Is it possible that rescuing the Idea of a Baryo/lepto-dynamic Field had some Relevance in the FermiLab Result?

Gauging baryon number, lepton number, or a combination thereof, is a well-known option in particle physics. In particular, the combination "B-L" is often gauged, e.g. in Pati-Salam unification.

Dozens of models have been proposed to explain the currently prominent experimental anomalies (muon g-2, B-meson decay), and one would expect gauged B or L or B-L to make an appearance somewhere. And indeed, checking last Friday's arxiv reveals a paper on "muon g-2" in the "B-L supersymmetric standard model".

I won't try to rate the objective attractiveness of such models as an explanation of the anomalies, compared to other kinds of model (leptoquark, gauged flavor symmetry...). There are many possibilities in physics, there are many clues to new physics, I don't find this particular conjunction of question (how to account for the anomalies) and answer (let's gauge baryon and/or lepton number) to be compelling, but there are people working on it.

However, I will say that the paper you mention, is not at all representative of most research of this kind.

First of all, the equation of motion for the baryonic gauge field is not the usual one; it also contains higher-derivative terms. Higher derivatives in gauge theory are generally considered problematic (e.g. "Ostrogradsky instability"), but there are loopholes, and they can be motivated, so it's an established niche area of research.

Second, the author wants to explain the accelerated expansion of the universe - normally attributed to dark energy - to the effects of the higher-derivative terms. I find this intriguing, because one of the mysteries of dark matter is the extent to which "dark matter effects" track the baryonic (visible) mass of galaxies, in the case of galactic rotation curves. Critics of dark matter consider this evidence that the rotation effects are instead due to "modified" gravity, since gravitational effects would show that precise dependence on the amount of baryonic mass. But what if they somehow derive from baryon number, via the baryonic gauge field? ... One would have to check if it made sense quantitatively, but for now I am just intrigued by the possibility of explaining dark-sector phenomena via a baryonic gauge field.

But the paper doesn't stop there. In section 4D, the author proposes a cosmological model, in which the universe consists of a giant cluster of matter galaxies, and a giant cluster of antimatter galaxies, orbiting a common center of gravity, with each cluster experiencing accelerated expansion due to higher-derivative baryon-number same-sign repulsion, but the two clusters bound by higher-derivative baryon-number opposite-sign attraction. He doesn't write the equations for this, and in footnote 5 it seems clear that he is inspired by the thought that this is a literal giant yin-yang symbol.

So this is an eccentric, creative paper, working with a form of the baryon gauge field that is not the usual. The alleged cosmological effects are due to the higher derivative terms, and would not appear in the particle physics models unless the higher derivative terms are included there too.