New Regions in the NMSSM with a 125 GeV Higgs

It is pointed out that mixing effects in the CP-even scalar sector of the NMSSM can give 6-8 GeV correction to the SM-like Higgs mass in moderate or large $\tan\beta$ regions with a small value of the singlet-higgs-higgs superfields coupling $\lambda\sim\mathcal{O}(0.1)$. This effect comes mainly from the mixing of the SM-like Higgs with lighter singlet. In the same parameter range, the mixing of the heavy doublet Higgs with the singlet may strongly modify the couplings of the singlet-like and the 125 GeV scalars. Firstly, the LEP bounds on a light singlet can be evaded for a large range of its masses. Secondly, the decay rates of both scalars can show a variety of interesting patterns, depending on the lightest scalar mass. In particular, a striking signature of this mechanism can be a light scalar with strongly suppressed (enhanced) branching ratios to $b\bar{b}$ ($gg$, $c\bar{c}$, $\gamma\gamma$) as compared to the SM Higgs with the same mass. The $\gamma\gamma$ decay channel is particularly promising for the search of such a scalar at the LHC. The 125 GeV scalar can, thus, be accommodated with substantially smaller than in the MSSM radiative corrections from the stop loops (and consequently, with lighter stops) also for moderate or large $\tan\beta$, with the mixing effects replacing the standard NMSSM mechanism of increasing the tree level Higgs mass in the low $\tan\beta$ and large $\lambda$ regime, and with clear experimental signatures of such a mechanism.


Introduction
The discovery of a SM-like Higgs particle has recently been announced by the LHC experiments [1,2]. Although its properties such as the production and decay rates into different channels still remain very uncertain [3,4], its mass is established to be around 125 GeV, with only a couple of GeV uncertainty, and this puts new constraints on the BSM models. In the minimal supersymmetric SM (MSSM) the Higgs tree-level quartic coupling is given by the electroweak gauge coupling, so that the theory predicts a tree-level upper bound for the Higgs mass to be equal M Z . It is well known that loop corrections, mainly from the top-stop loop, can significantly raise the Higgs mass in the MSSM. The mass of 125 GeV can be accommodated (with loop corrections giving 35 GeV) for certain range of values of the stop masses and left-right stop mixing parameter X t = A t − µ tan β. That range varies from M SUSY ≡ √ mt 1 mt 2 ≈ 700 GeV for the "maximal" stop mixing X t ≈ √ 6M SUSY to M SUSY ≈ O(5 TeV) for X t = 0 [5, 6] 1 . Such values of the stop mass parameters are well consistent with the absence so far of any stop signal at the LHC but may look high compared to the standard expectations based on the naturalness arguments. Awaiting for more experimental progress, one may discard those, after all quite subjective expectations, or one may hope that a light stop is still hidden in the data, and investigate the ways of reconciling the 125 GeV Higgs mass with stop mass parameters below the values quoted above. This necessarily requires a beyond MSSM scheme, with a larger tree-level Higgs mass than in the MSSM. (It is useful to note that stop loop radiative corrections ∆m rad h = 25 (30) GeV can be reached with M SUSY ≈ 300 (400) GeV for the maximal mixing and with M SUSY ≈ 1.5 (3) TeV for X t = 0). In this context, NMSSM has been discussed in the literature [9,10,11,12,13,14,15]. In the pre-discovery era, NMSSM was discussed mainly as a scenario allowing for a Higgs mass significantly above the values predicted by the MSSM [16,17,18,19,20]. The attention has been mostly focused on the new tree-level contribution to the Higgs mass coming from the singlet-doublet-doublet coupling in the superpotential, λSH u H d , which can be significant for low tan β values and O(1) values of λ. More recently, already after the discovery of the 125 GeV Higgs, the NMSSM has been discussed in the context of ameliorating the naturalness in the stop sector [21,22,23,24] also mainly for the same range of parameters. However, one may think that 125 GeV is close enough to the range expected in the MSSM, so that small corrections to the tree-level mass are worth considering. This is why it is interesting to investigate how significant may be the effect of the singlet-doublet mixing on the Higgs mass in the intermediate and large tan β region, where the MSSM tree-level value is ∼ M Z .
