Higgs Bosons at 98 and 125 GeV at LEP and the LHC

We discuss NMSSM scenarios in which the lightest Higgs boson $h_1$ is consistent with the small LEP excess at about 98 GeV in $e^+e^- \to Zh$ with $h\to b\anti b$ and the heavier Higgs boson $h_2$ has the primary features of the LHC Higgs-like signals at 125 GeV, including an enhanced $\gamma\gamma$ rate. Verification or falsification of the 98 GeV $h_1$ may be possible at the LHC during the 14 TeV run. The detection of the other NMSSM Higgs bosons at the LHC and future colliders is also discussed, as well as dark matter properties of the scenario under consideration.


I. INTRODUCTION
Data from the ATLAS and CMS collaborations [1,2] provide an essentially 5σ signal for a Higgs-like resonance, h, with mass of order 125 GeV. Meanwhile, the CDF and D0 experiments have announced new results [3], based mainly on V h associated production with h → bb, that support the ∼ 125 GeV Higgs-like signal. While it is certainly possible that the observed signals in the various production/decay channels will converge towards their respective Standard Model (SM) values, the current central values for the signal strengths in individual channels deviate by about 1-2 σ from predictions for the h SM . One of the most significant deviations in the current data is the enhancement in the γγ final state for both gluon fusion (gg) and vector boson fusion (VBF) production. Such a result is not atypical of models with multiple Higgs bosons in which the bb partial width of the observed h is reduced through mixing with a second (not yet observed at the LHC) Higgs boson, h , thereby enhancing the γγ branching ratio of the h [4][5][6][7][8][9]. In such models, a particularly interesting question is whether one could simultaneously explain the LHC signal and the small (∼ 2σ) LEP excess in e + e − → Zbb in the vicinity of M bb ∼ 98 GeV [10,11] using the h with m h ∼ 98 GeV. We recall that the LEP excess is clearly inconsistent with a SM-like Higgs boson at this mass, being only about 10 − 20% of the rate predicted for the h SM . Consistency with such a result for the h is natural if the h couples at a reduced level to ZZ, which, in turn, is automatic if the h has substantial ZZ coupling, as required by the observed LHC signals.
In this paper we demonstrate that the two lightest CP-even Higgs bosons 1 , h 1 and h 2 , of the Next-to-Minimal Supersymmetric Model (NMSSM) could have properties such that the h 1 fits the LEP excess at ∼ 98 GeV while the h 2 is reasonably consistent with the Higgs-like LHC signals at ∼ 125 GeV, including in particular the larger-than-SM signal in the γγ channel. The NMSSM [12] is very attractive since it solves the µ problem of the minimal supersymmetric extension of the SM (MSSM): the ad hoc parameter µ appearing in the MSSM superpotential term µĤ uĤd is generated in the NMSSM from the λŜĤ uĤd superpotential term when the scalar component S ofŜ develops a VEV S = s: µ eff = λs. The three CP-even Higgs fields, contained in H u , H d and S, mix and yield the mass eigenstates h 1 , h 2 and h 3 . A 125 GeV Higgs state with enhanced γγ signal rate is easily obtained for large λ and small tan β [5] (see also [7,8]). To describe the LEP and LHC data the h 1 and h 2 must have m h 1 ∼ 98 GeV and m h 2 ∼ 125 GeV, respectively, with the h 1 being largely singlet and the h 2 being primarily doublet (mainly H u for the scenarios we consider). In addition to the CP-even states, there are also two CP-odd states, a 1 and a 2 , and a charged Higgs boson, H ± . Verification of the presence of the three CP-even Higgs bosons and/or two CP-odd Higgs bosons would establish a Higgs field structure that goes beyond the two-doublet structure of the MSSM.

