摘要：The Majorana nature of massive neutrinos will be crucially probed in the next-generation experiments of the neutrinoless double-beta (0ν2β) decay. The effective mass term of this process, ⟨m⟩ee, may be contaminated by new physics. So how to interpret a discovery or null result of the 0ν2β decay in the foreseeable future is highly nontrivial. In this paper we introduce a novel three-dimensional description of |⟨m⟩ee|, which allows us to see its sensitivity to the lightest neutrino mass and two Majorana phases in a transparent way. We take a look at to what extent the free parameters of |⟨m⟩ee| can be well constrained provided a signal of the 0ν2β decay is observed someday. To fully explore lepton number violation, all the six effective Majorana mass terms ⟨m⟩αβ (for α,β=e,μ,τ) are calculated and their lower bounds are illustrated with the two-dimensional contour figures. The effect of possible new physics on the 0ν2β decay is also discussed in a model-independent way. We find that the result of |⟨m⟩ee| in the normal (or inverted) neutrino mass ordering case modified by the new physics effect may somewhat mimic that in the inverted (or normal) mass ordering case in the standard three-flavor scheme. Hence a proper interpretation of a discovery or null result of the 0ν2β decay may demand extra information from some other measurements.