This work quantitatively deals with the fundamental issue of the origin of particles. By focusing initially on the relation between mass and magnetic moments for baryons, we then show that a wealth of experimental data, including the form of the observed flux profiles of cosmic rays protons can be consistently analyzed together if one takes as the starting point of the model that these particles condense from a vacuum, in the form of loops of charge. This brings back the long standing issue of whether particles should strictly be treated theoretically as point-like objects, or otherwise might have an intrinsic motion formally accounted for, which might be related to an effective finite size. Such issue arises in the socalled zitterbewegung solution of the point-like particle´s Dirac equation, which introduces the intrinsic motion of a “point” electron in the center of mass frame. The present treatment also applies the Dirac equation, and we obtain regularized loop-like solutions for the fields representing embryonic baryons. The fundamental “proton state” is taken as a substrate, as proposed by Barut many years ago. A loop can be regarded as a particle “embryo” and is a sizeable ( wavepacket) rather than a point-like object, tenths of a femtometer big when detached from the vacuum parent state. Such vacuum state is predicted as 2.7 GeV above the proton rest mass, which is consistent with the average protons energy in the energy profile of interstellar cosmic rays. According to statistical mechanics, this characterizes U0 =3.71 GeV as the environment equilibrium energy in which protons were formed(big-bang conditions?). Other features of such energy profile can readily be understood from the present analysis.