On Particle Production from Bubble Collisions in the Non-runaway Regime

Abstract

Particle production from bubble collisions during First-Order Phase Transitions (FOPTs) has been studied as an efficient mechanism for baryogenesis and dark matter production, but existing semi-analytical treatments assume runaway bubbles with wall velocity $v_w\to 1$. We generalize this treatment to arbitrary $v_w< 1$, relevant for scenarios such as electroweak baryogenesis and transitions with significant wall friction. We first extend the analytical trapping-equation approach to finite-thickness boosted kink profiles for both elastic and inelastic collisions, then go beyond this by numerically solving the full Klein-Gordon equation without assuming $SO(1,1)$ symmetry or thin walls, across a broad grid of $v_w$ and potential shapes. We find the analytical generalization underestimates the true efficiency factor by orders of magnitude away from $v_w\to 1$, and provide new semi-analytic fit functions consisting of a power-law continuum plus a resonance peak, which reproduce the main spectral features of the numerical results across the parameter range studied. Applying these to a toy dark sector model, we show particle production is strongly suppressed as $v_w$ decreases from unity, enhanced for lighter produced particles, and that the relative contribution from the oscillatory peak differs from prior runaway-regime estimates. We also discuss limitations of the trapping equation and the off-shell effective-action truncation underlying this formalism.