with only a subleading singlet fraction,the new terms proportional to A2 will be most important.Note that the enhancement due to A is present even if there is no doublet singlet mixing at all.The coupling gh+-as a function of A is shown in Figure 1.It can be seen thatgh+-can be significantly enhanced,leading to a correspondingly enhanced partial di-photon width.This is shown in Figure 2 as a function of A and mH+.To use the tree-level mass of the charged Higgs directly as input,we solved for Ax, Ax= 4V2λus -4,(V2μs+usk)A-8bu+(4m2±-v2(g2-2λ2)sin(28)）.(7) While Ax is often chosen such that in the NMSSM the doublet-singlet mixing in the CP even Higgs sector is reduced,this freedom is lost by this approach.However,it turns out that the singlet fraction can be kept small by utilising the additional GNMSSM parameters,e.g.by choosing moderate finite values of u as shown in Figure 3. 0.20 140 0.15 A S] 0.10 0.05 40 20 0.005 0.8 0.9 1.0 1.11213141.5 0.8 0.9 1.01.11.2 13 14 1.5 入 Figure 3:Singlet fraction (left)and tree level mass (right)of the light Higgs doublet as a function of A.The blue dashed line shows the NMSSM case (=0),while for the red line u=-100 GeV was used.The other parameters are tan B=1.5,K=1.2,Us =240 GeV, mH±=l65GeV. 2.2 Enhancing the di-photon rate with charginos The chargino-Higgs vertex(PLg+Prg)h can be expressed as 安=-方（贴玲+(2东+2对） (8) 9对h=(9吃对n) (9) 5with only a subleading singlet fraction, the new terms proportional to λ 2 will be most important. Note that the enhancement due to λ is present even if there is no doublet singlet mixing at all. The coupling ghH+H− as a function of λ is shown in Figure 1. It can be seen that ghH+H− can be significantly enhanced, leading to a correspondingly enhanced partial di-photon width. This is shown in Figure 2 as a function of λ and mH± . To use the tree-level mass of the charged Higgs directly as input, we solved for Aλ, Aλ = 1 4 √ 2λvs  −4vs( √ 2µs + vsκ)λ − 8bµ + (4m2 H± − v 2 (g 2 2 − 2λ 2 )) sin(2β)  . (7) While Aλ is often chosen such that in the NMSSM the doublet-singlet mixing in the CP even Higgs sector is reduced, this freedom is lost by this approach. However, it turns out that the singlet fraction can be kept small by utilising the additional GNMSSM parameters, e.g. by choosing moderate finite values of µ as shown in Figure 3. 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 0.00 0.05 0.10 0.15 0.20 λ Singlet fraction 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 0 20 40 60 80 100 120 140 λ m h [GeV] Figure 3: Singlet fraction (left) and tree level mass (right) of the light Higgs doublet as a function of λ. The blue dashed line shows the NMSSM case (µ = 0), while for the red line µ = −100 GeV was used. The other parameters are tan β = 1.5, κ = 1.2, vs = 240 GeV, mH± = 165 GeV. 2.2 Enhancing the di-photon rate with charginos The chargino - Higgs vertex ˜χ − i (PLg L + PRg R)˜χ + j h can be expressed as g L χ˜ − i χ˜ + j h = − i 1 √ 2  g2V ∗ j1U ∗ i2Z h 2 + V ∗ j2  g2U ∗ i1Z h 1 + λU∗ i2Z h 3  , (8) g R χ˜ − i χ˜ + j h = (g L χ˜ − i χ˜ + j h ) ∗ . (9) 5