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 $\chi \equiv {\omega }^2-{\mathbf{k}}^2\gg M_h^2$, we find the universal result $\tilde{\varphi }(\chi )=-2V^{\prime }(2v_{\varphi }){\chi }^{-2}+O({\chi }^{-3}),$ implying that the spectral density scales as $F(\chi )\propto [V^{\prime }(2v_{\varphi }){]}^2{\chi }^{-4}$. Thus, heavy-particle production is localized near the instant of collision and, at leading order, depends on the scalar potential only through $V^{\prime }(2v_{\varphi })$. 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.

Comments: 43 pages, 5 figures, 1 table