A relaxed version of Koide's mass formula from Yukawaons: classical and SUSY scenarios.

We present a relaxed version of Koide's mass formula from a nonet Yukawaon scalar in the $\mathrm{SU}(3)$ flavor symmetry. Koide's character $K$, which involves the Standard Model fermion masses, is derived from vacuum expactation values of Yukawaons in both classical and supersymmetric scenarios. Requirements from the flavor symmetry and renormalizability leave two free parameters in the scalar potential or the superpotential of Yukawaons. One of the free parameters provides possible loop-level mass corrections, while the other parameter modulates Koide's character $K$ in the relaxed mass formula from the original formula. The parameter modulating $K$ may also provide quark mixing in a similar Yukawaon model coupled to the quark sector.