2025/12/09 by Chu, Xiaoyong, Pradler, Josef, Samart, Daris
Physics and Astronomy · #Dark Matter and Cosmic Phenomena #FOS: Physical sciences #High Energy Astrophysical Phenomena (astro-ph.HE) #High Energy Physics - Phenomenology (hep-ph) #High-Energy Particle Collisions Research #Quantum Chromodynamics and Particle Interactions
paper · doi:10.48550/arxiv.2512.08517
openalex publication_date 2025/12/09 · openalex created_date 2025/12/11 · openalex updated_date 2026/07/28
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 ππ amplitude in the complex energy plane. We determine the range of mπ/fπ for which a pole appears below the two-pion threshold, extract the corresponding residue, and, in the non-relativistic 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, EB ∼ mπ/20, we obtain |Ψ(0)|∼ O(0.1) mπ3/2, thereby supporting the parametric assumptions used in previous phenomenological analyses.