I carried out a study on the relationship between the squares of the charged Higgs boson Yukawa coupling constants associated with the charged Higgs boson, obtained in the context of the lepton-specific two Higgs doublet model (LS2HDM), starting from the fraction of new physics contributions to the total decay widths of leptonic tau decays. \(\tau ^{-} \rightarrow \mu ^{-} \bar{\nu }_\mu \nu _\tau \) and \(\tau ^{-} \rightarrow e^{-} \bar{\nu }_e \nu _\tau \) . To do it, I calculate the total decay widths of these processes in the context of the LS2HDM by considering that these leptonic tau decays are mediated through the exchange of charged electroweak gauge boson and charged Higgs boson, in such a way that these widths depend on the charged Higgs boson mass and the ratio between the vacuum expectation values of the two Higgs doublets, which are unknown parameters. After expressing the ratio between the new-physics contributions to the total decay widths at one-loop order, I explicitly assume the scalar mass degeneracy limit given by \(m_{A}=m_{H}=m_{H^{\pm }}\) . In this specific limit, the one-loop contributions of all Higgs bosons are suppressed with respect to the tree-level terms. As a result, the previously unknown parameters cancel out, leading to a direct relation between the squares of the charged Higgs boson Yukawa coupling constants that enter the calculation of the total decay widths. This relation depends on the values of the elements of the leptonic flavor mixing matrix, which are numerically estimated by assuming that mass matrices have two-zero textures. To validate the relationship found, we perform a self-consistency analysis using an assumption of hierarchy in the mass spectrum, resulting in this relationship satisfying the same hierarchy but now between the Yukawa coupling constants.
