AI 中文总结
研究高加速泡壁碰撞产生重粒子，利用标量序参量场推导紫外行为，通过数值解验证，得出解析产生率等结果，扩展到\((3 + 1)\)维并考虑有限泡半径，修正了紫外缩放，对暗物质和重子生成有影响。
AI 中文摘要
我们研究了通过高加速泡壁碰撞产生比宇宙学一阶相变特征尺度重得多的粒子。利用标量序参量场，我们推导了弹性和非弹性碰撞中其傅里叶空间分布的紫外行为。在\(\chi\equiv\omega^2-\mathbf{k}^2\gg M_h^2\)的区域，我们得到通用结果\(\tilde{\phi}(\chi) = -2V^\prime(2v_\phi)\chi^{-2}+O(\chi^{-3})\)，这意味着谱密度按\(F(\chi)\propto [V^\prime(2v_\phi)]^2\chi^{-4}\)缩放。因此，重粒子产生集中在碰撞瞬间附近，且在主导阶仅通过\(V^\prime(2v_\phi)\)依赖于标量势。我们用俘获方程的高精度数值解验证了这种行为，并仔细抑制了有限积分域的谱泄漏，在宽紫外范围内得到了一致结果。然后我们推导了一般重粒子阈值和费米子对的解析产生率及其宇宙学数密度和产额。最后，我们将分析扩展到\((3 + 1)\)维并纳入有限泡半径，发现相对于平行壁近似有一个量级为一的抑制。我们的结果修正了先前处理中使用的紫外缩放，对泡碰撞产生超重暗物质和重子生成有直接影响。
英文摘要
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.
Comments43 pages, 5 figures, 1 table
