Half-life of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mi>Xe</mml:mi> <mml:mprescripts/> <mml:none/> <mml:mn>136</mml:mn> </mml:mmultiscripts> </mml:math> for neutrinoless double- <mml:math xmlns:mml="http://w

The upper limit on the mass of the Majorana neutrino, extracted from the limits on the nonobservation of the neutrinoless double-$\ensuremath{\beta}$ ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) decay, is hampered by uncertainties in the matrix elements of the transition operators. Recently, we have shown that the values of the effective axial-vector current coupling constants (${g}_{A}^{\text{eff}}$) for the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ and the two-neutrino double-$\ensuremath{\beta}$ decays are close. This striking result was obtained for the first time by including vertex corrections and two-body currents in these matrix elements. In this Letter, we calculate the half-life for the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay (${T}_{1/2}^{0\ensuremath{\nu}}$) of $^{136}\mathrm{Xe}$ using this closeness and show the convergence of the half-life with respect to the variation of the method to determine ${g}_{A}^{\text{eff}}$. The closeness of the ${g}_{A}^{\text{eff}}$ of the two decay modes plays a decisive role in predicting ${T}_{1/2}^{0\ensuremath{\nu}}$. The appropriate value of ${g}_{A}^{\text{eff}}$ depends on the assumptions made for the sectors of the nuclear structure and transition operators of the calculations within the perturbation scheme. The value ${g}_{A}^{\text{eff}}\ensuremath{\approx}1$ is obtained when the ${\mathrm{SkM}}^{*}$ is used to describe the nuclear structure component, while a smaller value of ${g}_{A}^{\text{eff}}$ is obtained by applying a less realistic interaction like the SGII one.