Enhanced h → γγ rate in MSSM singlet extensions

OUTP-12-17P Bonn-TH-2012-20 Enhanced h>yy rate in MSSM singlet extensions Kai Schmidt-Hoberg,Florian Staub a Rudolf Peierls Centre for Theoretical Physics,University of Orford, 1 Keble Road,Ozford OX1 3NP,UK 81261060m bBethe Center for Theoretical Physics Physikalisches Institut der Universitat Bonn, NuBallee 12,53115 Bonn,Germany Abstract We study the di-photon rate in Higgs decays within singlet extensions of the supersymmetric standard model.In particular we point out that light charginos as well as a light charged Higgs can significantly contribute to the corresponding partial decay width,allowing for an explanation of the experimental indication whithin a natural supersymmetric model.This is in contrast to the 'light stau scenario'proposed within the framework of the MSSM which requires a large amount of electroweak fine tuning. ZAE89I 807I:AIXIe

OUTP-12-17P Bonn-TH-2012-20 Enhanced h → γγ rate in MSSM singlet extensions Kai Schmidt-Hoberga , Florian Staubb aRudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, UK bBethe Center for Theoretical Physics & Physikalisches Institut der Universit¨at Bonn, Nußallee 12, 53115 Bonn, Germany Abstract We study the di-photon rate in Higgs decays within singlet extensions of the supersymmetric standard model. In particular we point out that light charginos as well as a light charged Higgs can significantly contribute to the corresponding partial decay width, allowing for an explanation of the experimental indication whithin a natural supersymmetric model. This is in contrast to the ‘light stau scenario’ proposed within the framework of the MSSM which requires a large amount of electroweak fine tuning. arXiv:1208.1683v2 [hep-ph] 16 Oct 2012

1 Introduction Recently both ATLAS [1]and CMS [2]have presented evidence for a new bosonic state with mass m 125 GeV.While the data is consistent with the expectation from a standard model (SM)Higgs,both experiments see indications for an excess in the diphoton channel',while the diboson decays into WW*and 22*seem to be in accord with the SM expectation.In particular the enhanced di-photon rate has attracted much attention recently,see e.g.[4-17].Within the minimal supersymmetric standard model(MSSM)two possibilities to increase the rate pp-hy have been discussed: Higgs mixing effects can have an important impact on the diphoton rate,in particular via a suppression of the coupling to down-type fermions,which leads to an effective increase of the h-y channel [5].However,this would also lead to an increase in the branching fractions into WW*and 22*,which does not seem reflected in the data. The second possibility is to increase the loop induced Higgs photon coupling via some light charged states running in the loop.In the MSSM the only viable possibility was found to be a very light and strongly mixed stau [18,19],whereas the contributions from the charged Higgs and charginos turn out to be negligible.While an interesting proposal,the light stau scenario requires very large u.tan B,which implies very large corresponding electroweak fine-tuning. The electroweak fine-tuning can be substantially alleviated in singlet extensions of the MSSM,in part due to the new quartic Higgs coupling,giving an additional tree- level mass contribution to the light Higgs.The GNMSSM [20]based on a discrete R symmetry,Zf orZ[21,22],was found to be particularly interesting in this context [23]. The aim of this letter is to point out that in singlet extensions of the MSSM the coupling of the CP even neutral light Higgs to charginos as well as to the charged Higgs can be strongly enhanced,leading to a sizeable increase in the h-y rate.This allows for an explanation of the enhanced rate within a much less fine-tuned scenario.We find that this enhancement is rather sensitive to the value of the trilinear singlet-Higgs coupling and is significant only for values of A which become non-perturbative below the GUT scale,corresponding to the well known scenario of ASUSY [24],which has been argued to be favoured by fine-tuning considerations [25].It has also been argued recently that the unification of gauge couplings might even improve in such a setup [26].In this letter we don't assume any particular UV completion but rather study the GNMSSM at the electroweak scale. This letter is organised as follows:In the next section we briefly review the partial decay width of the Higgs boson h into two photons with a particular focus on the charged Isee however [3] 1

