Universality of Planck's constant and a constraint from the absence of h_bar-induced neutrino mixing

Abstract

You have probably often set hbar=1; but for what particle? I revisit here the possibility of a non-universal Planck-constant. Anomaly cancellation suggests that all particles in the same family perceive the same hbar at fixed charges e, g_w, g_s; the difference between the muon's and the electron's (and thus the first and second families) can be tightly constrained by the muon's anomalous magnetic moment,but constraints are weaker for the third family. Neutrino mixing could have proceeded a priori not only by the Lagrangian neutrino mass-term, but also by the kinetic term if Planck's constant was not equal for all three species. An experimental constraint follows as such contributions, characterized by oscillations proportional to the energy, as opposed to the inverse energy, have been generically analyzed in the past. This provides at the same time support for gauge invariance. On the other hand if hbar differs among particles while fixing the fine structure constants alpha_em, alpha_s, etc. instead of the charges, it affects the muonic atom puzzle without much constrain from g-2.