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

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.

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