AI 中文总结
该研究通过量子电动力学计算，修正小行星质量原初黑洞的正负电子发射率，发现2.2×10^16-1.7×10^17克范围内发射率净修正小于2%，小于半经典预言的5%抑制幅度。
AI 中文摘要
基于黑洞蒸发产物，霍金辐射对质量约为10^16克的原初黑洞（PBHs）作为暗物质候选体施加了严格约束，这促使人们需要对光子、电子和正电子的发射谱进行严谨建模。本文是两篇系列论文中的第二篇（系列第一篇见Vasquez等人[Phys. Rev. D, 112:063002 (2025)]），旨在证明电子和正电子的随机发射（即“随机电荷效应”，由Page[Phys. Rev. D, 16:2402 (1977)]首次用半经典论证预言）源于施瓦西时空上的量子电动力学（QED）。我们从哈密顿量的相关项（长程单极项：H_{int,0L}）出发，对精细结构常数（α）一阶近似下的e^±进行修正推导，证明半经典项也存在于QED计算中。我们还强调了分析中哪些项仅出现在量子力学方法内，无法用其他方式解释。研究发现，由于部分项的抵消，在2.2×10^16克至1.7×10^17克的质量范围内，e^±发射率的净修正小于2%，而此前半经典论证得出的抑制幅度高达5%。
英文摘要
Hawking radiation sets stringent constraints on Primordial Black Holes (PBHs) as a dark matter candidate in the $M\sim 10^{16}$ g regime based on the evaporation products produced by the black hole, motivating the need to rigorously model the photon, electron, and positron emission spectra. This manuscript is the second in a series of two papers (see Vasquez et al. [Phys. Rev. D, 112:063002 (2025)] for the first paper in the series) with the goal of proving the stochastic emission of electrons and positrons, known as the "stochastic charge effect" and first predicted by Page [Phys. Rev. D, 16:2402 (1977)] using semi-classical arguments, arises from quantum electrodynamics (QED) on a Schwarzschild spacetime. We derive the corrections to the $e^\pm$ from the relevant term in the Hamiltonian (the long-range monopole: $H_{\rm int,0L}$) to first order in the fine structure constant ($α$), and show that the semi-classical terms are also present in the QED calculation. We also highlight which terms in our analysis only appear within our quantum mechanical approach and cannot be explained otherwise. We find that due to some cancellation of terms, over the range of $2.2\times 10^{16}$ - $1.7\times 10^{17}$ g, the net correction to the $e^\pm$ emission rate is less than 2%, versus the suppression of up to 5% previously found by semi-classical arguments.
Comments32 pages, 5 figures, and 2 tables. To be submitted to Physical Review D
