Average number of the lightest supersymmetric particles in decay of superheavy particle with long lifetime

Abstract

We calculate the average number v of the lightest supersymmetric particles (LSPs) in a shower from the decay of the superheavy particle X by generalized DGLAP equations. If the primary decayed particles have color charges and the virtuality is approximately 10 - 10 GeV, the average number of the LSPs can become O(100). The result shows that the upper limit of the mass of the superheavy particle, whose decay can produce the observed abundance of dark matter, can increase from 10 12 GeV to 10 14 GeV. Since the typical scale of the inflaton mass of the chaotic inflation is approximately 10 13 GeV, the decay of the inflaton can produce the observed dark matter abundance if the reheating temperature is on the order of 1 GeV. Even for standard model particles with a virtuality Q ∼ 10 - 100 TeV, the average number of LSPs becomes O(0.1) for gluon, and O(0.01) for Higgs, which strongly constrains the scenario of nonthermal LSP production from the decay of moduli with a 10 - 100 TeV mass range.