In NMSSM, there are three physical neutral CP-even Higgs fields, H u , H d , S which are the real parts of the excitations around the real vevs, v u ≡ v sin β, v d ≡ v cos β, v s with v 2 = v 2 u + v 2 d ≈ (174GeV) 2 , of the neutral components of doublets H u , H d and the singlet S (we use the same notation for the doublets and the singlet as for the real parts of their neutral components). It is more convenient for us to work in the basis (ĥ,Ĥ,ŝ), whereĥ = H d cos β + H u sin β,Ĥ = H d sin β − H u cos β andŝ = S. Theĥ field has exactly the same couplings to the gauge bosons and fermions as the SM Higgs field. The fieldĤ does not couple to the gauge bosons and its couplings to the up and down fermions are the SM Higgs ones rescaled by tan β and − cot β, respectively. The mass eigenstates are denoted as s, h, H, with the understanding that h is the SM-like Higgs.
In this paper we point out thatŝ −ĥ mixing effects can significantly contribute to m h , increasing it by 6-8 GeV, in the intermediate or large tan β region, making the NMSSM attractive also in that range of tan β. Important for this scenario is theŝ −Ĥ mixing, which becomes significant for larger values of tan β and can lead to a suppression of the s → bb decay rate (where s is the singlet-dominated scalar), so that the LEP bounds on a lighter than 114 GeV scalar coupling to the Z boson based on that decay channel are evaded. 2 The maximum mixing contribution to m h is then limited by much weaker bounds obtained from the s → hadrons signature. The effects discussed in this paper require smallish values of the coupling λ, O(0.1). Thus, the two regions of the NMSSM parameters, the low tan β one and the one considered here are clearly different.
Theŝ−Ĥ mixing at intermediate and large tan β has another interesting effect. It alters the decay rates of both s and h. They become correlated in an interesting way with the correction ∆m mix h and show a variety of interesting patterns, depending on the lightest scalar mass. In particular, a striking signature of this mechanism can be a light scalar with strongly suppressed (enhanced) branching ratios to bb (gg, cc, γγ) as compared to the SM Higgs with the same mass. The γγ decay channel is particularly promising for the search of such a scalar at the LHC.
In section 2 we recall the structure of the CP-even scalar sector and discuss the effects of theŝ −ĥ mixing on the Higgs mass, with the LEP bounds on a light scalar taken into account. In section 3 we discuss the potential role of theŝ −Ĥ mixing and the parameter range for which our mechanism can be relevant. In section 4 we give the predictions for the production and decays of the 125 GeV scalar if 5-8 GeV of its mass comes from theŝ −ĥ mixing effects. In section 5 we briefly discuss the prospects for the discovery of a light scalar at the LHC and in section 6 we give a summary of the considered here scenario.

CP-even scalar sector in NMSSM
In this section we recall the necessary for us facts about the CP-even scalar sector of NMSSM [28]. Several versions of NMSSM has been proposed so far [29,30,31]. We would like to keep our discussion as general as possible so we assume the NMSSM specific part of the superpotential to be: 3 (1) The first term is the source of the effective higgsino mass parameter, µ eff ≡ λv s (we drop the subscript "eff" in the rest of the paper), while the second term parametrizes various versions of NMSSM. In the simplest version, known as the scale-invariant NMSSM, f (S) ≡ κS 3 /3. We assume also quite general pattern of soft SUSY breaking terms (we follow the conventions used in [28]): (2) Various versions of NMSSM studied in the literature [29,30,31] belong to some subclass of the above setup. In the scale-invariant NMSSM, m 2 3 = m 2 S = ξ S = 0. Let us parametrize the mass matrix of the hatted fields as follows: vs . We neglected all the radiative corrections except those toM 2 hh which we parametrize by (δm 2 h ) rad . The first two terms in eq. (4) are the "MSSM" terms, with where M SUSY ≡ √ mt 1 mt 2 (mt i are the eigenvalues of the stop mass matrix at M SUSY in the DR renormalization scheme) and X t ≡ A t − µ/ tan β with A t being SUSY breaking top trilinear coupling at M SUSY .