1 Introduction Recently both ATLAS [1] and CMS [2] have presented evidence for a new bosonic state with mass m ∼ 125 GeV. While the data is consistent with the expectation from a standard model (SM) Higgs, both experiments see indications for an excess in the diphoton channel1 , while the diboson decays into WW∗ and ZZ∗ seem to be in accord with the SM expectation. In particular the enhanced di-photon rate has attracted much attention recently, see e.g. [4–17]. Within the minimal supersymmetric standard model (MSSM) two possibilities to increase the rate pp → h → γγ have been discussed: Higgs mixing effects can have an important impact on the diphoton rate, in particular via a suppression of the coupling to down-type fermions, which leads to an effective increase of the h → γγ channel [5]. However, this would also lead to an increase in the branching fractions into WW∗ and ZZ∗ , which does not seem reflected in the data. The second possibility is to increase the loop induced Higgs photon coupling via some light charged states running in the loop. In the MSSM the only viable possibility was found to be a very light and strongly mixed stau [18, 19], whereas the contributions from the charged Higgs and charginos turn out to be negligible. While an interesting proposal, the light stau scenario requires very large µ · tan β, which implies very large corresponding electroweak fine-tuning. The electroweak fine-tuning can be substantially alleviated in singlet extensions of the MSSM, in part due to the new quartic Higgs coupling, giving an additional tree￾level mass contribution to the light Higgs. The GNMSSM [20] based on a discrete R symmetry, ❩ R 4 or ❩ R 8 [21,22], was found to be particularly interesting in this context [23]. The aim of this letter is to point out that in singlet extensions of the MSSM the coupling of the CP even neutral light Higgs to charginos as well as to the charged Higgs can be strongly enhanced, leading to a sizeable increase in the h → γγ rate. This allows for an explanation of the enhanced rate within a much less fine-tuned scenario. We find that this enhancement is rather sensitive to the value of the trilinear singlet-Higgs coupling and is significant only for values of λ which become non-perturbative below the GUT scale, corresponding to the well known scenario of λSUSY [24], which has been argued to be favoured by fine-tuning considerations [25]. It has also been argued recently that the unification of gauge couplings might even improve in such a setup [26]. In this letter we don’t assume any particular UV completion but rather study the GNMSSM at the electroweak scale. This letter is organised as follows: In the next section we briefly review the partial decay width of the Higgs boson h into two photons with a particular focus on the charged 1 see however [3] 1

Higgs and chargino contributions.To this end we will perform a simple analysis using tree-level masses to highlight the main features.In Section 3 we will then perform a complete numerical analysis at one-loop including the leading two-loop contributions in the Higgs sector.Section 4 contains our summary and conclusions. 2 The h->yy partial decay width To start our discussion let us briefly review the partial decay width of the Higgs boson h into two photons within the MSSM and its singlet extensions.It can be written as (see e.g.[27) Ih-= Gua2m 128V2m3 ∑N.Q号giA2(r)+gwwA(nw） m9hH+H二A6(rH±) 2cwmH± +∑2mw e+2a mx (1) x corresponding to the contributions from charged SM fermions,W bosons,charged Higgs and charginos as well as the contributions of charged sleptons and squarks.In the SM the largest contribution is given by the W-loop,while the top-loop leads to a small reduction of the decay rate.In this work we will focus in particular on the contributions from charged Higgs and charginos running in the loop.From Eq.(1)it can be seen that the contribution from the charginos is suppressed by m,while the contribution from the charged Higgs is suppressed by m.The amplitudes A:at lowest order for the spin-1,spin-and spin-0 particle contributions are given by [27] A/2(r)=2r+(r-1)f(r】r-2 A(r)=-2r2+3r+3(2r-1)f(r月r-2 A6(r)=-r-f(r〗r-2 (2) with T=m/4m?and f(r)=arcsin2vT for T 1. In the following we will analyse the partial Higgs decay width into two photons 2

Higgs and chargino contributions. To this end we will perform a simple analysis using tree-level masses to highlight the main features. In Section 3 we will then perform a complete numerical analysis at one-loop including the leading two-loop contributions in the Higgs sector. Section 4 contains our summary and conclusions. 2 The h → γγ partial decay width To start our discussion let us briefly review the partial decay width of the Higgs boson h into two photons within the MSSM and its singlet extensions. It can be written as (see e.g. [27]) Γh→γγ = Gµα 2m3 h 128√ 2π 3     X f NcQ 2 f ghf fA h 1/2 (τf ) + ghWW A h 1 (τW ) + m2 W ghH+H− 2c 2 W m2 H± A h 0 (τH± ) + X χ ± i 2mW mχ ± i ghχ+ i χ − i A h 1/2 (τχ ± i ) +X f˜ i ghf˜ if˜ i m2 f˜ i NcQ 2 f˜ i A h 0 (τf˜ i )     2 , (1) corresponding to the contributions from charged SM fermions, W bosons, charged Higgs and charginos as well as the contributions of charged sleptons and squarks. In the SM the largest contribution is given by the W-loop, while the top-loop leads to a small reduction of the decay rate. In this work we will focus in particular on the contributions from charged Higgs and charginos running in the loop. From Eq. (1) it can be seen that the contribution from the charginos is suppressed by mχ ± i , while the contribution from the charged Higgs is suppressed by m2 H± . The amplitudes Ai at lowest order for the spin–1, spin– 1 2 and spin–0 particle contributions are given by [27] A h 1/2 (τ ) = 2[τ + (τ − 1)f(τ )] τ −2 A h 1 (τ ) = −[2τ 2 + 3τ + 3(2τ − 1)f(τ )] τ −2 A h 0 (τ ) = −[τ − f(τ )] τ −2 (2) with τi = m2 h /4m2 i and f(τ ) = arcsin2 √ τ for τ ≤ 1. In the following we will analyse the partial Higgs decay width into two photons 2

