One-flavon flavor: A single hierarchical parameter $B$ organizes quarks and leptons at $M_Z$

Abstract

Flavor hierarchies emerge from a single hierarchical parameter $B$ in a one-flavon Froggatt--Nielsen scheme. Fixing $B=5.357$ from charged-lepton ratios ($m_e:m_μ:m_τ\!\propto\!e^5:e^2:1$, $e=1/B$), we reproduce quark masses and CKM targets at $M_Z$ with $O(1)$ coefficients. The same $e$ gives viable lepton textures and benchmarks for $U_{\rm PMNS}$, $\sum m_ν$, and $m_{ββ}$. Compact correlations ($|V_{us}|,|V_{cb}|,|V_{ub}|,θ_{13}^{\rm PMNS}$) follow from powers of $e$.

Figures (1)

• Figure 1: Underlying $\mathcal{O}(1)$ coefficients, extracted by dividing observables by their predicted FN scaling power $p$. Masses are converted to Yukawas $y_f = m_f/v_f$ assuming a Type-II 2HDM, with $v_{\rm SM}=174.1$ GeV. Up-sector coefficients $\{y_u,y_c,y_t\}$ (using $v_u \approx v_{\rm SM}$) and mixing coefficients $\{|V_{ij}|,\theta_{13}\}$ are independent of $\tan\beta$. Down-sector and lepton coefficients $\{y_d,y_s,y_b,y_e,y_\mu,y_\tau\}$ scale as $\approx \tan\beta$ (since $y_f = m_f/v_d$ and $v_d \simeq v_{\rm SM}/\tan\beta$). The plot shows that $\tan\beta=40$ keeps these coefficients $\mathcal{O}(1)$, while $\tan\beta=10$ suppresses them to $\sim 0.1$. Powers $p$ are $\{y_u,y_c,y_t\}:\{7,3,0\}$, $\{y_d,y_s,y_b\}:\{4,2,0\}$, $\{y_e,y_\mu,y_\tau\}:\{5,2,0\}$, $\{|V_{us}|,|V_{cb}|,|V_{ub}|,\theta_{13}^{\rm PMNS}\}:\{1,2,3,1\}$. For the single--Higgs SM baseline, one instead takes $v_f=v_{\rm SM}$ for all fermions; the down-sector and lepton coefficients are then uniformly reduced by a factor $\sim 1/40$, leaving the hierarchy of exponents unchanged (see Appendix \ref{['app:coeffs']}).