⚛️ phenomenology

Self-interacting dark matter from radiative bound-state-formation feedback

This paper demonstrates that radiative bound-state formation, particularly through the emission of charged scalars, can generate significant elastic scattering cross sections for self-interacting dark matter via unitarity feedback, even when the baseline elastic amplitude is zero, thereby providing a viable mechanism to explain galactic structure observations.

Original authors: Marcos M. Flores, Kalliopi Petraki, Thomas Pignard

Published 2026-10-21

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CC BY 4.0

Original authors: Marcos M. Flores, Kalliopi Petraki, Thomas Pignard

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Dark matter is the invisible substance that makes up most of the universe's mass, holding galaxies together with its gravity. While we know it exists because of how stars move and how light bends around massive objects, we do not know what it is made of. One leading idea suggests that dark matter particles might bump into each other, a behavior known as self-interaction. If these particles collide often, they could explain why the centers of small galaxies look different than our current theories predict. For this to work, the collisions must happen frequently when particles move slowly, as they do in small galaxies, but rarely when they move quickly, as they do in massive galaxy clusters.

To achieve this specific behavior, physicists often imagine that dark matter particles interact through a new, invisible force carried by a light particle called a mediator. This setup creates a long-range attraction, similar to how magnets pull on each other from a distance. However, if this force is strong enough to cause collisions, it also opens the door for more dramatic events. Just as an electron can lose energy by emitting a photon when it slows down, dark matter particles could lose energy by emitting a new particle and snapping together to form a bound pair, much like a planet orbiting a star. This process, called bound-state formation, is usually treated as a separate event from simple collisions. But a new study by Marcos M. Flores, Kalliopi Petraki, and Thomas Pignard reveals that these two processes are deeply linked. They found that the very act of forming these pairs creates a feedback loop that forces the particles to collide with each other, even if they were not supposed to interact at all before.

The researchers focused on a specific model where dark matter consists of particles that carry a hidden electric charge. In this scenario, two dark matter particles can come together and emit a charged particle to form a stable, bound pair. The team realized that in quantum physics, you cannot simply calculate the chance of a collision and the chance of forming a pair separately. Because the particles can turn into a pair and then potentially turn back, the mathematics requires that these possibilities be added together in a specific way to keep the laws of physics consistent. When the researchers performed this calculation, they discovered a surprising result: the process of forming bound states generates a new type of collision between the dark matter particles.

This is significant because, in their model, the dark matter particles normally do not feel any long-range force when they approach each other. They should pass right by one another without bouncing. Yet, the feedback from the bound-state formation creates an effective force that causes them to scatter. It is as if the particles are not directly pushing against each other, but are instead reacting to the possibility of becoming a pair, which in turn makes them bounce. The researchers found that this newly generated collision rate is not constant; it changes dramatically depending on how fast the particles are moving. At high speeds, the effect is tiny. But as the particles slow down, the likelihood of them colliding grows rapidly, eventually reaching levels strong enough to influence the structure of galaxies.

The study also examined what happens when the particle emitted during the pairing process has a small amount of mass. In the idealized case where this emitted particle is massless, the collision rate would keep growing as the particles slow down. However, because the emitted particle has mass, there is a limit to how much energy can be released. This acts as a natural brake, stopping the growth of the collision rate at very low speeds. Instead of growing forever, the collision rate flattens out and stays constant. This behavior is crucial for matching the observations of the universe. It allows the dark matter to interact strongly enough to reshape the cores of small, slow-moving dwarf galaxies, while remaining weak enough in fast-moving galaxy clusters to avoid contradicting observations there.

The implications differ depending on whether the universe contains equal amounts of dark matter and its mirror image, known as antiparticles, or if it is dominated by just one type. In a universe with equal amounts, the usual collisions between matter and antimatter are already strong enough to explain the data, and this new feedback effect plays a secondary role, mostly filling in gaps where the usual collisions are weak. However, in a universe where only one type of dark matter exists, the usual collisions vanish entirely. In this case, the feedback effect discovered by the team becomes the sole source of interaction. It provides a mechanism for these particles to collide and influence galaxy shapes even when no other force is present to make them bounce.

The researchers confirmed their findings through detailed numerical simulations, checking how the collision rates behave across a wide range of speeds and particle masses. They showed that this mechanism can satisfy the strict requirements set by observations of galaxy clusters and dwarf galaxies simultaneously. While the study focuses on the mathematical consistency of these interactions, it opens a new path for understanding how dark matter might behave. It suggests that the invisible architecture of the universe could be shaped not just by direct forces, but by the subtle, indirect consequences of particles constantly trying to bind together and then breaking apart. This work adds a vital piece to the puzzle of dark matter, showing that the rules governing how particles stick together are inextricably linked to how they bounce off one another.

Technical Summary: Self-interacting dark matter from radiative bound-state-formation feedback

Problem Statement
Observations of galactic structure suggest that dark matter (DM) possesses self-interactions that are sizable at the low velocities characteristic of dwarf galaxies and subhalos, yet remain weak at the higher velocities of galaxy clusters. This velocity dependence is naturally realized in models where DM interacts via light force mediators, leading to non-perturbative, long-range dynamics. However, the presence of light mediators also enhances inelastic processes, such as radiative bound-state formation (BSF). When inelastic channels open, the optical theorem imposes coupled unitarity constraints on elastic and inelastic scattering amplitudes. Standard treatments that resum only the elastic interaction kernel are insufficient in this regime. Specifically, the absorptive contributions from open inelastic channels must be incorporated into the two-particle self-energy kernel. The authors investigate the feedback of these inelastic processes—specifically radiative BSF via charged-scalar emission—on elastic scattering. A key motivation is to determine whether this feedback can generate a non-zero elastic cross section even when the baseline elastic amplitude vanishes, and to assess its phenomenological viability for Self-Interacting Dark Matter (SIDM).

