New Polynomial Law of Hadron Mass

Abstract

A simple and general law of mass, intrinsically with zero freely-adaptable parameters, is shown to be valid for all the hadrons with one or more flavored (s, c, or b) quarks/antiquarks, both baryons and mesons. It establishes correspondences H-->{P_i} between these hadrons with at least one flavored constituent, H, and specific sets of lighter particles, {P_i}, in which the total baryon and lepton numbers are conserved. The law is polynomial with a varying degree that univocally depends only on the particles involved. Its statement may be given straightforwardly in terms of the binomial series converging to 1/sqrt{1-beta}. It asserts that, for each hadron H, there exists a certain set of lighter particles {P_i}, together with a specific reference hadron h_0 that fixes the mass scale, such that, for a value of the sum of this power series equal to the mass of H, a definite partial sum of the series equals the total mass of particles {P_i}. The starting, independent data in the rule are the masses of the hadrons with exclusively unflavored (u and d) constituents (among which, our hadrons h_0, such as the proton or pion) and the masses of leptons. The consequence of the law is a pre-discretization of the mass spectrum of the hadrons containing at least one flavored constituent, on account of which the mass of any of them may only assume one of the values aprioristically determined by the total masses of lighter particles.