Large language models (LLMs) have shown the capability to generate fluent and logical content, presenting significant challenges to machine-generated text detection, particularly text polished by adversarial perturbations such as paraphrasing. Current zero-shot detectors often employ Gaussian distributions as statistical measure for computing detection thresholds, which falters when confronted with the heavy-tailed statistical artifacts characteristic of adversarial or non-native English texts. In this paper, we introduce T-Detect, a novel detection method that fundamentally redesigns the curvature-based detectors. Our primary innovation is the replacement of standard Gaussian normalization with a heavy-tailed discrepancy score derived from the Student's t-distribution. This approach is theoretically grounded in the empirical observation that adversarial texts exhibit significant leptokurtosis, rendering traditional statistical assumptions inadequate. T-Detect computes a detection score by normalizing the log-likelihood of a passage against the expected moments of a t-distribution, providing superior resilience to statistical outliers. We validate our approach on the challenging RAID benchmark for adversarial text and the comprehensive HART dataset. Experiments show that T-Detect provides a consistent performance uplift over strong baselines, improving AUROC by up to 3.9\% in targeted domains. When integrated into a two-dimensional detection framework (CT), our method achieves state-of-the-art performance, with an AUROC of 0.926 on the Books domain of RAID. Our contributions are a new, theoretically-justified statistical foundation for text detection, an ablation-validated method that demonstrates superior robustness, and a comprehensive analysis of its performance under adversarial conditions. Ours code are released at https://github.com/ResearAI/t-detect.