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) 5
with 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
0.4 03 0.0 0.0 0.5 10 1.5 20 Figure 4:The chargino couplings as a function of A.The dashed,blue line is for the wino- like chargino and the red,dotted line for the Higgsino-like chargino.Note,to show only the dependence on A,we kept the involved rotation matrices in the vertex constant for all values of A.The Higgs and chargino mixing matrices have been calculated using the input values tan B=1.3,A=0.8,K=0.9,AA=23 GeV,KA =-400 GeV,Us =265 GeV,M2=2 TeV, and all non-NMSSM parameters have been set to zero.This leads to(0.61,0.72,0.32). The unitary matrices which diagonalise the chargino mass matrix can be expressed by two rotation matrices with the angles and For the interaction of the light chargino we can write explicitly 吃= V292os业sim$2+i血业cosΦZg)+Asin亚sinΦz约. (10) The first observation is that unlike in the case of the charged Higgs,the couplings to the neutral doublet Higgs components are MSSM like and additional terms appear only due to mixing with the singlet state.To get more insight in this expression we can take the limit tan B→1 for whichΦ~亚，leading to 9安对A=-526os业si(2+Z约)）+入si2业Z） (11) There are two limits of interest: The light chargino is mostly wino-like (->0):the coupling to the Higgs is very suppressed. ·The light chargino is a Higgsino:(亚→π/2)：the first term vanishes and depending and the sign of A and the second term can contribute positively or negatively. 6
0.0 0.5 1.0 1.5 2.0 0.0 0.1 0.2 0.3 0.4 λ g˜χ − i ˜χ + i h/i Figure 4: The chargino couplings as a function of λ. The dashed, blue line is for the winolike chargino and the red, dotted line for the Higgsino-like chargino. Note, to show only the dependence on λ, we kept the involved rotation matrices in the vertex constant for all values of λ. The Higgs and chargino mixing matrices have been calculated using the input values tan β = 1.3, λ = 0.8, κ = 0.9, λAλ = 23 GeV, κAκ = −400 GeV, vs = 265 GeV, M2 = 2 TeV, and all non-NMSSM parameters have been set to zero. This leads to Z h ' (0.61, 0.72, 0.32). The unitary matrices which diagonalise the chargino mass matrix can be expressed by two rotation matrices with the angles Ψ and Φ. For the interaction of the light chargino we can write explicitly g L χ˜ − i χ˜ + j h = − i √ 2 n g2(cos Ψ sin ΦZ h 1 + sin Ψ cos ΦZ h 2 ) + λ sin Ψ sin ΦZ h 3 o . (10) The first observation is that unlike in the case of the charged Higgs, the couplings to the neutral doublet Higgs components are MSSM like and additional terms appear only due to mixing with the singlet state. To get more insight in this expression we can take the limit tan β → 1 for which Φ ∼ Ψ, leading to g L χ˜ − i χ˜ + j h = − i √ 2 g2 cos Ψ sin Ψ(Z h 1 + Z h 2 ) + λ sin2 ΨZ h 3 . (11) There are two limits of interest: • The light chargino is mostly wino-like (Ψ → 0): the coupling to the Higgs is very suppressed. • The light chargino is a Higgsino: (Ψ → π/2): the first term vanishes and depending and the sign of λ and Z h 3 the second term can contribute positively or negatively. 6