Regularities in electromagnetic decay widths

We revisit Sakurai’s remark on the regularities of lepton-pair widths for mesons, extending the panorama to radiative X → γγ decays. The regularities persist, and somehow surprisingly some of them seem to relate with Fermi’s constant -or Z-. Back in 1978, Sakurai took the opportunity of a festscrift [11] to remark how the study of vector meson decays V → γ → ee, when extended to J/Ψ and Υ, seemed to have confirmed an empirical rule of Yennie [14] about the universality of Γ(V → ee). On other hand a universality in the effective coupling gXγγ for pseudoscalars X = π, η is well known popularly and we have recently noticed that it seems to extend to vector mesons, particularly to J/Ψ, when interpreted as a virtual process for total decay width. And also radiative transitions as Σ → Λγ happen to be in the adequate range. Our purpose here is to review all the radiative decays well measured in the modern data tables in order to establish how significant these regularities are. 1 All total decay widths We can try to get some perspective by plotting all the decay rates of subnuclear particles. This can be done straightly from the tables provided by the particle data group [15] in its website http://pdg.lbl.gov/. One can see three layers corresponding to decays strong, electromagnetic or weak, with the neutron being appart from the rest of weak decaying particles due to its quark composition. The area of strong decay is actively pushed forward by experimentalists, and one can see how the actual advances hit on one hand the need of having a noticeable width in the resonance plot, say Γ < E0, and on the other hand enough area. We have plotted the lines E0 Γ = (1GeV ) , Γ = kE0 (k = 1, 0.5, 0.25) as reference, but we excuse ourselves about plotting the mass against spin dependence famously reported in Chew-Frautschi plots. When particles can not decay strongly -either because there are no other hadronic mode available, or because any available mode should change quark flavours or because asymptotic freedom activates OZI rulethey give way to electromagnetic decay or to weak decay. In the weak decay area spectator models and other approaches (even plain dimensional analysis) point to a Γ ∼ m scaling, and we have drawn one such line from the muon. Note that such line in a spectator model should be used to meet the mass value of the decaying quark, not of the whole particle. The intermediate area, electromagnetic or radiative decays (we are using both terms as exchangeable ones in this context), is the one we are interested. We have EUPT, Univ de Zaragoza, Campus de Teruel, 44003 Teruel, Spain email: [email protected]