Detecting LLM-generated text in specialized and high-stakes domains like medicine and law is crucial for combating misinformation and ensuring authenticity.However, current zeroshot detectors, while effective on general text, often fail when applied to specialized content due to domain shift.We provide a theoretical analysis showing this failure is fundamentally linked to the KL divergence between human, detector, and source text distributions.To address this, we propose DivScore, a zero-shot detection framework using normalized entropybased scoring and domain knowledge distillation to robustly identify LLM-generated text in specialized domains.We also release a domainspecific benchmark for LLM-generated text detection in the medical and legal domains.Experiments on our benchmark show that Di-vScore consistently outperforms state-of-theart detectors, with 14.4% higher AUROC and 64.0% higher recall (0.1% false positive rate threshold).In adversarial settings, DivScore demonstrates superior robustness to other baselines, achieving on average 22.8% advantage in AUROC and 29.5% in recall.Code and data are publicly available 1 .