The third term in eq. (4) is the new tree-level contribution coming from the λSH u H d coupling.
We recall that the eigenstates ofM 2 are denoted as s, h, H. We are interested in the parameter range such that m s < m h < m H , so that theŝ −ĥ mixing pushes the m h up. We also require m h < 2m s to avoid h → ss decays [33].
Quite generally, the mass of the SM-like Higgs reads: The (δm 2 h ) mix term originates mainly from the ĥ ,ŝ mixing and is positive (negative) when the singlet-dominated scalar is lighter (heavier) then the SM-like Higgs scalar. In the moderate and large tan β regime, the tree-level contribution coming from the λSH u H d coupling is suppressed so one has to investigate in detail the potential effects of (δm 2 h ) mix .

The effects of theŝ −ĥ mixing on the Higgs mass
In the case of no-mixing withĤ, theŝ −ĥ mixing is determined by the 2 × 2 block of the mass matrixM 2 : where the entries are given by eqs. (4), (6) and (8). The matrix (12) is diagonal in the basis In order to quantify the effect of theŝ −ĥ mixing on the Higgs mass it is useful to introduce ∆ mix such that: TradingM 2 hh ,M 2 ss ,M 2 hs for the two mass eigenvalues m h , m s and the coupling g s of the singletdominated state to the Z boson (normalized to the corresponding coupling of the SM Higgs), one obtains a simple formula for ∆ mix : where in the last, approximate equality we used the expansion in g 2 s 1. It is clear from the above formula that a substantial correction to the Higgs mass from the mixing is possible only for not too small couplings of the singlet-like state to the Z boson and that m s m h is preferred. However, LEP has provided rather strong constraints on the states with masses below O(110) GeV that couple to the Z boson because such states could be copiously produced in the process e + e − → sZ.
For those LEP searches that rely on the identifications of b and τ in the final states [34], constraints on g 2 s depend on the s branching ratios and the LEP experiments provide constraints on the quantity ξ 2 defined as: 4  Table 14 in Ref. [34], while the green line corresponds to Figure 2 of [35]. Right: The LEP limits translated to the upper limits on ∆ mix using eq. 14 assuming ξ 2 bb = g 2 s and ξ 2 jj = g 2 s for the red and green line, respectively.
The LEP constraints on ξ 2 bb are reproduced by the red line in the left panel of Figure 1. Since we assume in this subsection thatŝ mixes only withĥ, all the couplings of s are those of the SM Higgs multiplied by a common factor g s . This implies that the branching ratios of s are exactly the same as for the SM Higgs. Therefore, the limits on ξ 2 bb depicted by the red line in Figure 1 are, in fact, also the limits on g 2 s . Using eq. (14) we can translate the constraints on g 2 s into limits for the maximal allowed correction from the mixing, ∆ max mix , as a function of m s . These are presented in the right panel of Figure 1. Notice that in this case the correction from the singlet-doublet mixing can reach about 6 GeV in a few-GeV interval for m s around 95 GeV, where the LEP experiments observed the 2σ excess in the bb channel. This is interesting since such correction combined with the tree-level values ∼ M Z (for moderate and large tan β) gives m h ≈ 125 GeV with ∆m rad h ≈ 30 GeV. However, for m s 90 GeV the allowed value of ∆ max mix drops down very rapidly to very small values. In Figure 2 we present an example of the NMSSM parameters for which mixing withĤ is negligible and ∆ mix ≈ 6 GeV can be obtained. Note that theĥ −ŝ mixing, thus also ∆ mix , grows with tan β as a consequence of the suppression of the second term in the parenthesis in M 2 hs at large tan β, see eq. (8). This example demonstrates also the fact that λ is generically at most O(0.1). Larger values of λ typically lead to too largeM 2 hs (after taking into account the LEP limit on the chargino mass which imply µ 100 GeV) leading to a negative determinant of the mass matrix. Therefore, this scenario is the most natural at moderate and large tan β. 5 It is also clear from Fig. 1 that similar correction O(5) GeV to the Higgs mass can be obtained from theŝ −ĥ mixing for a larger range of the singlet-dominated scalar mass m s , provided one can evade the LEP bounds given by the red curve in the left panel of Fig. 1 by suppressing the sbb and sττ couplings. This is because in such a case, s decays predominantly into charm quarks and gluons and b-tagging cannot be used to enhance the signal over background ratio so the most stringent constraints on g 2 s come from the flavour independent Higgs searches in hadronic final states at LEP [35]. Those searches give constraints on a quantity ξ 2 jj defined as: which are reproduced by the green line in the left panel of Fig. 1. Noting that for suppressed sbb and sττ couplings, BR(s → jj) ≈ 1 so ξ 2 jj ≈ g 2 s , we can translate those constraints into the upper bound on ∆ mix . Indeed, the upper bound ∆ max mix is then given by the green curve in the right panel of Fig. 1.
We show in the next section thatŝ −Ĥ mixing can significantly change the decay rates of s and also of h. 6 Firstly, the ∆ max mix shown by the green line in Fig. 1 can then be obtained for a broad range 60 GeV < m s < 110 GeV, and secondly the decay rates of s and h can have interesting patterns.
small tan β can only be obtained if (2µ − Λ sin(2β)) (which entersM 2 hs ) is finely-tuned to be below O(10GeV). 6 A suppression of the s → bb decay rate is possible for any value of m s but for m s in the few-GeV interval around 95 GeV there is no gain in ∆ max mix because the red and green curves in Fig. 1 practically overlap there.

Singlet mixing with both doublets and the suppression of the sbb coupling
We now go back to the general case in which mixing withĤ may be present. As in the previous section, we begin with the implications following from the general structure of the mass matrix.
Mixing withĤ leads to the modification of Higgs couplings to fermions. Denoting the masseigenstates s, h, H by xŝ we get where x is s, h or H. Note that the couplings to the vector bosons depend only on theĥ components, as in the case of only (ĥ,ŝ) mixing discussed in the previous subsection.
In the region of moderate and large tan β even small component ofĤ in the singletdominated Higgs may give a large contribution to the couplings to b quark due to tan β enhancement. On the other hand, the couplings to the up-type quarks are almost the same as those to the gauge bosons, C tx ≈ C Vx . Particularly interesting is the case when g s has the opposite sign to β (H) s because then C bs C ts , C Vs is possible. In the regime C bs C ts , C Vs , the (otherwise dominating) s branching ratios to bb and ττ are strongly suppressed and s decays mainly to gg and cc. The ratio Γ(s → gg)/Γ(s → cc) is roughly the same as for the SM Higgs so e.g. for m s = 90 GeV it equals about 1.5 [36,37] and approximately scales like m 2 s for other masses [38]. In this regime the standard LEP Higgs searches [34] that used b-tagging cannot be applied to constrain this scenario. In such a case, the most stringent constraints comes from the flavour independent search for a Higgs decaying into two jets at LEP [35]. These constraints are weaker and allow for values of g 2 s above 0.3 for m s around 100 GeV and the limit rather slowly improves as m s goes down, as seen from the left panel of Figure 1. In consequence, the constraints on ∆ max mix are also weaker. As can be seen from the right panel of Figure 1, when s → bb decays are suppressed ∆ mix above 5 GeV is viable for a large range of m s with a maximum of about 8 GeV for m s around 100 GeV.
