H$_{u}$ Q$_{L}$ D$_{R}$ H ∗ u Q$_{L}$ U$_{R}$ Y † u Y$_{d}$ Y$_{u}$ H$_{d}$ ( a ) ( b ) h Q$_{L}$ D$_{R}$ h Q$_{L}$ U$_{R}$ ¯ Y U † 1 ¯ Y D 1 ¯ Y U 1 H FIG. 1: FCNCs induced by radiative corrections (a) without imposing symmetry and (b) with Z$_{2}$ or U (1) symmetry which is broken softly in Higgs potential. where η F = diag( η$_{F}$$_{1}$, η$_{F}$$_{2}$, η$_{F}$$_{3}$ ) is a new diagonal matrix and the elements are undetermined complex parameters. Based on Eq. (6), the corresponding charged Higgs interactions could be written as where all flavor indices are suppressed and V = V U L V D † L is the Cabibbo-Kobayashi-Maskawa (CKM) matrix. For comparison, if we take η$_{U}$$_{i}$ = cot β and η$_{D}$$_{i}$ = η$_{ℓ}$$_{i}$ = tan β ( i =1-3), Eq. (14) can be restored to the type-II THDM. According to Eq. (14), the effective Hamiltonian for d$_{j}$ → u$_{i}$ℓ ¯ ν$_{ℓ}$ mediated by H ± is found by where we have used G$_{F}$ = 1 $_{/}$√$_{2}$$_{v}$ 2 and (¯ u$_{i}$d$_{j}$ )$_{S}$$_{±}$$_{P}$ = ¯ u$_{i}$ (1 ± γ$_{5}$ ) d$_{j}$ . With the definition of P -meson decay constant, given by L H ± = [ ¯ U$_{R}$ ¯ Y U † 2 D$_{L}$ + ¯ U$_{L}$ ¯ Y D 1 D$_{R}$ + ¯ ν$_{L}$ ¯ Y ℓ $_{1}$ℓ$_{R}$ ] H + + h.c. , = √$_{2}$ v ¯ u [ m dia † U η † $_{U}$V P$_{L}$ + V η $_{D}$m dia D P$_{R}$ ] d H + + √$_{2}$ v ¯ ν η $_{ℓ}$m dia ℓ P$_{R}$ℓ H + + h.c. , (14) H ± = − G$_{F}$ V$_{ij}$ √$_{2}$ η ∗ $_{ℓ}$m$_{ℓ}$ m 2 H ± [ η ∗ $_{U$_{i}$}$m$_{U}$$_{i}$ (¯ u$_{i}$d$_{j}$ )$_{S}$$_{−}$$_{P}$ + η$_{D}$$_{j}$m$_{D}$$_{j}$ (¯ u$_{i}$d$_{j}$ )$_{S}$$_{+}$$_{P}$ ] ( ¯ ℓν$_{ℓ}$ )$_{S}$$_{−}$$_{P}$ (15) 〈 0 | ¯ q $^{′}$γ$_{µ}$ γ$_{5}$q | ¯ P ( p ) 〉 = − if$_{P}$ p$_{µ}$ , 〈 0 | ¯ q $^{′}$γ$_{5}$ q | ¯ P ( p ) 〉 = i f$_{P}$ m 2 P m$_{q}$ + m$_{q}$ ′ , 6