L004 $R_{\mu e}^{\rm Au}$

In a warped lepton-flavor extension, \(\mu-e\) conversion probes more than the dipole structure tested by \(\mu\to e\gamma\). Tree-level or loop-induced lepton-quark vector and scalar operators, flavor-changing \(Z\)-like couplings, Higgs-mediated scalar currents, and dipoles can all contribute to the same coherent nuclear final state. A heavy target such as gold is useful as an existing benchmark, but its interpretation is target and operator dependent.

Since the arXiv:0804.1954 RS-flavor baseline, no newer gold-target result has replaced the SINDRUM II bound in the PDG listing (L004.yaml:pdg\_or\_equivalent.primary\_current\_limit; L004.yaml:pdg\_or\_equivalent.post\_2008\_baseline). The major change is the experimental program around lighter targets: the Mu2e Technical Design Report states an aluminum conversion search aiming for sensitivity approximately four orders of magnitude beyond the previous world-best conversion limits (L004.yaml:pdg\_or\_equivalent.post\_2008\_developments[0]), and the COMET Phase-I TDR quotes an aluminum sensitivity goal \(3.1\times10^{-15}\) with an expected \(90\%\) upper limit \(7.0\times10^{-15}\) (L004.yaml:pdg\_or\_equivalent.post\_2008\_developments[1]). Thus the gold limit remains the published benchmark, while future comparisons will need target-by-target translations.

The experimental statement is robust: it is a null search normalized to the ordinary muon-capture rate on gold. The mapping to RS parameters is not a single-number rescaling. It requires a lepton-quark effective operator basis, gold nuclear overlap integrals and capture normalization, and a convention for combining dipole, scalar, and vector amplitudes. Comparisons with aluminum or titanium limits are therefore model- and operator-dependent.

NO. The required greps over quarkConstraints/, qcd/, flavorConstraints/, neutrinos/, yukawa/, warpConfig/, solvers/, scanParams/, and tests/ found no SINDRUM, Mu2e, COMET, \(R_{\mu e}\), gold conversion, or muon-to-electron conversion implementation. The only adjacent charged-LFV code is the dipole-only \(\mu\to e\gamma\) checker at flavorConstraints/muToEGamma.py:75, called by the scan at scanParams/scan.py:524.

HIGH. A production constraint needs a new \(\mu-e\) conversion observable, lepton-quark Wilson coefficients, target-specific gold nuclear inputs, capture-rate normalization, and likely shared EFT matching/running with \(\mu\to e\gamma\) and \(\mu\to3e\). This is a new mode calculation, not an input-value update to the existing dipole checker.

Process-local source keys before bibliography consolidation: PDG2026\_MuonAuConversion, SINDRUMII2006\_GoldMuE, Mu2eTDR2015, COMETPhaseITDR2020, and CFW2008.