The Exposure-Background Duality in the Searches of Neutrinoless Double Beta Decay

Tremendous efforts are required to scale the summit of observing neutrinoless double beta decay ($0 \nu \beta \beta$). This article quantitatively explores the interplay between exposure (target mass X data taking time) and background levels in $0 \nu \beta \beta$ experiments. In particular, background reduction can substantially alleviate the necessity of unrealistic large exposure as the normal mass hierarchy (NH) is probed. The non-degenerate (ND)-NH can be covered with an exposure of O(100) ton-year, which is only an order of magnitude larger than those planned for next generation projects - provided that the background could be reduced by 0($10^{-6}$) relative to the current best levels. It follows that background suppression will be playing increasingly important and investment-effective, if not determining, roles in future $0 \nu \beta \beta$ experiments with sensitivity goals of approaching and covering ND-NH.