This is a crosspost from Physics Forums about the state of experimental searches for proton decay and the implications of those searches for "grand unified theories" (GUTs) which often predict proton decay.
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 Super-Kamiokande Experiment has used an independent method to exclude proton decay and related di-nucleon decays involving protons to charged leptons, neutrinos, photons and neutral and invisible to the experiment's detector's X particles, up to very large mean lifetimes on the order of 10^31 to 10^32 years.
So, over the life of the universe, the fraction of protons that decay as measured by these methods is less than one per 10^21protons (in words, less than one hundred per gram of protons, and probably less than ten per gram of protons).
Previous studies using other methods have set a minimum proton lifetime on the order of 10^33 to 10^34 years, i.e. 1.0 to 0.1 such decays per gram of protons over the entire lifetime of the universe, or put another way, less than 1 such decay per 10 kilotons of protons per year (a measurement of truly stunningly great precision). A kiloton of protons is pretty much indistinguishable in mass from a kiloton of hydrogen at this level of precision in measurement."
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 10^31.
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.