Existence of bound states in SIMP dark sectors
- Author(s)
- Daris Samart, Xiaoyong Chu, Josef Pradler
- Abstract
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 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, 𝐸𝐵 ∼𝑚𝜋/20
, we obtain |Ψ(0)| ∼𝒪(0.1)𝑚3/2𝜋, thereby supporting the parametric assumptions used in previous phenomenological analyses.- Organisation(s)
- Particle Physics
- External organisation(s)
- Khon Kaen University, University of the Chinese Academy of Sciences, Österreichische Akademie der Wissenschaften (ÖAW)
- Journal
- Physical Review D
- Volume
- 114
- No. of pages
- 26
- ISSN
- 2470-0010
- DOI
- https://doi.org/10.1103/qbd1-wqgl
- Publication date
- 08-2026
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 103034 Particle physics
- Portal url
- https://ucrisportal.univie.ac.at/en/publications/3a70b6cd-0af4-4d19-9cc2-34e49252ae44