140 -300 LASS 2/-H+H6 -500 -600 0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 入 入 Figure 1:Left panel:size of the different contributions to the coupling gh+-proportional to the down-fraction (red),up-fraction (blue)and singlet-fraction(green)as a function of A. Right panel:The overall coupling gh+-as a function of A.Note,we have kept all rotation matrices involved in the vertex constant to show only the dependences on A.The values of the additional parameters in both cases have been tan B =1.3,K=1.0,KA=-500 GeV, AA=-25 GeV,Us 282 GeV.We calculated the Higgs mixing matrices for A 1.0 and obtained for the scalar HiggsZ(-0.23,-0.91,0.35). within a generalised version of the NMSSM,which has a superpotential of the form w=Wa+写++ASH.+s8+3.S (3) 1 =WxMISSM+HH++ (4) where Wyukawa is the MSSM superpotential generating the SM Yukawa couplings and WNMSSM corresponds to the normal NMSSM with a Z3 symmetry.We use the freedom to shift the vev Us to set the linear term in S in the superpotential to zero,=0.Such a superpotential can arise from an underlying Z or Z symmetry as discussed in [22]. The corresponding general soft SUSY breaking terms associated with the Higgs and singlet sectors are given by Vson m2ls2+mi lhul2+mialhal2 bp haha+MAashaha+s+h.e. 1 + (5) We give the mass matrices of the neutral and charged Higgs particles as well as of the neutralino and chargino in Appendix A.For more details on the model,see [23].The MSSM or NMSSM limits can easily be obtained by setting the appropriate parameters to zero 3

0.0 0.5 1.0 1.5 2.0 -600 -500 -400 -300 -200 -100 0 λ cd,u,s H + H − h [GeV] 0.0 0.5 1.0 1.5 2.0 0 20 40 60 80 100 120 140 λ g H + H − h/i [GeV] Figure 1: Left panel: size of the different contributions to the coupling ghH+H− proportional to the down-fraction (red), up-fraction (blue) and singlet-fraction (green) as a function of λ. Right panel: The overall coupling ghH+H− as a function of λ. Note, we have kept all rotation matrices involved in the vertex constant to show only the dependences on λ. The values of the additional parameters in both cases have been tan β = 1.3, κ = 1.0, κAκ = −500 GeV, λAλ = −25 GeV, vs = 282 GeV. We calculated the Higgs mixing matrices for λ = 1.0 and obtained for the scalar Higgs Z h i ' (−0.23, −0.91, 0.35). within a generalised version of the NMSSM, which has a superpotential of the form W = WYukawa + 1 3 κS3 + (µ + λS)HuHd + ξS + 1 2 µsS 2 (3) ≡ WNMSSM + µHuHd + ξS + 1 2 µsS 2 (4) where WYukawa is the MSSM superpotential generating the SM Yukawa couplings and WNMSSM corresponds to the normal NMSSM with a ❩3 symmetry. We use the freedom to shift the vev vs to set the linear term in S in the superpotential to zero, ξ = 0. Such a superpotential can arise from an underlying ❩ R 4 or ❩ R 8 symmetry as discussed in [22]. The corresponding general soft SUSY breaking terms associated with the Higgs and singlet sectors are given by Vsoft = m2 s |s| 2 + m2 hu |hu| 2 + m2 hd |hd| 2 +  bµ huhd + λAλshuhd + 1 3 κAκs 3 + 1 2 bss 2 + ξss + h.c. . (5) We give the mass matrices of the neutral and charged Higgs particles as well as of the neutralino and chargino in Appendix A. For more details on the model, see [23]. The MSSM or NMSSM limits can easily be obtained by setting the appropriate parameters to zero. 3

