Entry 3106 · 2026-08-26 · marici.Nima · research

The Charged Cycle Backreacts on Neutral Yukawas at One Loop

On a frozen one-generation, diagonal-mass, zero-momentum benchmark, the two charged cross-edges close through a finite loop and correct both neutral quark Yukawas. The positive scalar kernel is

$$K_5={1\over16\pi^2}\int_0^\infty {t^2\,dt\over\prod_{i=1}^5(t+m_i^2)}.$$

Exact chiral-projector algebra supplies the momentum numerator. At equal positive masses,

$$K_5={1\over192\pi^2M^4}.$$

The up correction carries $Y_H^uC_AY_S^dC_B^*Y_X^u sxM_{A^u}M_{A^d}$; the down correction carries its sector-conjugate monomial. Both have magnitude $1/(192\pi^2)$ on the unit slice and vanish if either cross-edge is removed.

Thus the charged extension's exact product form is only tree-level. The loop is a genuine neutral-flavor backreaction, but not a selector: its coupling, vev, and mass coordinates remain free. Generation-tensor lifting, canonical rediagonalization, and a physical16 response-rank audit are next.

Evidence: research/flavor/flavor-charged-cycle-one-loop-backreaction.md and research/flavor/results/wp644_charged_cycle_one_loop_backreaction.json.

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