Are SM B & L conservation violations through sphalerons possible?

[ohwilleke]

TL;DR Summary

A new Letter seems to state that baryon number and lepton number violations in Standard Model sphaleron states aren't mathematically possible after all. I'm not asking if the claim is really true or not. But I want to make sure I understand the claim that is being made properly.

It isn't often that you see this many bold claims in a five page Letter, the abstract and citations of which appears below.

The conclusion I find most interesting is this Letter's conclusion that contrary to the current consensus understanding of the mathematics of the Standard Model (mostly the QCD part), there is actually no mechanism by which baryon number and lepton number violation can occur in the Standard Model via sphaleron states.

Sphaleron interactions at very high energies are the only interactions in the Standard Model of Particle Physics that violate the separate conservation of baryon number and lepton number, although these interactions still conserve baryon number minus lepton number (B-L).

The Letter seems to argue that an overlooked aspect of the consensus vanilla mathematics of the QCD part of the Standard Model (which is a nonabelian gauge theory) actually rules out this possibility.

But this terse Letter could be more clear than it is on this point. It also doesn't help that the author, who is writing in English, is evidently not fluent in English at the native language speaker level of fluency. This is certainly no ding to the author's accomplishments or scientific merit, but it does make the Letter harder to understand.

I'm trying to determine, however, if the claim being made in the Letter is really that strong, or if I'm missing or misunderstanding some subtle limitation in this claim (e.g. that one kind of B&L conservation violation in the Standard Model with a sphaleron is ruled out while other sphaleron sourced violations are not, or that the Letter is not ruling out non-perturbative effects).

To be clear, I'm not asking for an evaluation of the merit of the claim being made, I'm just trying to be sure that I understand what the Letter is asserting that its author has discovered.

Put another way, I'm looking for an intermediate level description of one part of an advanced level paper.

The Letter's abstract, its citation, and a link to a 54 page power point presentation further elaborating on the 5 page letter is as follows:

We show that the topological charge of nonabelian gauge theory is unphysical by using the fact that it always involves the unphysical gauge field component proportional to the gradient of the gauge function. The removal of Gribov copies, which may break the Becchi-Rouet-Stora-Tyutin symmetry, is irrelevant thanks to the perturbative one-loop finiteness of the chiral anomaly. The unobservability of the topological charge immediately leads to the resolution of the Strong CP problem. We also present important consequences such as the physical relevance of axial U(1) symmetry, the θ-independence of vacuum energy, the unphysicalness of topological instantons, and the impossibilities of realizing the sphaleron induced baryogenesis as well as the chiral magnetic effect. The unphysical vacuum angle and the axial U(1) symmetry also imply that the CP phase of the Cabibbo-Kobayashi-Maskawa matrix is the sole source of CP violation of the standard model.

Nodoka Yamanaka, "Unobservability of topological charge in nonabelian gauge theory" arXiv:2212.10994 (December 21, 2022) (Letter. It will be followed by a full paper. Slides explaining graphically the discussion are given in this https URL).

Full paper at https://arxiv.org/abs/2212.11820

 

[mitchell porter]

The Letter seems to argue that an overlooked aspect of the consensus vanilla mathematics of the QCD part of the Standard Model (which is a nonabelian gauge theory) actually rules out this possibility.

I'd put it differently. The author thinks he has discovered that one of the many breakthrough concepts of 1970s quantum field theory, topological charge, is illusory, with numerous implications e.g. sphalerons don't do anything, there's no need for axions, and the mass of the eta-prime meson needs a different explanation.

The argument seems to boil down to the assertion that the path integral for topological charge involves an unphysical degree of freedom (longitudinal mode of the gauge field), see slide 12. The crucial part of the path integral is the coupling of an axially charged field to the gauge field tensor and its dual (see the triangle diagram in slide 23). He argues that the field values are infinitesimal here (slide 21) and so we don't need to worry about Gribov ambiguity (slides 15-17), and we also don't need to worry about complications from external fields outside the triangle (slide 22) because of 't Hooft anomaly matching / the Adler-Bardeen nonrenormalization theorem.

Surely we can find a classic calculation involving topological charge, carried out in a formalism where the author's argument is supposed to be valid, and check whether the argument makes sense?

Meanwhile, if you want a physics blogger to ask about this stuff, you could try Peter Woit, since his thesis was about topological charge!