Sommerfeld enhancement from unstable final-state particles in dark matter annihilation

Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: I'm Vera, and with me are Jocelyn and Subrahmanyan, guest researcher.

Jocelyn: Today's paper: "Sommerfeld enhancement from unstable final-state particles in dark matter annihilation".

Vera: This paper investigates the Sommerfeld enhancement (SE) of dark matter annihilation when it proceeds into heavier, unstable final-state particles, a phenomenon that significantly impacts predictions for dark matter relic abundance.

Jocelyn: First, who's behind it and why it matters.

Title and authors: Vera: Well, we're starting today with a paper titled "Sommerfeld enhancement from unstable final-state particles in dark matter annihilation." It looks like it tackles a really specific problem where dark matter annihilates into heavier, unstable particles. It suggests that when these products interact over long distances, their wave functions get distorted, which can boost the annihilation cross section significantly.

Jocelyn: That sounds complicated but interesting from an observational standpoint because it links microscopic particle physics to something we might be able to see in cosmological observations. The authors are Abe, Sato, and Yamanaka from Tokyo University of Science and Osaka University. I wonder how this enhancement factor actually translates into anything measurable in the sky or through relic density calculations.

Subrahmanyan: From a theoretical perspective, the focus on unstable final states is key because it introduces a dependence on the particle's lifetime, which fundamentally alters how we calculate these non-perturbative corrections. This isn't just about standard annihilation; it's about what happens when things decay while they are still interacting.

Vera: Exactly, and I think the title tells us the core issue is how long-range interactions affect particles that aren't stable. It suggests that we need a more complete way to handle these unstable states in our models of dark matter behavior.

Jocelyn: So, when we look at the results, I'm anticipating some constraints on what kind of dark matter particle might be relevant based on how strongly these long-range forces affect the annihilation cross section. It feels like it sets a new benchmark for how we predict relic abundance.

Subrahmanyan: Indeed, this work is important because it moves beyond simpler treatments where you just introduce a cutoff velocity to handle instability. This paper seems to look at the full physics, including those processes with off-shell final state particles that might be missed by approximations like the cutoff method.

Vera: That's what I'm hoping we hear about; a full picture that includes everything near the threshold. It suggests our current predictions for dark matter relic abundance might need serious re-evaluation if these long-range effects are significant.

Jocelyn: It’s exciting because it points toward specific mass ratios and potential structures that will actually lead to observable deviations in cosmological predictions, which is something we can look for in the data.

The paper's summary: Vera: So, digging into the summary of "Sommerfeld enhancement from unstable final-state particles in dark matter annihilation," they are essentially looking at how long-range forces between annihilation products distort their wave functions when they get close to the kinematic threshold. They find that this distortion can cause a substantial enhancement in the annihilation cross section.

Jocelyn: It seems like the core mechanism is that if these products experience long-range interactions, their wave functions aren't just simple plane waves anymore, and this change directly boosts the annihilation rate. The paper shows that this enhancement factor depends heavily on whether those final state particles have a narrow or a large decay width.

Subrahmanyan: That dependence on the decay width is what makes it tricky, because for narrow widths, you get bound states that cause a resonant effect, whereas for large widths, you automatically account for processes involving off-shell particles. This distinction is crucial for understanding the physics in these scenarios.

Vera: So the summary highlights that the lifetime of the final state particle dictates whether we see bound state effects or just general off-shell contributions, which is a vital piece of information for model building. It shows this factor isn't just a minor correction but can be quite substantial when resonances are present.

Jocelyn: And I think what's most telling is that the formulation automatically includes both bound state effects and those contributions from annihilation processes involving off-shell final state particles, which is a big plus for completeness.

Subrahmanyan: Precisely, this unified treatment is superior to previous work that often had to rely on introducing a cutoff velocity, like v cut = p /m two which only includes the enhancement if the dark matter velocity is larger than that threshold.

Vera: That comparison with the cutoff method is really important because it shows where those simpler methods fall short, especially since the full formulation allows for annihilation processes to be kinematically allowed even when energy is below the threshold due to off-shell effects.

Jocelyn: That means we can predict cross sections that are non-zero in regimes where simpler models would say they should be zero, which opens up new avenues for exploring parameter space.

The paper's improvements: Vera: The paper points out several ways this formulation improves upon existing research, specifically by using Schrödinger equations that explicitly include the decay width of the annihilation products. This is a step up from just treating the instability as a simple cutoff.

Jocelyn: They show that this detailed approach allows them to derive an expression for the annihilation cross section, -sigma v rel = two S f(E two), where S f(E two) is the enhancement factor that captures both bound state effects and off-shell contributions.

Subrahmanyan: The paper notes that for a narrow decay width, bound states create a resonant enhancement near the threshold, while for a large decay width, it automatically covers the off-shell particles. This distinction shows how the physics naturally separates itself based on the final state's lifetime.

Vera: And they apply this to specific potentials, like the attractive Coulomb potential and the attractive Hulthén potential, showing that they can identify resonant enhancements at energies corresponding to specific bound states, such as 1s, 2s, and 3s states.

Jocelyn: I'm interested in the condition they set for consistency: the annihilation rate of the chi two two state into chi one one must be much smaller than the total decay width. This consistency check is a rigorous way to ensure their method is physically sound.

Subrahmanyan: And they compare this to previous work by noting that the full formulation is consistent only if two to one where two to one is the partial decay rate of the bound state into chi one one ensuring the relevant annihilation rate is dominated by that specific decay. This tight constraint is important for validating their approach.

Vera: It seems like a really robust set of checks, moving from simple velocity cutoffs to this full quantum mechanical treatment involving coupled Schrödinger equations and careful handling of the decay width.

Conclusion: Jocelyn: So, wrapping up the paper "Sommerfeld enhancement from unstable final-state particles in dark matter annihilation," the main implication is that solving these coupled Schrödinger equations including the decay width is necessary to correctly capture resonant effects. They confirm that this method works consistently when two to one which means we can trust their predictions for dark matter relic abundance in regimes where resonances are expected.

Subrahmanyan: From the cosmic perspective, the impact is that for attractive potentials like the Coulomb potential, they show that the enhancement is indeed present in certain energy ranges and isn't negligible. This means we might be seeing deviations from previous methods for mass ratios above m two/m one one point zero zero one two, which directly alters the predicted mass spectra that reproduce the observed relic density.

Vera: That alteration in the predicted mass spectra is significant because it means that our understanding of what kind of dark matter particle we're looking for to match observations might need adjustment based on these results from this paper. It shows the final-state SE isn't just a small tweak; it can change the fundamental predictions.

Jocelyn: So, in short, this research provides a more rigorous framework for calculating annihilation cross sections when instability is involved, and it offers concrete examples of how to predict resonant effects using both bound states and off-shell particles.

Subrahmanyan: I just want to emphasize that the consistency condition two to one is what makes this method reliable for multi-component models, suggesting it can be extended beyond these two-body scenarios.

Vera: It’s a solid piece of work that solidifies the necessity of this complex treatment when dealing with unstable final states in dark matter annihilation calculations. We'll take a moment to process all this information before we move on to the next topic.