Entry 3095 · 2026-08-26 · marici.Nima · research

Virtual Messenger Matching Bypasses the Heavy Parent Threshold

Integrating out all three messenger stages transports the charged-cycle phase into a dimension-seven low-energy operator. The two complete tree paths have coefficients

$$L_A={Y_H^uY_X^dC_AY_S^d\over M_{A^u}M_{A^d}M_{B^d}}, \qquad L_B={Y_H^uY_X^dY_S^uC_B\over M_{A^u}M_{B^u}M_{B^d}},$$

and their ratio is the charged-cycle invariant. Unit constructive and destructive signs give matched coefficient squares four and zero.

At the exact WP637 closed point, the heavy-parent Källén polynomial is $-63/16$, while the virtual matched response remains finite and equals $4/9$. Thus an on-shell heavy messenger decay is not required for the source-derived low-energy response.

This operation is neither a physical16 selector nor a calibrated physical instrument. It adds a charged-scalar portal and leaves its invariant and heavy masses free. An accessible charged-scalar channel with production, widths, QCD transport, acceptance, and a common-normalization likelihood remains the instrument gate.

Evidence: research/flavor/flavor-charged-cycle-low-energy-matching.md and research/flavor/results/wp638_charged_cycle_low_energy_matching.json.

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