Well of course the big problem is that the only way to truly close the parameter space would be to be able to probe matter at the GUT scale, or roughly a quadrillion times the energy we can currently produce at the LHC. All of particle physics today is hoping that the Standard Model is wrong when it predicts an energy Desert (particle physics) - Wikipedia where there is nothing new to see.
If a business magnate was suspected of embezzling $17,613,816,408, and his brother’s Swiss bank account suddenly had a deposit of $17,613,816,408, and they argued that it was just a fine-tuning coincidence and that it’s perfectly plausible that those numbers are the same randomly, you’d presumably laugh at their audacity.
This is the level of fine tuning the strong CP problem represents. It very much is a problem that needs investigation. Occam’s razor demands it. It’s way too likely that we’re missing something deep and explanatory.
But more than that, the proposed mechanism for solving the issue uses the same mathematical infrastructure that is already a fundamental part of how the Standard Model operates. The introduction of a spontaneously broken symmetry is at the very heart of the SM and is what leads to the presence of one (or more) Higgs bosons. The axion is in the same vein, and the additional symmetry (to go with all the others already present) doesn’t feel like an overreach at all, especially since it solves the very real strong CP problem and also provides a dark matter candidate particle as a bonus.
This isn’t an accurate description of the dark matter search strategy. People aren’t making up new particles and then searching for their new particle. Rather, two main classes of dark matter candidates have been around for donkey’s years: WIMPs and axions. They both – but mostly WIMPs – can be added as an extension to the Standard Model in countless ways, and people indeed continually explore these ways. But that is all largely irrelevant to the actual search. The search simply cares about the mass and the effective coupling (think “interaction probability”) of the particle. And the 2D parameter space of mass and coupling is large.
In fact, to claim that the search has been unsuccessful, one must invoke arguments that I think you would eschew. In particular: The WIMP explanation for dark matter has a history beyond just “weakly interacting” and “massive”. Indeed, the field was very excited by the so-called WIMP miracle. The miracle is that a particle with (1) an interaction strength roughly the same as things like neutrinos (so, the well-known “weak interaction” strength) and (2) a mass roughly the same as the electroweak scale (so, like the Higgs mass or Z/W boson masses) yields the right dark matter density in the current universe. A miracle! It’s so tidy, it has to be right! And, supersymmetry was a hot topic over the past decades that happened to easily yield suitable WIMPs.
However, the actual mass and coupling of the WIMP (or WIMPs) could be wildly different from these miracle values. But, it was at least a motivation for where to start searching. Alas, nothing has been found in that region.
So, which region to focus on next? Two answers: (1) wherever is experimentally easiest to access next, or (2) wherever your next favorite “miracle!” lives. Ideally, you can do both. In the case of WIMPs – regardless of any fancy new models that motivate a particle at some particular mass or coupling values – the searches are simply striving to go to lower masses and lower coupling strengths. That’s all there is to be done. For axions, the details of the story are different but the result is the same: search first in the most “natural” areas, and then continue. (Axion searches have only tipped their toes so far into the “natural” range, though.)
It is a separate question whether physicist effort is being spent “optimally”. I certainly have my own opinions about where resources ($$$) should go and where they are perhaps less likely (in my subjective estimation) to yield progress. But that’s why we have decadal planning procedures and standing project prioritization committees. And at the moment, on the whole, these searches are still considered cost effective (in part because they aren’t as expensive anyway, in comparison to the behemoths in the field).
Discussed above, but to be sure: the axion picture came about in the 1970s and neither it nor the WIMP picture for dark matter has changed substantively since then. The search isn’t like whack-a-mole. It’s just a matter of improving the technology to be able to detect such subtle signals (and ever more subtler ones after, as the easiest masses and couplings to access are ruled out first).
For the record, I am playing a bit of devil’s advocate here. At least I’m arguing with what I think is Sabine’s position, which I may have slightly misinterpreted. In any case, my actual position isn’t quite as strong as it might sound.
It’s something that deserves an explanation, certainly. What I’d counter is that the idea that we’re missing something explanatory is supposition. Occam’s Razor is just a guideline, after all–while we’d certainly like it if one particle could explain multiple unknowns, there does come a point where you have narrowed the remaining search space so much that multiple alternatives become more likely.
I may have chosen a somewhat bad example with the strong CP problem. Specifically because there isn’t a really obvious anthropic argument for it–it doesn’t seem like the universe would blow up if it were violated, unlike many other fine-tuning problems, such as the small cosmological constant. Still, looking around, it seems that anthropic arguments aren’t quite ruled out, either.
And, well, supersymmetry has been something of a bust as well. So the miracle may not have been so miraculous after all. Of course, the same things are true there: we just haven’t built a big enough particle accelerator, so we can’t rule out supersymmetry just yet.
Maybe, but neither is very satisfying. #1 is like the joke about the drunk man searching for his car keys under the streetlamp at night. That isn’t where he lost them, but it’s the only place where he can see.
Ok, a true Bayesian would say no problem: we have to multiply by the probability of finding them, if they’re there, so sometimes it’s actually better to search where you can find things, even if the odds of them actually being there are lower. It’s just not a good position to be in.
As for #2, there do seem to be quite a few miracles in physics floating around–they’re a dime a dozen in string theory, for example, where somehow the math works out so well that it can’t be a coincidence, can it? But that hasn’t been so productive, either.
I don’t really have any answers here. Maybe the search is as close to optimal as it could realistically get. It could just be that we’re in a really difficult part of the physics landscape, where the “easy” pieces have come together and it really is just a long, arduous search for the rest (the “desert”, as Lumpy mentions). It just seems that we aren’t trying quite hard enough to make a map of the problem instead of blindly fumbling around with our arms stretched out, hoping to slightly expand the small area where we’ve searched.