Measuring neutrino mass in light of ACT DR6 and DESI DR2

The recent release of high-precision cosmological data, particularly the small-scale cosmic microwave background (CMB) measurements from ACT and baryon acoustic oscillation (BAO) data from DESI, has opened a new landscape for probing the neutrino mass. In this work, we present updated constraints on the total neutrino mass, $\sum m_\nu$, and its hierarchy within the $\Lambda$CDM, $w$CDM, holographic dark energy (HDE), and $w_0w_a$CDM models, using the latest ACT DR6, DESI DR2, and DESY5 datasets. We find that the upper limits on $\sum m_\nu$ are critically governed by the evolutionary behavior of the dark energy equation of state. Specifically, models exhibiting early-time quintessence features (e.g., HDE) yield the most stringent constraints, whereas those allowing for early-time phantom behavior (e.g., $w_0w_a$CDM) result in significantly looser bounds. Despite these model-dependent variations, we observe a robust hierarchy dependence across all scenarios, where the inverted hierarchy consistently yields weaker constraints and the degenerate hierarchy consistently yields tightest constraints. Our analysis demonstrates that the improved small-scale CMB information from ACT, combined with high-precision BAO data, systematically tightens the limits on $\sum m_\nu$, providing a crucial benchmark for future neutrino mass measurement.