Dispersive constraints on fermion masses

We demonstrate that fermion masses in the Standard Model (SM) can be constrained by dispersion relations obeyed hadronic and semileptonic decay widths of a fictitious heavy quark $Q$ with an arbitrary mass. These relations, imposing stringent connections between high-mass low-mass behaviors widths, correlate mass chiral symmetry breaking scale. Given known input from leading-order expansion threshold for products, we solve physical width. It is shown charm (bottom) $m_c= 1.35$ GeV ($m_b= 4.0$ GeV) determined relation $Q\to du\bar d$ ($Q\to c\bar ud$) $2m_\pi$ ($m_\pi+m_D$), where $m_\pi$ ($m_D$) denotes pion ($D$ meson) Requiring su\bar d\mu^+\nu_\mu$, u\tau^-\bar\nu_\tau$) $m_\pi+m_K$ ($m_\pi+m_\mu$, $m_\pi+m_\tau$) yields same mass, $m_K$ being kaon constrain strange (muon, $\tau$ lepton) to $m_s= 0.12$ ($m_\mu=0.11$ GeV, $m_\tau= 2.0$ GeV). Moreover, all predicted corresponding above agree data. pointed out our formalism similar QCD sum rules probing resonance properties, Pauli interference (weak annihilation) provides higher-power effect necessary establishing solutions (semilaptonic) widths. This work suggests parameters SM may not free, but arranged properly achieve internal dynamical consistency.