Single Parameter Matching of Ordinary and Novel (Dark Matter) Particles From Their Physical Equalities to Their Physical Differences

Abstract

Novel (dark matter) particles, while known to exist, refuse to show up explicitly. Theoretical approaches within the Standard
 Model (SM) as for example, looking for the dark photon with Feynman diagrams, in the process γγ −→ e+e , is
 still inconclusive (Xu, I. et al., 2022). However, empirical-like methods can give the proof about the existence of dark
 matter, see for instance (Clowe, D. et al., 2006). Hence it is reasonable trying to understand as to why ordinary and novel
 (dm) particles differ so much from each other. This we wish to do with solutions of the bicubic equation for particle
 limiting velocities ( ˇ Soln, J., 2014-2022). Once we have the solutions for novel and ordinary particle limiting velocities
 from ( ˇ Soln, J. 2021.1.2, 2022), we first establish, with the help of evolutionary congruent parameters, ordinary z1 and
 novel z2, satisfying z1 ⪯ 1and z2 ⪰ 1,the smooth matching point of equal values for ordinary and novel particles at
 z1 = z2 = 1. At this point the limiting velocities and other physical quantities of ordinary and novel particles have
 equal values, which can be also characterized by z1× z2 = 1; this, consistent with Discriminants of ordinary and novel
 limiting velocity solutions, is extended everywhere, so that z2 = 1/ z1. the novel particle limiting velocity solutions
 reveal congruent angle α, contained now in z1 and z2, and as such can also serve as another evolutionary parameter. The
 smooth matching point is now α = π/2. If physically equivalent ordinary and novel particles move away from this point
 to α ̸= π/2, they will physically be different from each other. In other words, the novel particle is in z2 ⪰ 1 territory, and
 the ordinary particle is in z1 ⪯ 1 territory and direct interactions are likely impossible. With this formalism, we investigate
 physical differences between ordinary and novel particles, when moving away from α = π/2. In tis article, we largely
 are dealing with high energy leptons together with relevant photons with congruent parameter ranges of 0 ≺ α ⪯ π/2,
 0 ≺ z1 ⪯ 1,∞≻ z2 ⪰ 1. In fact due to a large interest in photons, here, within this formalism, we evaluate very precisely
 limiting velocities for the ordinary and novel photons. From these evaluations, we deduce numerically that congruent angles
 of novel and ordinary photons are related through the quantum jump α(γN) = 2α(γ), which is verified also for other
 particles. Hence, the general quantum jump between congruent angles of limiting velocities associated with ordinary and
 novel particles is α(xN) = α(x), where x = γ, e, ν, etc. The congruent angle quantum jump connects every ordinary
 particle, such as electron e, or neutrino ν,respectively, to novel electron eN and novel neutrino νN. This, definitively is a
 rather simple way to identify novel particles. All that one needs is to find them.