> The standard model seems fine without vacuum energy > 0
This a bit confusing due the vacuum energy being a part of standard model.
> Are you aware of any experiment that suggests it, beyond the apparent acceleration of the expansion of the universe?
Yes. Heisenberg uncertainty, the BCS theory of superconductivity, the Higgs field. Also, the paper you linked provides a few.
>> However, to my knowledge no one has shown that source theory or another S-matrix based approach can provide a complete description of QED to all orders.
Quantization of electrodynamics.
>> In QCD confinement would seem to present an insuperable challenge to an S-matrix based approach, since quarks and gluons do not appear in the physical S-matrix.
Quantum chromodynamics.
But ultimately, the paper you linked is uninterested in showing that the vacuum energy is 0, and rather is intended to show that from their formulation the Casimir effect is able to be explained away without a vacuum state > 0 under certain conditions. This important distinction is central to the paper.
>> Even if one could argue away quantum zero point contributions to the vacuum energy, the problem of spontaneous symmetry breaking remains: condensates that carry energy appear at many energy scales in the Standard Model.
That said I’m skeptical of their methods. Since you are clearly an advocate for this paper, can you explain the crux of the paper, namely:
>> Casimir forces can be calculated without reference to the vacuum and, like any other dynamical effect in QED, vanish as α → 0.
What is even meant by allowing the fine structure constant to go to 0?
Because the stability of the standard model requires it to be constant.
And how a model that allows such a thing is a better representation of what is “real“.
Because the conclusion gets a bit wishy washy as it moves from the rigor of its maths to philosophy. (“real” vs “unreal”)
>> Still, no known phenomenon, including the Casimir effect, demonstrates that zero point energies are “real”.
In that regard I think the author would agree with my gp that rather than worry about “real”ness, to look at vacuum state as a consequence of the model we use to describe what we collectively accept as “real”.