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High-energy standard model (SM) particles in the early Universe are generatedby the decay of heavy long-lived particles. The subsequent thermalizationoccurs through the splitting of high-energy primary particles into lower-energydaughters in primordial thermal plasma. The principal example of such processesis reheating after inflation caused by the decay of inflatons into SMparticles. Understanding of the thermalization at reheating is extremelyimportant as it reveals the origin of the hot Universe, and could open up newmechanisms for generating dark matter and/or baryon asymmetry. In this paper,we investigate the thermalization of high-energy SM particles in thermalplasma, taking into account the Landau--Pomeranchuk--Migdal effect in theleading-log approximation. The whole SM particle content and all the relevantSM interactions are included for the first time, i.e., the full gaugeinteractions of SU(3)$_c\times$SU(2)$_L\times$U(1)$_Y$ and the top Yukawainteraction. The distribution function of each SM species is computed bothnumerically and analytically. We have analytically obtained the distributionfunction of each SM species after the first few splittings. Furthermore, wedemonstrate that, after a sufficient number of splittings, the particledistributions are asymptotic to certain values at low momentum, independent ofthe high-energy particles injected by inflaton decay. The results are useful tocalculate the DM abundance produced during the pre-thermal phase. An example isprovided to illustrate a way to calculate the DM abundance from the scatteringbetween the thermal plasma and high-energy particles in the cascade.

Cascades of high-energy SM particles in the primordial thermal plasma