Existence of bound states in SIMP dark sectors
Daris Samart, Xiaoyong Chu, Josef Pradler · Physical review. D/Physical review. D. · 2026
In strongly interacting massive particle (SIMP) scenarios, dark matter is comprised of stable dark pions whose 3 → 2 or 4 → 2 reactions set the dark matter relic abundance. Recent work has shown that shallow two-pion bound states significantly affect the freeze-out, but did not establish whether such states actually form. In this work we demonstrate that a scalar isosinglet bound state does exist in a well-defined region of parameter space by solving an on shell Lippmann-Schwinger equation in a chiral-unitary framework and analyzing the S -wave π π amplitude in the complex energy plane. We determine the range of m π / f π and the momentum cutoff for which a pole appears below the two-pion threshold, extract the corresponding residue, and, in the nonrelativistic limit, obtain the bound-state wave function at the origin, | Ψ ( 0 ) | , which controls bound-state-assisted annihilation and decay rates relevant for catalyzed freeze-out. Comparing this T-matrix based result with variational estimates using simple finite-range potentials, we find agreement within order-one factors for shallow binding. For binding energies of order the freeze-out temperature, E B ∼ m π / 20 , we obtain | Ψ ( 0 ) | ∼ O ( 0.1 ) m π 3 / 2 , thereby supporting the parametric assumptions used in previous phenomenological analyses.