The physical mass-squared matrices are given by As expected, the linear combinations T r (Δ † $_{R}$Δ$_{R}$ ) = Δ −− R Δ ++ R + Δ − $_{R}$Δ + R + ¯ Δ 0 $_{R}$Δ 0 $_{R}$, (8) Δ † $_{R}$Δ$_{R}$ − Δ$_{R}$Δ † R =   ¯ Δ 0 $_{R}$Δ 0 R − Δ −− R Δ ++ R √$_{2(Δ}$ − $_{R}$Δ ++ R − ¯ Δ 0 $_{R}$Δ + $_{R}$) √$_{2(Δ}$ −− R Δ + R − Δ − $_{R}$Δ 0 $_{R}$) − ¯ Δ 0 $_{R}$Δ 0 R + Δ −− R Δ ++ R   , (9) ˜ Φ † $_{R}$Δ † $_{R}$Φ$_{R}$ = φ 0 $_{R}$φ 0 $_{R}$¯ Δ 0 R $_{+}$√$_{2}$$_{φ}$ 0 $_{R}$φ + $_{R}$Δ − R − φ + $_{R}$φ + $_{R}$Δ −− R . (10) V$_{R}$ = m 2 $_{4}$Φ † $_{R}$Φ$_{R}$ + m 2 $_{6}$T r (Δ † $_{R}$Δ$_{R}$ ) + 1 2 λ 1 (Φ † $_{R}$Φ$_{R}$ ) 2 + 1 2 λ 2 [ T r (Δ † $_{R}$Δ$_{R}$ )] 2 + 1 4 λ 3 T r (Δ † $_{R}$Δ$_{R}$ − Δ$_{R}$Δ † $_{R}$) 2 + f 1 (Φ † $_{R}$Φ$_{R}$ ) T r (Δ † $_{R}$Δ$_{R}$ ) + f 2 Φ † $_{R}$(Δ † $_{R}$Δ$_{R}$ − Δ$_{R}$Δ † $_{R}$)Φ$_{R}$ + µ (Φ † $_{R}$Δ$_{R}$ ˜ Φ$_{R}$ + ˜ Φ † $_{R}$Δ † $_{R}$Φ$_{R}$ ) , (6) Φ † $_{R}$Φ$_{R}$ = φ − $_{R}$φ + R + ¯ φ 0 $_{R}$φ 0 $_{R}$, (7) 4 Let 〈 φ 0 R 〉 = v 4 and 〈 Δ 0 R 〉 = v 6 , as already noted, then the minimum of V$_{R}$ is given by V 0 = m 2 $_{4}$v 2 4 + m 2 $_{6}$v 2 6 + 1 2 λ 1 v 4 4 + 1 2 λ 2 v 4 6 + 1 2 λ 3 v 4 6 + f 1 v 2 $_{4}$v 2 6 − f 2 v 2 $_{4}$v 2 6 + 2 µv 2 $_{4}$v 6 , (11) where v 4 , 6 are determined by ∂V 0 ∂v 4 = 2 v 4 [ m 2 4 + λ 1 v 2 4 + ( f 1 − f 2 ) v 2 6 + 2 µv 6 ] = 0 , (12) ∂V 0 ∂v 6 = 2 v 6 [ m 2 6 + ( λ 2 + λ 3 ) v 2 6 + ( f 1 − f 2 ) v 2 $_{4}$] + 2 µv 2 4 = 0 . (13) M $^{2}$( Reφ 0 $_{R}$, Re Δ 0 $_{R}$) =   2 λ 1 v 2 4 2( f 1 − f 2 ) v 4 v 6 + 2 µv 4 2( f 1 − f 2 ) v 4 v 6 + 2 µv 4 2( λ 2 + λ 3 ) v 2 6 − µv 2 $_{4}$/v 6   , (14) M $^{2}$( Imφ 0 $_{R}$, Im Δ 0 $_{R}$) =   − 4 µv 6 2 µv 4 2 µv 4 − µv 2 $_{4}$/v 6   , (15) M $^{2}$( φ ± $_{R}$, Δ ± $_{R}$) =   2 v 6 ( f 2 v 6 − µ ) − √$_{2}$$_{v}$$_{4}$$_{(}$$_{f}$$_{2}$$_{v}$$_{6}$ − µ ) − √$_{2}$$_{v}$$_{4}$$_{(}$$_{f}$$_{2}$$_{v}$$_{6}$ − µ ) v 2 $_{4}$/v 6 ( f 2 v 6 − µ )   , (16) M $^{2}$(Δ ±± R ) = 2 f 2 v 2 4 − 2 λ 3 v 2 6 − µv 2 $_{4}$/v 6 . (17) ( v 4 Imφ 0 R + 2 v 6 Im Δ 0 $_{R}$) √ v 2 4 + 4 v 2 6 , ( v 4 φ ± R $_{+}$√$_{2}$$_{v}$$_{6}$$_{Δ}$ ± $_{R}$) √ v 2 4 + 2 v 2 6 where