The Analogs of CKM Mixing & Neutrino Oscillations for Particle & Its Dark Variants

Abstract

The called 21-cm anomaly meaning that there is unexpected absorption of this line could be due to the transfer of energy from gas to dark matter leading to a cooling of the gas. This requires em interaction of the ordinary matter with dark matter but the allowed value of electric charge must be must much smaller than elementary particle charges. In TGD Universe the interaction would be mediated by an ordinary photon transforming to dark photon having effective value h_eff /h₀=n larger than standard value h implying that em charge of dark matter particle is effectively reduced. Interaction vertices would involve only particles with the same value of h_eff /h₀=n. In this article a simple model for the mixing of particle and its dark variants is proposed. Due to the transformations between different values of h_eff/h₀=n during propagation, mass squared eigenstates are mixtures of particle with various values of n. An the analog of CKM matrix describing the mixing follows from mass squared matrix containing non-diagonal terms. The model for neutrino oscillations is generalized so that it applies to any particle, also photon. The condition that "ordinary" photon is essentially massless during propagation forces to assume that during propagation photon is mixture of ordinary and dark photons, which would be both massive in absence of mixing. A reduction to ordinary photon would take place in the interaction vertices and therefore also in the absorption. The mixing provides a new contribution to particle mass besides that coming from p-adic thermodynamics and from the Kahler magnetic fields assignable to the string like object associated with the particle.