I've never been a fan of the axion as a solution of the strong CP non-problem. A new paper suggests that using an axion to address the lack of CP violation in the strong force also has other technical problems.
The non-viability of the QCD axion also makes the axion-like particle dark matter candidate less well motivated.
The axion, originally postulated by Peccei and Quinn to solve the strong CP problem, has become of great interest in particle and astroparticle phenomenology.
Yet it has a problem. It is widely assumed that the axion leaves the nonperturbative features of QCD, such as the axial anomaly and chiral symmetry breaking, unscathed. This is, however, not the case.
It turns out that the anomalous coupling of the axion to the gauge bosons can be integrated partially, leaving behind a path integral extending over topologically trivial gauge potentials only. This has far reaching consequences. We conclude that the Peccei-Quinn axion extension of the Standard Model is not a viable theory.
Gerrit Schierholz, "Repercussions of the Peccei-Quinn axion on QCD" arXiv:2307.08310 (July 17, 2023).
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How old is our universe? New study says Big Bang might have happened 27 billion years ago
https://academic.oup.com/mnras/advance-article-abstract/doi/10.1093/mnras/stad2032/7221343?redirectedFrom=fulltext&login=false
The study is dubious garbage as I explained at https://www.physicsforums.com/threads/new-research-puts-age-of-the-universe-at-26-7-billion-years.1054053/#post-6914905
This QCD-revisionist paper is kind of the reverse of the one you blogged about here. The one last year was arguing that there is no such thing as topological charge. This one is arguing that QCD needs topological charge (which is the conventional view), and that QCD+axion is unviable because it produces a theory without topological charge (not the conventional view).
The conventional view of QCD is that theta is a free parameter which empirically is close to zero. Schierholz has been proposing for thirty years that theta is dynamically driven to zero.
So, just to emphasize, he's making two *mathematical* claims (not physical claims) in contradiction to everyone else in the field: That the theta angle of QCD, rather than being a free parameter, dynamically goes to zero by itself. And that QCD coupled to an axion field, does not even have a theta parameter.
Also, to make his argument that QCD+axion is physically unviable, he appeals to something that all his colleagues *do* agree with, which is that you need topological charge to explain certain hadronic observations.
I'll emphasize that there is a difference between a theory in which topological charge is a well-defined property that happens to equal zero, and a theory in which there is no property of topological charge at all. Schierholz's whole claim with regard to axions, seems to be that when you couple an axion field to QCD, rather than integrating over field configurations with different winding topology, arriving at an expectation value for topological charge, you should project out field configurations with nontrivial topology, excluding them apriori and thus allowing no possibility of topological fluctuation of the gauge field, and no possibility of topological charge.
I assume that the only reason Schierholz's "heresy" has survived this long, is the gap between lattice calculation, heuristic approximation, and rigorous results, when it comes to QCD. There's no rigorous proof of anything when it comes to QCD, but there are ansatz and lattice calculations which add up to the conventional paradigm. Schierholz, meanwhile, has different ansatze and different lattice calculations to buttress his own paradigm. For example, on the ansatz side, he insists on performing a particular integration involving the axion field, in a different way than usual.
Anyway, hopefully it's clear that there's no real reason to trust the claims in this paper, since they don't involve a physical argument, but rather an idiosyncratic interpretation of the non-rigorous mathematical evidence.
@Mitchell
That's a helpful explanation.
As a postscript, today I studied what it is that string theory says about axions - where roughly speaking, an axion is a scalar whose vev will drive the theta angle of some gauge group to zero.
Basically, compactification produces many axion-like string states. However, they either tend to all be superheavy (and thus too heavy to be the hypothesized QCD axion), or if there is a light axion, there tend to be many different species of light axion (which should have phenomenological consequences). So basically, a generic string model that has a light QCD axion will also have an "axiverse" of other light axion species contributing to the dark matter.
My own favorite approach to "why QCD theta equals zero" is still the massless up quark, partly because Gia Dvali wrote a paper arguing that for this solution, the eta-prime meson basically functions as an axion! Unfortunately, he's written a bunch of other papers about how there has to be an axion for every gauge group, which I think are just wrong. Anyway, I thought this might interest you.
Thanks. Dvali's paper is now on my "to read" list.
My favorite heuristic answer to the strong CP "problem" continues to be the fact that the QCD gluon doesn't have rest mass, so gluons move at the speed of light and don't experience the passage of time in their own reference frame (just like photons in QED which also doesn't have CP violation), so it makes no sense of them to violate t-symmetry, which is equivalent to violations of CP conservation.
Also, just because QCD can have a theta term doesn't mean it has to have one. No observations require it, so Occam's razor means it is unnecessary.
It isn't our place as scientists to tell Nature that it must choose dimensionless physical constants of O(1).
With regard to your idea about up quarks with a mass of zero, I can see where you are coming from but:
(1) At the observed level the up quark has non-zero mass at more than eight sigma, so the relevant CP violation precent quantity would have to be some quantity other than observed effective rest mass would have to be zeroed out (e.g., in the SM all SM fermions have zero rest mass prior to considering their Higgs field interactions, which might be the correct way to think about it for purposes of CP violation).
(2) My explorations of extending Koide's rule masses for quarks considering all three opposite type quarks that a quark can transform into via W boson interactions (as opposed to the mere two other possibilities that exists for charged leptons in the original Koide's rule) by starting with a Koide triple of the two most probable W boson transforms and tweaking that value by approximate the mass of the omitted quark transformation probability times the probability of the transformation, favors a baseline mass very close to a zero up quark mass when just considering the impacts of the up, down and strange quark triple, before figuring in modification of that value for up quark to bottom quark transformations via W bosons. Tweaking the light quark triple to account for up quark to bottom quark transformations then bring the up quark mass to close to experimentally measured value. So, there's that. It is sort of like putting in a "texture zero" in an initial matrix used to get quark masses in some theories for rest mass in quarks.
(3) Also, I am quite impressed by the observation that all weakly interacting SM fundamental particles have rest mass (all fermions with the possible exception of the lightest neutrino, the W, the Z, and the Higgs boson), while no SM fundamental particles that don't interact via the weak force have rest mass (photons, gluons, and hypothetically, gravitons), a coincidence that I suspect is fundamental. So, in both the up quark and the lightest neutrino mass, I think that this theoretical consideration strongly favors a very small non-zero value by any reasonable definition, rather than a zero rest mass value.
Of course, when something is true, there can be multiple logical reasons for its truth (there are dozens or hundreds of different proofs of the Pythagorean theorem, for example).
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