The flavour of SU(15) composite quarks and leptons

We study the flavour structure of an $SU(15)_p$ confining chiral gauge theory in which the Standard Model (SM) quarks, leptons, and Higgs emerge as composite bound states. The couplings of two scalar fields in the conjugate antisymmetric ($\overline{\mathbf{105}}$) and conjugate symmetric ($\overline{\mathbf{120}}$) representations of $SU(15)_p$ provide two $SU(4)_F$ flavour-breaking spurions that generate both the SM Yukawa couplings and the flavour-changing processes. The up and down Yukawa matrices are tightly-correlated due to a "right-handed isospin" symmetry, which predicts a trivial CKM matrix in the absence of spontaneous symmetry breaking. The lepton Yukawas are correlated with the quarks due to a common source of flavour spurions. With a judicious Froggatt-Nielsen-like texture for the two flavour spurions we find that a benchmark fit with $\mathcal{O}(1)$ non-perturbative coefficients reproduces all six quark masses, three charged lepton masses, and the CKM matrix. The same spurions mediate charged lepton flavour violation, neutral meson mixing, rare kaon decays, and induce electric dipole moments. We compare the reach on the compositeness scale $\Lambda_{\rm pre}$ across these observables in the numerical benchmark and find that the electron EDM and $K^0$-$\bar{K}^0$ mixing provide the strongest sensitivity, reaching $\mathcal{O}(10^4)$ TeV, the lower end of the range probed by proton decay, while $\mu\to e\gamma$, $D^0$-$\bar{D}^0$ mixing, and $\mu$-$e$ conversion give complementary reach at $10^2$-$10^3$ TeV. The projected electron EDM sensitivity extends this to $\mathcal{O}(10^6)$ TeV, beyond the reach of planned proton decay searches.