Methodology
The authors analyze a scalar dark sector model containing a complex scalar DM field $X$ and a light scalar mediator $\varrho$ , both charged under a global $U(1)_D$ symmetry. The charges are assigned such that $X$ has charge $q_X=1$ and $\varrho$ has $q_\varrho=2$ , allowing the trilinear interaction $X^2\varrho^\dagger$ .

Baseline Dynamics: In this setup, same-charge particles ( $XX$ ) experience no long-range potential, while particle-antiparticle pairs ( $XX^\dagger$ ) interact via a Yukawa potential. However, $XX$ pairs can undergo radiative capture into $XX^\dagger$ bound states ( $B$ ) with the emission of a charged scalar $\varrho$ : $XX \to B(XX^\dagger) + \varrho$ .
Unitarization: The authors employ a unitarization formalism where the absorptive contributions from the BSF channel are resummed into the incoming state's self-energy kernel. This involves calculating the unregulated BSF amplitudes and cross sections, summing over the tower of accessible bound levels, and incorporating the principal-value (dispersive) contributions encoded in a Hermitian matrix $W_\ell$ .
Regulated Scattering: The resummation modifies the scattering amplitudes to satisfy coupled unitarity constraints. The authors derive expressions for the regulated elastic ( $x^{elas}_{\ell, reg}$ ) and viscosity cross sections, distinguishing between the effects of the absorptive kernel and the dispersive contributions from $W_\ell$ .
Phenomenological Analysis: The study evaluates the resulting velocity-dependent cross sections against SIDM benchmarks for galaxy clusters, dwarf galaxies, and subhalos. They compare two scenarios: symmetric DM (equal $X$ and $X^\dagger$ populations) and asymmetric DM (only $X$ survives).

Key Contributions and Results

Generation of Elastic Scattering from Inelasticity: The primary finding is that BSF feedback can generate a sizable elastic scattering cross section for same-charge particles ( $XX$ ) even in the absence of a baseline long-range elastic potential. This occurs because the inelastic transition $XX \to B + \varrho$ feeds back into the elastic channel via unitarity.
Velocity Dependence and Low-Velocity Enhancement:
- For a massless emitted boson, the induced elastic cross section grows rapidly as velocity decreases. In the low-velocity limit ( $v_{rel} \lesssim 4\alpha_\varrho^2$ ), the total elastic cross section scales as $\sigma^{elas}_{reg} \propto v_{rel}^{-4}$ , and the viscosity cross section exhibits a similarly steep dependence. This growth is driven by the increasing number of partial waves contributing to the capture process.
- Unlike standard Coulomb scattering, the partial-wave sums for BSF-induced scattering remain convergent at fixed velocities due to dynamical suppression of high- $\ell$ capture.
- For a massive mediator, the growth is curtailed at very low velocities by a kinematic cutoff on the accessible bound levels. If the ground-state capture channel remains open, the cross section approaches a constant s-wave plateau; otherwise, it vanishes.
Role of Dispersive Contributions: The inclusion of principal-value contributions ( $W_\ell$ ) is crucial. The authors show that these dispersive effects generally suppress or leave unchanged the generated elastic cross section relative to the approximation where $W_\ell=0$ , but they can significantly enhance the viscosity cross section by altering the interference between neighboring partial waves.
Comparison with Yukawa Scattering:
- In symmetric DM, the conventional Yukawa scattering between $XX^\dagger$ typically dominates the elastic transport. The BSF-induced $XX$ scattering is generally subleading, except near Yukawa antiresonances (Ramsauer-Townsend zeros) where the baseline Yukawa amplitude is suppressed. However, even in these regions, the parameter space satisfying cluster constraints is not significantly expanded.
- In asymmetric DM, where the $XX^\dagger$ channel is absent, BSF feedback provides the sole source of elastic self-interaction. This opens a qualitatively different realization of SIDM where the interaction is generated entirely by inelastic feedback. The resulting velocity dependence can satisfy cluster constraints while providing strong scattering at dwarf and subhalo scales.
Analytic Structure: The study highlights the importance of the analytic structure of the BSF amplitudes in the complex momentum plane. The resummation of the absorptive kernel, combined with the tower of bound-state poles, creates a distinct dynamical regime compared to hard inelastic processes like annihilation.

Significance
The paper demonstrates that inelastic processes, specifically radiative bound-state formation, are not merely sinks for particle flux but actively generate elastic scattering through unitarity feedback. This mechanism provides a novel pathway for Self-Interacting Dark Matter, particularly in asymmetric scenarios where baseline long-range forces between like-charged particles are absent. The authors claim that this feedback can produce velocity-dependent cross sections that satisfy astrophysical constraints across different halo scales, offering a distinct phenomenological signature compared to standard long-range potential models. The work complements their companion study on annihilation feedback, together providing a comprehensive picture of how inelasticity regulates elastic scattering in dark sectors with light mediators.

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