Non-universality Relationships for Charged Higgs Boson Yukawa Couplings in the Two Higgs Doublet Model Type III

In the context of the two Higgs doublet model type III with flavor-changing neutral currents at the tree level, I obtain non-universality relationships of charged Higgs boson Yukawa coupling constants by calculating the widths of the pure leptonic decays of the tau lepton \(\tau \rightarrow e \bar{\nu }_e \nu _\tau\) $\tau \to e{\overline{\nu }}_e{\nu }_{\tau }$ and \(\tau \rightarrow \mu \bar{\nu }_\mu \nu _\tau\) $\tau \to \mu {\overline{\nu }}_{\mu }{\nu }_{\tau }$ . To this end, I first calculate these total widths by including the effects of the exchanges of the Higgs boson \(H^-\) $H^{-}$ and the gauge boson \(W^-\) $W^{-}$ , with the purpose to obtain the flavor-violating contribution \(\Delta _l^{H^-}\) ${\mathrm{\Delta }}_l^{H^{-}}$ and then to calculate the fraction \(\Delta _\mu ^{H^-}/\Delta _e^{H^-}\) ${\mathrm{\Delta }}_{\mu }^{H^{-}}/{\mathrm{\Delta }}_e^{H^{-}}$ . By writing this fraction in terms of the experimental and electroweak standard model branching ratios of these decays and assuming that flavors of neutrino and antineutrino in the final state are defined but unknown, I obtain fractions of charged Higgs boson Yukawa coupling constants that differ from one. These fractions establish non-universality relationships associated with the scalar interaction in contrast to the universality relationships associated with the electroweak interaction.