By comparing muon (µ ±) production, and decay rates in the cosmic plasma as a function of temperature, Rafelski and Yang found that the temperature at which µ ± disappear from the Universe is about Tdisappear ≈ 4.195 MeV. Below this temperature the µ ± decay rate is faster than the production rate.
Rafelski and Yang in their recent paper presented the thermal production and the natural decay rate of muons µ ± in the primordial Universe as a function of temperature. They concluded that µ ± disappear from the Universe at about T = T_disappear ≈ 4.195 MeV, the temperature at which the natural µ ± decay rate overwhelms production rate. The characteristic expansion rate 1/H(T_disappear) = 0.084 s in that epoch is 3.8 × 104 longer compared to the muon lifespan τ_µ = 2.2µ s, therefore muons vanish quasi-instantaneously on the scale of the Universe expansion time.
We also relate the muon abundance to baryon abundance. The number density muons (nµ±) and Baryons (nB) abundances are equal at the temperature T ≈ 4.212 MeV ≧ Tdisappear, where nµ± /nB(Tdisappear) ≈ 0.911. We see that the muon pair abundance T = 6 MeV exceeds that of baryons by a factor 1000.— told Rafelski, first author of the study.
To characterize the physics situation more precisely, they have also evaluated the density ratio between µ ± and baryons in the Universe as a function of temperature. They considered as a function of temperature the density ratio between µ ± and the baryon inventory in the Universe. They assumed that the ratio B/S, baryon per entropy, measured today applies in this primordial epoch. Using this understanding of Universe entropy content, and of ee¯ annihilation neutrino reheating, they have shown that both abundances are equal within the error margin of measured entropy and baryon content values: At the temperature T ≈ 4.212 MeV they have nµ± /nB = 1 while the density ratio at the muon disappearance temperature nµ± /nB(Tdisappear) ≈ 0.911. Since only about half of baryons are protons, as long as muons are present, they have always at least four charged nonrelativistic muons for each proton and then, rather suddenly, muons disappear.
The primary insight of their work is that aside of protons and neutrons, other nonrelativistic charged particles, both positively and negatively charged muons, µ ±, are present in kinetic thermal equilibrium and in nonnegligible abundance T > T_disappear ≈ 4.2 MeV, with a cosmic coincidence of muon pair and baryon abundances coinciding at T_disappear within error margin in regard to baryon abundance in the Universe. Presence of muon pairs offers a new and tantalizing model building opportunity for anyone interested in baryon-antibaryon separation in the primordial Universe, strangelet formation, and perhaps other exotic primordial structure formation mechanisms.
Moreover, our result furthermore shows that muons remain in thermal equilibrium abundance in the entire time period in which strangeness evolves down to T_disappear ≃ 4.2 MeV. We will return to this context in another report.— Concluded authors of the study.
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Reference: Jan Rafelski, Cheng Tao Yang, “The muon abundance in the primordial Universe”, ArXiv, pp. 1-10, 2021. https://arxiv.org/abs/2103.07812
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