2.1 Enhancing the di-photon rate with a charged Higgs 1.8 1.8 1.6 1.6 1.4 1.4 1.2 12 10 10 150 180 190 200 210 220 180 190 200 210 220 mH+[GeV] mH+[GeV] Figure 2:Approximate analysis at tree level in the(m,A)plane.Left panel:partial di- photon width from the charged Higgs normalized to the SM(top and W)contributions.Right panel:tree-level mass of the light doublet Higgs.The input parameters have been tan B=1.3, K=1.1,Heff =220 GeV and kAx =-500 GeV. The couplingg-in the GNMSSM is given by (taking all parameters real for simplicity) 知as8p0r-分++后-29ms2时2究 -vsin82(5-X)+(gf+95-22)cos28Zg 4[,A+V2μ+((4+，)+sim20]Zg (6) where denote the entries of the Higgs mixing matrix in the (hd,hs)-basis. In the MSSM limit the charged Higgs often reduces the effective coupling of the Higgs to two photons because of negative interference with the others contributions:the sign of the interaction is fixed by the electroweak parameters(tan B,g1,g2,Mz)and the Higgs mixing angle.In the(G)NMSSM,new contributions proportional to A2 and other singlet parameters arise.The terms proportional to the additional singlet parameters couple to the singlet fraction of the light Higgs.Since we are interested in a mostly SM-like Higgs 4

2.1 Enhancing the di-photon rate with a charged Higgs 1.2 1.4 1.6 1.8 2.25 2.75 180 190 200 210 220 1.0 1.2 1.4 1.6 1.8 mH+ [GeV] λ 50 75 100 120 130 150 180 190 200 210 220 1.0 1.2 1.4 1.6 1.8 mH+ [GeV] λ Figure 2: Approximate analysis at tree level in the (mH± , λ) plane. Left panel: partial di￾photon width from the charged Higgs normalized to the SM (top and W) contributions. Right panel: tree-level mass of the light doublet Higgs. The input parameters have been tan β = 1.3, κ = 1.1, µeff = 220 GeV and κAκ = −500 GeV. The coupling ghH+H− in the GNMSSM is given by (taking all parameters real for simplicity) ghH+H− = i 4  v cos β h 2(λ 2 − g 2 2 ) + (g 2 1 + g 2 2 − 2λ 2 ) cos 2β i Z h 1 − v sin β h 2(g 2 2 − λ 2 ) + (g 2 1 + g 2 2 − 2λ 2 ) cos 2β i Z h 2 − 4λ h vsλ + √ 2µ + ( √ 1 2 (Aλ + µs) + vsκ) sin 2β i Z h 3  (6) where Z h i denote the entries of the Higgs mixing matrix in the (hd, hu, s)-basis. In the MSSM limit the charged Higgs often reduces the effective coupling of the Higgs to two photons because of negative interference with the others contributions: the sign of the interaction is fixed by the electroweak parameters (tan β, g1, g2, MZ) and the Higgs mixing angle. In the (G)NMSSM, new contributions proportional to λ 2 and other singlet parameters arise. The terms proportional to the additional singlet parameters couple to the singlet fraction of the light Higgs. Since we are interested in a mostly SM-like Higgs 4

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 wino￾like 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

The couplingas a function of is shown in Figure 4 for the wino and Higgsino limit.The corresponding enhancement of the partial di-photon width due to the light chargino relative to the SM contributions as well as the tree-level mass of the light Higgs are shown in Figure 5.It can be seen that for light charginos and large values of A,the chargino loop can be several times larger than the sum of the top and W-boson. 1.6F 1.6F 1.5 1.5 110 100 <1.4 1.4 1.5 130 125 1.3 1.3 140 2 200 210220 230240250 200 210220 230 240250 mxt Gev] mxt [Gev] Figure 5:Approximate analysis at tree level in the (m)plane.Left panel:partial di- photon width from the chargino normalised to the top and W contributions.Right panel: tree-level mass of the light doublet Higgs.The other parameters are tan B=1.2,K=1.1, mH+=180 GeV and KAs =-500 GeV. It has recently be pointed out that the chargino loop can also be important in SU(2)L triplet extensions of the MSSM [28].Similarly to our case,also there large superpotential couplings between the Higgs and the triplets must be present to generate a large enough loop contribution. 3 Analysis including the Higgs mass and other con- straints After we have discussed the basic principle in the last section at tree-level,we turn now to a full-fledged numerical analysis.Given that we try to explain an enhanced Higgs branching ratio into two photons with rather light charged particles in the loop,we have to be careful not to cause dangerous contributions to precision observables.This leads 7