We should also comment on the fact that for C bs C ts , C Vs the s branching ratios to the gauge bosons are also enhanced (with respect to the SM Higgs predictions) by a factor that can exceed 10. In spite of such a large enhancement the Higgs searches in these channels performed at LEP [39] are less constraining than the above-discussed searches with hadronic decays. On the other hand, the LHC searches in the diphoton channel may, in principle, have a potential to give additional constraints on this scenario (i.e. reduce the allowed value of ∆ max mix ). In fact, s → γγ decays could already be seen at the LHC but the SM Higgs searches in the diphoton channel have been performed only for masses above 110 GeV. This will be discussed in more detail in section 5 In the above discussion we assumed that the strong suppression of the s coupling to b quarks is possible. Let us now discuss in which part of the NMSSM parameter space such situation may hold. As already stated, this may happen only for not too small values of tan β and a negative ratio β At large tan β,M 2 hH ≈ −2(M 2 Z −λ 2 v 2 )/ tan β is very small so the second terms in the numerator and the denominator are typically subdominant 7 which means that β HsM 2 hs < 0 (we recall that m 2 s <M 2 hh in our case) which leads to the following condition for the NMSSM parameters: which is satisfied only if µΛ > 0. In the following discussion we will assume, without loss of generality, Λ > 0 and µ > 0. It is straightforward to show in the limit of large tan β that C bs may vanish only if where If the condition (22) is satisfied then C bs ≈ 0 corresponds to two values of tan β: which in the limit r 2 2Λ 2 µ 2 are given by: Let us now demonstrate some numerical examples in which the suppression of C bs is present and substantial values of ∆ mix is obtained without violating the LEP constraints. In Figure 3 a tan β-dependence of ∆ mix is presented. It is clear from this Figure that substantially larger ∆ mix is consistent with the LEP data due to the suppression of the sbb coupling. In the left panel, m s = 100 GeV and ∆ mix can be almost 8 GeV. The role of the suppression of the sbb coupling is even more important for lighter singlet-dominated states. In the right panel, m s = 75 GeV and ∆ mix can reach 6 GeV at large tan β, while without the suppression it would be below 2 GeV.
It can also be seen from Figure 3 that there exist values of tan β for which the sbb coupling is strictly zero. Nevertheless, such a strong suppression is not necessary to avoid the LEP constraints. In fact it is enough to suppress BR(s → bb) by about 25% in the case of m s = 100 GeV and by a factor of three for m s = 75 GeV. This implies rather large range of tan β with significant correction from the mixing consistent with the LEP data. 7 Strictly speaking, the second terms in the numerator and the denominator can dominate for Λ → 0 because thenM 2 Hs → 0. In such a case β (H) s /g s is negative ifM 2 hH > 0 which is possible only if λ 2 v 2 > M 2 Z . However, for λ 2 v 2 > M 2 Z and Λ → 0 the mass matrix has a negative eigenvalue ifM 2 ss <M 2 hh (which is a necessary condition for s to be lighter than h). In our analysis we use the eigenvalues of the Higgs mass matrix as input parameters while the diagonal entries of this matrix are output parameters. Such procedure is justified because any values of the diagonal entries can be obtained by adjusting the soft terms in appropriate way. However, it is natural to ask whether the required values of soft terms are reasonable. One cannot answer this question in a model-independent way so let us focus on the no-scale version of NMSSM which is the most popular one and calculate the soft terms in some representative examples. In such a case, µ = λv s , B = A λ + κv s and Λ = A λ + 2κv s . Requiring the correct electroweak minimum, for the parameters used in the left panel of Figure 3 one obtains for tan β = 25 (corresponding to ∆ mix ≈ 7.3 GeV): while for the parameters used in the right panel of Figure 3 one obtains for tan β = 35 (corresponding to ∆ mix ≈ 6 GeV):

Production and decays of the 125 GeV Higgs
