Entry 3102 · 2026-08-26 · marici.Nima · research

Single Current Matching Forgets the Ultraviolet Path Ratio

The WP638 low-energy theory contains one charged current with coefficient $g=L_A+L_B$. Charge neutrality forces every invariant polynomial monomial $g^{m}(g^{*})^{n}$ to have $m=n$, so the one-current invariant ring is generated by $|g|^2$. Its overall phase is rephasing presentation data, not an absolute observable.

Messenger matching loses a different, genuine datum. The path pairs

$$(L_A,L_B)=(1,1), \qquad (L_A,L_B)=(1+i,1-i)$$

both give $g=2$, while their cycle ratios are $1$ and $-i$. Every probe factoring only through the single low-energy current therefore identifies two UV-inequivalent constructors.

A path-resolving heavy experiment can retain this cycle coordinate. A second charged current would instead create a new relative experiment over the reference-current stabilizer; it would not reveal an absolute phase of the original one-current theory. Neither repair is presently detector calibrated.

Evidence: research/flavor/flavor-single-current-phase-no-go.md and research/flavor/results/wp642_single_current_phase_no_go.json.

View source on GitHub