The coupling gχ˜ − i χ˜ + j h as a function of λ is shown in Figure 4 for the wino and Higgsino limit. The corresponding enhancement of the partial di-photon width due to the light chargino relative to the SM contributions as well as the tree-level mass of the light Higgs are shown in Figure 5. It can be seen that for light charginos and large values of λ, the chargino loop can be several times larger than the sum of the top and W-boson. 1.25 1.5 2.5 3 200 210 220 230 240 250 1.2 1.3 1.4 1.5 1.6 mχ˜ + 1 [GeV] λ 80 100 110 125 130 140 200 210 220 230 240 250 1.2 1.3 1.4 1.5 1.6 mχ˜ + 1 [GeV] λ Figure 5: Approximate analysis at tree level in the (m χ˜ + 1 , λ) plane. Left panel: partial di￾photon width from the chargino normalised to the top and W contributions. Right panel: tree-level mass of the light doublet Higgs. The other parameters are tan β = 1.2, κ = 1.1, mH± = 180 GeV and κAκ = −500 GeV. It has recently be pointed out that the chargino loop can also be important in SU(2)L triplet extensions of the MSSM [28]. Similarly to our case, also there large superpotential couplings between the Higgs and the triplets must be present to generate a large enough loop contribution. 3 Analysis including the Higgs mass and other con￾straints After we have discussed the basic principle in the last section at tree-level, we turn now to a full-fledged numerical analysis. Given that we try to explain an enhanced Higgs branching ratio into two photons with rather light charged particles in the loop, we have to be careful not to cause dangerous contributions to precision observables. This leads 7

to additional constraints on the model.The most important observables are briefly discussed in the following: Anomalous magnetic moment of the muon:(g-2)of the muon is almost or- thogonal to the di-photon rate in our setup,in contrast to what was argued in the MSSM light stau scenario with slepton mass universality [29.The reason is that the slepton masses and mixings and correspondingly g-2 can be changed without chang- ing the di-photon rate.While it can happen that there are large contributions from pseudoscalars [30,31,these contributions can always be cancelled against the slepton contributions. p-parameter:the term ASHHa breaks the custodial SU(2)L present in the MSSM and SM.In general this can cause large contributions for instance to p =1-p ()where IIzz,IIww are the self-energies of the massive vector bosons. mw mz However,the size of the contributions caused by the singlet interaction is much smaller than in the case of a triplet interaction ArHuTHa and usually save [28,32. Top decays:A light charged Higgs boson can open new decay channels of the top quark like tH+b-betv.Recent searches at the LHC put upper bounds on the BR(t->H+b)in the range of 2-3%[33,34]. Radiative b decay:a very severe constraint comes from BR(b->sy),which we will therefore discuss in a bit more detail.2 The ratio of SUSY to SM contributions can be written as [35-38 R= BRb→s9sUsY≈1-2.55△C,+1.57(AC,)2, BR(b→SY)sM (12) where AC,are the new physics contributions to the Wilson coefficient of the electro- magnetic dipole operator (in our case mainly due to the charged Higgs and chargino states).Adding to the uncertainty of the SM prediction Br(B -Xsy)sM =(3.15+ 0.23).10-4 [36,37]an intrinsic SUSY error of 0.15 as well as the error of the experi- mental world average Br(BX,)xp=(3.43+0.22).10-4[40],leads to the following 95%CL bound R=0.87,1.31 (13) 2We would like to thank U.Haisch for illuminating discussions on this point. 8

