Final bound-state formation effect on dark matter annihilation

If two annihilation products of dark matter(DM)particles are non-relativistic and couple to a light force mediator,their plane wave functions are modified due to multiple exchanges of the force mediator.This gives rise to the final state Sommerfeld(FSS)effect.It is also possible that the final state particles form a bound state.Both the FSS effect and final bound-state(FBS)effect need to be considered in the calculation of the DM relic abundance.The annihilation products can be non-relativistic if their masses are comparable to those of the annihilating DM particles.We study the FSS and FBS effects in the mass-degenerate region using two specific models.Both models serve to illustrate different partial-wave contributions in the calculations of the FSS and FBS effects.We find that the FBS effect can be comparable to the FSS effect when the annihilation products couple strongly with a light force mediator.Those effects significantly modify the DM relic abundance.