated in a 2017 paper considering the DUNE experiment. The Particle Data Group summarizes the experimental literature on proton decay here.
Another 2015 paper looked at prospects for improving the current limitation with experiments that were in progress. So, anyway, we are probably due for a new experimental result sometime in the next year or two. On the other hand, there has only been a one or two order of magnitude improvement in the experimental exclusion since 1979 when it was about 1031.
The experimental exclusion for proton decay is one of the most strict exclusions in the area of experimental tests of the SM, along with baryon number violation and lepton number violation which are also very throughly ruled out to the current limits of experimental precision. But, efforts to further limit the parameter space of these things continues because lots of theories that it would be nice to have be true call for them.
There is certainly no GUT that works yet, that has been proposed. Papers exploring GUTs are written on a regular basis month in and month out and have been for decades. FWIW, my gross perception from reading a lot of pre-prints without doing a proper statistical analysis is that the most popular directions are minimalist GUTs such as SU(5) and minimal SU(10) GUTs (see also, e.g. SM particles plus a small number of massless scalar bosons and maybe a gravitino) and E8 theories. And, of course, there are always proton decay is just around the corner papers (also here).
Glashow opined about a year ago that the non-detection of proton decay pretty much ruled out SU(5) unification models which are the most minimalist theoretically possible GUTs. Non-detection of SUSY-GUT particles has also been problematic as there are naive reasons to expect that they should appear not later than 20 TeV and we are now ruling out these particles in the single digit TeV range.
A prediction for proton decay assuming virtual blackholes as a mediator was made in this 2017 paper. A 2017 paper makes a (funding driving IMHO) argument that proton decay might first start to be discernible in a 100 TeV collider. Another 2017 paper argues that non-detection of proton decay implies strict SUSY parameter space limits.
A notable 2016 paper explored a mechanism by which a GUT that did not predict proton decay could be realized. Another more recent paper along the same lines is discussed in this thread.
Thank you for your detailed reply with links; it's helpful.
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