New sum rules of the Koide type

Alejandro Rivero

doi:10.1016/j.physletb.2026.140510

paper

New sum rules of the Koide type

arXiv:2606.10060 · doi:10.1016/j.physletb.2026.140510

Abstract

We report a mass rule of Koide type with inverse shape, \[m_i=M^{(d)} (w_0+w_i)^{-2}.\] It applies to the down-quark sector with numerical precision comparable to that of the direct charged-lepton sum rule $m_{i} = M^{(l)} (z_{0} + z_{i})^{2}$ . For central mass values, Koide ratio reaches exactly $2/3$ near 280 TeV under Standard Model renormalisation-group running. We also review other rules of the direct kind involving quarks.