Physicists Report New Mass Sum Rules for Quarks Following Koide Pattern
Researchers have reported a new mass relation of the Koide type — using an inverse-square formula — that applies to the down-quark sector with numerical precision comparable to the well-known charged-lepton Koide rule. The original Koide rule, discovered in 1982, is an empirical formula relating the masses of the electron, muon, and tau lepton with surprising accuracy, and has long intrigued physicists seeking patterns beyond the Standard Model. The new inverse rule suggests a deeper, possibly symmetrical structure connecting quark and lepton mass hierarchies, potentially offering clues to physics at very high energy scales.
A paper published in Physics Letters B and posted to arXiv reports a new empirical mass relation of the Koide type, expressed as an inverse-square formula m_i = M (w_0 + w_i)^{-2}, applied to the three down-type quarks (down, strange, bottom). The authors find that this 'inverse Koide rule' achieves numerical precision comparable to the original direct Koide rule for charged leptons, which has a Koide ratio of exactly 2/3. Under Standard Model renormalization-group running — the procedure that accounts for how particle masses effectively change with energy scale — the Koide ratio for the down-quark sector reaches exactly 2/3 near an energy of approximately 280 TeV. The paper also reviews other direct-type Koide-like rules involving quarks, broadening the survey of such empirical regularities. These findings are purely phenomenological at this stage, meaning they describe observed numerical patterns without yet providing a theoretical mechanism explaining why such relations should hold. If confirmed and theoretically grounded, such rules could point toward new symmetry principles or unification structures operating at very high energies well beyond current collider reach.
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- arXiv physicsCenter
New sum rules of the Koide type
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