The physically meaningful Aharonov-Bohm phase of a test quark in a superfluid is that of the dressed charge

The claim states the Hayashi camp's position in the vortex-statistics debate. Primary sources read for this and the prior pass: Y. Hayashi, "Higgs-confinement continuity and matching of Aharonov-Bohm phases," Phys. Rev. Lett. 132, 221901 (2024), arxiv.org/abs/2303.02129, which computes Aharonov-Bohm phases in lattice models and finds smooth connection between the confining and Higgs regimes; and A. Cherman, T. Jacobson, S. Sen, L. G. Yaffe, "Line operators, vortex statistics, and Higgs versus confinement dynamics," JHEP 06 (2024) 200, arxiv.org/abs/2401.17489, which constructs the phase of a vortex-line operator linking an electric Wilson line in a 2+1D lattice gauge theory and shows it distinguishes the regimes.

How the subclaims weigh. The load-bearing premise on the affirming side, that physical test-quark states in a superfluid are unavoidably dressed by the gapless mode↗︎, appears essentially undisputed as a statement about finite-energy states; the opposing camp's reply targets the choice of probe, not the dressing mechanism. The agreed fact that dressed-quasiparticle phases interpolate smoothly↗︎ makes the dressed prescription internally coherent but cannot by itself establish that the dressed phase is the meaningful one. On the denying side, the lattice demonstration that the undressed correlator phase changes non-analytically↗︎ is solid published analysis showing the undressed quantity has sharp gauge-invariant structure; whether that structure is physically meaningful is precisely what the detectability criterion↗︎ decides. That criterion subclaim has now been assessed in its own right and stands contested, which matches the reading this assessment already rested on: both camps' inferences are valid conditional on opposite answers to a definitional question, so the verdict is contested rather than supported or contradicted. This is a symmetric, published disagreement about the choice of observable, not an evidential imbalance.

The follow-up flagged as undigested in the prior pass has now been read: T. Hayata, Y. Hidaka, D. Kondo, "Phase transition on superfluid vortices in Higgs-Confinement crossover," JHEP 03 (2025) 006, arxiv.org/abs/2411.03676, demonstrates by Monte Carlo simulation in a U(1)gauge x U(1)global model that spontaneous Z2 flavor symmetry breaking occurs on vortex worldlines in the Higgs regime but not the confining regime, with the two regimes separated by a second-order transition of 2D Ising universality class, despite the bulk showing only a crossover. This is a genuine, in-principle-detectable sharp distinction localized on vortices. It strengthens the general position that the Higgs and confining regimes are not everywhere smoothly connected, and it shows the non-analytic structure seen by undressed probes can align with a real localized transition. It does not, however, adjudicate the specific criterion question this claim turns on, namely whether the dressed or undressed Aharonov-Bohm phase is the physically meaningful one; the vortex-localized order parameter is a different diagnostic. A search for direct 2025 rebuttals from either camp on the phase-choice question found none that resolves it.

No credence is given: the claim is a definitional or criterion choice, not a yes-or-no empirical matter, and a single probability would be false precision. What would change the verdict: a result showing that measurable consequences (vortex-quasiparticle scattering cross-sections, transport coefficients, or an experimentally realizable interference protocol) are controlled by one phase or the other, which would convert the criterion dispute into an empirical one; or a demonstration tying the correlator nonanalyticity necessarily to the vortex-localized transition, which would consolidate the denying side's case that sharp structure is physical.