The mixing effects affect not only the branching ratios and production cross-section of s but also those of h. Moreover, they are correlated so the scenario may be tested also by the measurements of the signal strengths for the 125 GeV Higgs. In order to set a notation let us define the signal strengths modifiers as: In the case of theĥ −ŝ mixing, with the effects ofĤ neglected, all the h couplings are multiplied by a common factor 1 − g 2 s . This implies that all the h branching ratios are the same as for the SM Higgs while the production cross-section (in all channels) is smaller by a factor 1 − g 2 s so R (h) i = 1 − g 2 s for all channels. This means that, after taking into account the LEP constraints, ∆ mix > 5 GeV implies 0.75 R (h) i 0.83. In the full 3 × 3 mixing case at large tan β, the couplings to the up-type quarks are almost the same as those to the gauge bosons, s so the production cross-section is still smaller than the SM prediction by a factor 1−g 2 s . However, the couplings to the down-type fermions can be substantially modified, as seen from eq. (17). Since the bb channel dominates the decays of the 125 GeV SM Higgs (BR SM (h → bb) ≈ 58% and BR SM (h → ττ ) ≈ 6%) such modifications lead to important effects for all the other branching ratios. If β (H) h /g h is negative (positive) then the h couplings to b and τ are smaller (larger) than in the SM which leads to the enhancement (suppression) of the Higgs branching ratios to the gauge bosons and two photons. This ratio is given by and its sign is: SinceM 2 hH is small, the enhancement (suppression) of the h coupling to b requiresM 2 HsM 2 hs < 0 (> 0). Note that this is the opposite condition to that for the s coupling so if the s coupling to b is enhanced (suppressed) then the h coupling to b is suppressed (enhanced). As it was discussed in the previous section, for the m s in the range between about 90 and 105 GeV, ∆ mix can exceed 5 GeV with the LEP constraints satisfied independently of the sbb coupling and both discussed above options are interesting. From the current experimental viewpoint the suppressed h coupling to b is more welcome in order to compensate the suppression of the h production cross-section and end up with R (h) 8 However, given the present tension between the CMS and ATLAS results the case with the enhanced h coupling to b is certainly not excluded.
The predictions for R (h) γγ are very similar to R (h) V V because the reduced couplings to top and W (which contribute to the h → γγ decay in the SM) are almost the same at large tan β, V V , which is preferred by the ATLAS data, is possible only if contributions of SUSY particles to the h → γγ decay width is non-negligible. It was shown in Refs. [41,32] that such enhancement can be substantial for light higgsinos and λ ∼ O(1). However, we found that this effect is small in our case since λ is required to be O(0.1) at most. The most promising way to obtain the γγ enhancement would be the presence of very light staus with strong left-right mixing which may be possible if tan β is large [42].

s with strongly suppressed couplings to b and τ
It is crucial to note that the couplings of h and s to b are correlated. It is the purpose of this subsection to investigate the implications of the strongly suppressed s couplings to b for the production rates of h.
In order to study quantitatively the correlation between the correction to the Higgs mass from mixing and the production rates for h we performed a numerical scan over the NMSSM parameter space for various values of m s and m H while keeping fixed m h = 125 GeV. In the scan we also fixed µ = 150 GeV. For other values of µ the results of the scan are the same provided that the following transformation of parameters is used: This is becauseM 2 hs andM 2 Hs are invariant under the above transformation whileM 2 hH is only marginally affected so its impact on the numerical results is negligible. The remaining parameters where scanned on a grid, see Table 1 for the scanned parameters ranges and step sizes. In order to emphasize that obtaining substantial values of ∆ mix does not require any fine-tuning the grid is not dense, as clearly seen from Table 1. In Figure 4 a scatter plot of ∆ mix versus m s is presented. The LEP constraints discussed before have been taken into account. It can be seen that ∆ mix up to about 9 GeV can be obtained for m s ≈ 100 GeV but for such large values of ∆ mix R (h) V V < 0.5 is predicted, which is in tension with the LHC Higgs data. 9 Nevertheless, demanding R V V > 0.7, which is well consistent with the LHC data within the experimental errors, can be obtained for a wide range of values between m h /2 and 105 GeV.
