Particle productions during collisions of highly boosted bubble walls

Abstract

We investigate the production of particles much heavier than the characteristic scale of a cosmological first-order phase transition through collisions of highly boosted bubble walls. Using the scalar order-parameter field, we derive the ultraviolet behavior of its Fourier-space profile for both elastic and inelastic collisions. In the regime $χ\equivω^2-\mathbf{k}^2\gg M_h^2$, we find the universal result $\tildeϕ(χ) = -2V^\prime(2v_ϕ)χ^{-2}+O(χ^{-3}),$ implying that the spectral density scales as $F(χ)\propto [V^\prime(2v_ϕ)]^2χ^{-4}$. Thus, heavy-particle production is localized near the instant of collision and, at leading order, depends on the scalar potential only through $V^\prime(2v_ϕ)$. We verify this behavior using high-precision numerical solutions of the trapping equation, carefully suppressing spectral leakage from the finite integration domain, and obtain agreement over a broad ultraviolet range. We then derive analytical production rates for general heavy-particle thresholds and for fermion pairs, together with their cosmological number density and yield. Finally, we extend the analysis to $(3+1)$ dimensions and incorporate the finite bubble radius, finding an order-one suppression relative to the parallel-wall approximation. Our results revise the ultraviolet scaling used in previous treatments and have direct implications for superheavy dark-matter production and baryogenesis from bubble collisions.