to additional constraints on the model. The most important observables are briefly discussed in the following: Anomalous magnetic moment of the muon: (g − 2)µ of the muon is almost or￾thogonal to the di-photon rate in our setup, in contrast to what was argued in the MSSM light stau scenario with slepton mass universality [29]. The reason is that the slepton masses and mixings and correspondingly g − 2 can be changed without chang￾ing the di-photon rate. While it can happen that there are large contributions from pseudoscalars [30, 31], these contributions can always be cancelled against the slepton contributions. ρ - parameter: the term λSHuHd breaks the custodial SU(2)L present in the MSSM and SM. In general this can cause large contributions for instance to δρ = 1 − ρ = ΠWW (0) m2 W − ΠZZ (0) m2 Z where ΠZZ, ΠWW are the self-energies of the massive vector bosons. However, the size of the contributions caused by the singlet interaction is much smaller than in the case of a triplet interaction λT HuT Hd and usually save [28, 32]. Top decays: A light charged Higgs boson can open new decay channels of the top quark like t → H+b → be+ν. Recent searches at the LHC put upper bounds on the BR(t → H+b) in the range of 2-3% [33, 34]. Radiative b decay: a very severe constraint comes from BR(b → sγ), which we will therefore discuss in a bit more detail.2 The ratio of SUSY to SM contributions can be written as [35–38] R ≡ BR(b → sγ)SUSY BR(b → sγ)SM ' 1 − 2.55∆C7 + 1.57(∆C7) 2 , (12) where ∆C7 are the new physics contributions to the Wilson coefficient of the electro￾magnetic dipole operator (in our case mainly due to the charged Higgs and chargino states). Adding to the uncertainty of the SM prediction Br(B → Xsγ)SM = (3.15 ± 0.23) · 10−4 [36, 37] an intrinsic SUSY error of 0.15 as well as the error of the experi￾mental world average Br(B → Xsγ)exp = (3.43 ± 0.22)· 10−4 [40], leads to the following 95% CL bound R = [0.87, 1.31] . (13) 2We would like to thank U. Haisch for illuminating discussions on this point. 8

In the limit of a pure Higgsino-like chargino and a decoupled wino,these contributions can be approximated by △C+ tan(m+fa(m/m), 1 (14) △C m M3 t.(m M2)-uXtcanm f3(m/M2) (15) mμ2 with X:=A-Her/tan B and loop functions [41,42] i(x)= 7x-5x2-8x3,3x3-2x2 72c-19+12c-血x, 3x-5x2.3z2-2x f2(x)= 12x-1p+6c-1y nz, 7x2-13x3,3x4+2.x3-2x2 f3(x)= 12(e-103+ 6(x-1)4 Inx. (16) 500 300， mi=1 TeV 1.31 mH+300 GeV 280 260 240 125 1.3 1.25 200 180 160 100 100 200 300 400 5s00 400 600 800 100 mH+[GeV] mi [GeV] Figure 6:The ratio R as a function of the chargino mass and the charged Higgs mass (left) and stop mass(right).In both plots X:=0,M2=2 TeV and tan B=1 have been used While the charged Higgs loop depends only on the mass of the Higgs (and the top quark),the chargino loop depends on the stop sector as well as on the wino mass M2 in addition.In order to evade the experimental bound on R either the charged Higgs has to be sufficiently heavy,or there has to be a cancellation between the contributions 9

In the limit of a pure Higgsino-like chargino and a decoupled wino, these contributions can be approximated by ∆C H+ 7 ' 1 tan2 β f1(m2 t /m2 H+ ) + f2(m2 t /m2 H+ ) , (14) ∆C χ˜ + 7 ' − m2 t m2 t˜ M2 2 µ 2 eff f1(m2 t˜/M2 2 ) − µXt tan β m2 t m4 t˜ M2 2 µ 2 eff f3(m2 t˜/M2 2 ) , (15) with Xt = At − µeff/ tan β and loop functions [41, 42] f1(x) = 7x − 5x 2 − 8x 3 72(x − 1)3 + 3x 3 − 2x 2 12(x − 1)4 ln x , f2(x) = 3x − 5x 2 12(x − 1)2 + 3x 2 − 2x 6(x − 1)3 ln x , f3(x) = 7x 2 − 13x 3 12(x − 1)3 + 3x 4 + 2x 3 − 2x 2 6(x − 1)4 ln x . (16) 100 200 300 400 500 100 200 300 400 500 1.31 1.25 1.2 1.1 m˜χ + [GeV] mH+ [GeV] mt˜ = 1 TeV 200 400 600 800 1000 160 180 200 220 240 260 280 300 1.31 1.25 1.2 1.1 m˜χ + [GeV] mt˜ [GeV] mH+ = 300 GeV Figure 6: The ratio R as a function of the chargino mass and the charged Higgs mass (left) and stop mass (right). In both plots Xt = 0, M2 = 2 TeV and tan β = 1 have been used. While the charged Higgs loop depends only on the mass of the Higgs (and the top quark), the chargino loop depends on the stop sector as well as on the wino mass M2 in addition. In order to evade the experimental bound on R either the charged Higgs has to be sufficiently heavy, or there has to be a cancellation between the contributions 9