The reduction of R (h) V V is due to the h production cross-section suppressed by a factor 1 − g 2 s and the suppressed BR(h → V V ), as a consequence of the enhanced hbb coupling. However, for m s between about 90 and 105 GeV, where the LEP constraints on g 2 s are not so strong 8 Such a scenario was investigated for low tan β in [40] with a special attention to possible γγ rate enhancement for the 125 GeV Higgs. 9 Notice that maximal values of ∆ mix for a given m s in Figure 4 are slightly larger than the corresponding values in the right panel of Figure 1. This is because in Figure 1 BR(s → jj) = 1, i.e. g 2 s = ξ 2 jj , is assumed, while for the points from the numerical scan that are consistent with the LEP data the sbb and sττ couplings are not exactly zero so BR(s → ττ ) > 0 leading to g 2 s > ξ 2 jj .   and m s is still significantly below 125 GeV, suppression of the sbb coupling is not necessary for obtaining substantial values of ∆ mix . Therefore, in that range R (h) V V > 1 can be obtained with ∆ mix 5 GeV. Such solutions are characterised by the enhanced sbb coupling and suppressed hbb coupling.
Since for moderate and large tan β, C V ≈ C t , the predictions for R  ZZ by a few percent. We should stress that our analysis is performed at tree level. It is well known that at large tan β SUSY threshold correction to the bottom quark Yukawa coupling may be substantial [43,44]. If those corrections act in such a way that the loop-corrected C b h is smaller than the tree-level value then the h branching ratio into gauge bosons is enhanced. Thus, in principle some regions of the NMSSM parameter space may exist in which ∆ mix reaches 8 GeV and R (h) V V is around one, without violation of the LEP constraints. However, a detailed study of such corrections is beyond the scope of this paper.

Prospects for discovery of s at the LHC
Let us now discuss prospects for discovery of s at the LHC. What the experiments observe is the product of the production cross-section and the branching ratios: If the s branching ratio to bb is not strongly modified as compared to that of the SM Higgs, the signal strengths in all channels are universally suppressed R is about 0.9 with the data that have been analysed so far i.e. 5 fb −1 of the 7 TeV data and 13 fb −1 of the 8 TeV data [46,47]. From a naive extrapolation to higher luminosities one expects that about 200 fb −1 of the 14 TeV run will be required to test this scenario.

s with strongly suppressed couplings to b and τ
It should be clear from the previous section that the scenario with a strong suppression of the sbb and sτ τ couplings can be constrained by the precision measurements of the 125 GeV Higgs couplings. Even more interesting is the fact that the LHC is already well prepared for a discovery of s. This is because in this scenario the total decay width of s is strongly reduced so all the s branching ratios, except those for the s decays to the down-type fermions, are strongly enhanced.
Particularly interesting is the γγ final state. 11 In Figure 5 we present the predictions for R (s) γγ assuming maximal value of g 2 s consistent with the LEP s → jj data (corresponding to maximal value of ∆ mix allowed by the LEP data) as a function of m s . In the extreme case when the sbb and sτ τ couplings are suppressed to zero (the black line in Figure 5), the γγ signal from s decays is stronger than that from the SM Higgs with the same mass for the whole range of m s . For m s around 100 GeV the enhancement can almost reach a factor of three.
As we already mentioned, it is not necessary to suppress the sbb and sτ τ couplings exactly to zero. In fact, it is enough to suppress them to the level for which the LEP constraints on ξ 2 bb are satisfied. The blue line in Figure 5 correspond to the minimal suppression of sbb and sτ τ couplings required to satisfy the constraints on ξ 2 bb . Even in this case R (s) γγ > 1 for a wide 10 Particularly interesting possibility is the singlet-like Higgs with mass about 98 GeV because it can explain the LEP excess in the bb channel [45]. 11 The possibility of large γγ rate enhancement for the singlet-like NMSSM boson was noticed in Ref. [48]. In contrast to the present paper, in Ref. [48] small values of tan β ≈ 3 were considered. γγ is about 0.6 which already constrain the allowed values of g 2 s , thus also ∆ max mix , for this particular mass. Therefore, one can expect that the LHC searches are sensitive enough to probe this scenario in the γγ channel also for smaller values of m s .
Since the expected limit on R for masses below 100 GeV using the available data if these were analysed.

Conclusions
We have studied in detail the mixing between the three physical scalars s, h and H of the CPeven scalar sector of the NMSSM. In a large parameter range, it can lead to several interesting, often correlated, effects. First of all, theŝ −ĥ mixing can give 6-8 GeV contribution to the mass of the SM-like scalar h in the moderate and large tan β region and with λ ∼ O(0.1). This is interesting because the 125 GeV mass is then obtained with significantly lower stop masses in the stop-top loops. The geometric mean of the stop masses, M SUSY , can be below about 400 GeV (2 TeV) for the maximal contribution from stop mixing (with no stop mixing at all). Thus, the NMSSM is interesting also beyond the usually considered region of low tan β and λ ∼ O(1).
Theŝ −ĥ mixing contribution to m h depends mainly on the mixing angle between the two fields (i.e. on the sZZ coupling g s ) and on their mass difference. Thus the effect is constrained by the LEP bounds on g s vs m s obtained assuming for s the SM Higgs branching ratios and with b and τ identification in the final state, or without such particle identification assuming BR(s → hadrons) = 1. The two experimental bounds almost overlap for m s in the 5 GeVinterval around 95 GeV but for other s masses the bound based on the detection of two nonidentified hadronic jets is much weaker. For m s in the 5 GeV-interval around 95 GeV the O(6 GeV) mixing contribution to m h can thus be obtained independently of the decay modes of s. However, for other values of m s the mixing contribution is much smaller, unless the LEP bound based on the b and τ identification is evaded, i.e. if s → bb is suppressed strongly enough. In the latter case, the 5-8 GeV effect is obtained for the range 60-110 GeV of m s , consistently with the LEP bound based on the search for two hadronic jets, with BR(s → hadrons) = 1.
Interestingly enough, a strong s → bb suppression can be present due to theŝ −Ĥ mixing (with negligible effect on theŝ −ĥ sector), which is important in the considered region because of the tan β enhancement of the scalar down quark couplings. Thus the LEP bounds can be evaded. The lightest scalar s has then enhanced branching ratios into ZZ * , W W * and γγ. The latter one is a particularly promising signature for the LHC searches for a scalar lighter than 110 GeV, with suppressed bb decay channel. The signal strength in the γγ channel of this scalar may be larger than that of the SM Higgs, even by a factor of three. In fact, if such singlet-like scalar with mass below 110 GeV really exists it could have already been discovered at the LHC if the already collected data were analysed in this range of masses. Thus, we strongly encourage the ATLAS and CMS collaborations to extend their Higgs searches in the γγ channel to masses in the 60-110 GeV range.
Theŝ−Ĥ mixing modifies also the h decays, in a way anti-correlated with the s decays. The ones suppressed for s are enhanced for h and vice versa. Thus, the large mixing contribution to m h can be present together with a variety of interesting patterns for the h production and decays. If m s is between about 90 and 105 GeV, the mixing correction to m h exceeding 5 GeV does not require the suppression of the sbb coupling and e.g. BR(h → γγ) can be either enhanced or suppressed as compared to the SM prediction. If m s is smaller or larger than the values given above, the large mixing effect is generically correlated with suppressed rates in ZZ, W W and γγ channels and enhanced ones in bb, τ τ channels for h. The magnitude of that suppression (enhancement) depends on the particular choice of parameters.
The effects considered in this paper do not require any particular fine tuning of the NMSSM parameters and are present in a large part of parameter space.