II. HIGGS BOSON PRODUCTION AND DECAY
The main production/decay channels relevant for current LHC data are gluon fusion (gg) and vector boson fusion (VBF) with Higgs decay to γγ or ZZ * → 4 . The LHC also probes W, Z+Higgs with Higgs decay to bb, a channel for which Tevatron data is relevant, and W W →Higgs with Higgs→ τ + τ − . We compute the ratio of the gg or VBF induced Higgs cross section times the Higgs branching ratio to a given final state X, relative to the corresponding value for the SM Higgs boson, as where h i is the i th NMSSM scalar Higgs, and h SM is the SM Higgs boson, taking m h SM = m h i .
In the context of any two-Higgs-doublet plus singlets model, not all the R h i are independent. For In order to display the ability of the NMSSM to simultaneously explain the LEP and LHC Higgs-like signals, we turn to NMSSM scenarios with semi-unified GUT scale soft-SUSY-breaking.
By "semi-unified" we mean universal gaugino mass parameter m 1/2 , scalar (sfermion) mass parameter m 0 , and trilinear coupling A 0 ≡ A t = A b = A τ at the GUT scale, but m 2 Hu , m 2 H d and m 2 S as well as A λ and A κ are taken as non-universal at M GUT . Specifically, we use points from scans performed using NMSSMTools 3.2.0 [13][14][15], which includes the scans of [8] supplemented by additional runs following the same procedure as well as specialized MCMC chain runs designed to focus on parameter regions of particular interest. All the accepted points correspond to scenarios that obey all experimental constraints (mass limits and flavor constraints as implemented in NMSSMTools, Ωh 2 < 0.136 and 2011 XENON100 constraints on the spin-independent scattering cross section) except that the SUSY contribution to the anomalous magnetic moment of the muon, δa µ , is too small to explain the discrepancy between the observed value of a µ [16] and that predicted by the SM. For a full discussion of the kind of NMSSM model employed see [7,8,17].
We first display in Fig. 1  gg (γγ) > 1 as preferred by LHC data. In all the remaining plots we will impose the additional requirements: R h 2 gg (γγ) > 1 and 0.1 ≤ R h 1 V BF (bb) ≤ 0.25. In the following, we will refer to these NMSSM scenarios as the "98 + 125 GeV Higgs scenarios".
To repeat, the R h 2 gg (γγ) > 1 requirement is such as to focus on points that could be consistent (within errors) with the enhanced γγ Higgs signal at the LHC of order 1. 5  the γγ signal arising from the h 1 for both production mechanisms is quite small and unlikely to be observable. Note the two different R h 2 gg (γγ) regions for which Ωh 2 lies in the WMAP window, one with R h 2 gg (γγ) ∼ 1.6 (region A, red diamonds) and the other with R h 2 gg (γγ) ∼ 1.1 (region B, orange diamonds). As we will show later, region A corresponds to m χ 0 1 ∼ 77 GeV and mt 1 between 197 GeV and 1 TeV, while the region B corresponds to m χ 0 1 > 93 GeV and mt 1 > 1.8 TeV. These same two regions will emerge in many subsequent figures. If R h 2 gg (γγ) ends up converging to a large value, then masses for all strongly interacting SUSY particles would be close to current limits if the present 98 + 125 GeV LEP-LHC Higgs scenario applies.
The bottom row of the figure focuses on the bb final state. We observe the reduced R h 2 gg (bb) and R h 2 V BF (bb) values that are associated with reduced bb width (relative to the SM) needed to have enhanced R h 2 gg (γγ) and R h 2 V BF (γγ). Meanwhile, the R h 1 gg (bb) and R h 1 V BF (bb) values are such that the h 1 could not yet have been seen at the Tevatron or LHC. Sensitivity to R h 1 gg (bb) (R h 1 V BF (bb)) values from 0.05 to 0.2 (0.1 to 0.25) will be needed at the LHC. This compares to expected sensitivities after the √ s = 8 TeV run in these channels to R values of at best 0.8. 4 Statistically, a factor of 4 to 10 improvement requires integrated luminosity of order 16 to 100 times the current L = 10 fb −1 .
Such large L values will only be achieved after the LHC is upgraded to 14 TeV, although we should note that the luminosity required to probe this signal at 14 TeV could be lower than indicated by this simple estimate as the sensitivity to the Higgs signal improves at higher energies. Finally, the reader should note that for WMAP-window points the largest R h 1 V BF (bb) values occur for region A described above for which supersymmetric particle masses are as small as possible.  , mt 1 , mt 2 , mq, mg, and the mixing parameter

III. OTHER NMSSM PARTICLES AND PARAMETERS
It is also very interesting to consider expectations for the other NMSSM particles in these scenarios. For this purpose, we present a series of plots. Figure 3 displays the pseudoscalar masses in the m a 1 -m a 2 plane. We do not plot m h 3 nor m H ± since their masses are such that m h 3 m H ± m a 2 for the scenarios considered. We note that small m a 1 is typical of the WMAPwindow points. We discuss discovery prospects for the a 1 later in the paper. The masses of some crucial SUSY particles are displayed in Fig. 4. We observe the typically low values of m χ 0 1 and m χ ± 1 , the possibility of mt 1 as small as 197 GeV, the mostly modest values of the mixing parameter (A t − µ cot β)/ √ mt 1 mt 2 , and the fact that the predicted mq and mg are beyond current experimental limits, although the lowest values (as found in particular in region A) may soon be probed. Note that mg can be below m R (as common in constrained models when m 0 is large) for some points, including the points in region A. Low values of m χ 0 1 are typical for the scan points, but more particular to this model are the rather low values of m χ ± 1 . ATLAS and CMS are currently performing analyses that could in principle be sensitive to the m χ ± 1 values predicted in this model.
For some points, m χ ± 1 −m χ 0 1 can be rather small, implying some difficulty in isolating the leptons or jets associated with χ ± 1 → χ 0 1 +X decays. However, it should be noted that for the WMAP-window points m χ ± 1 − m χ 0 1 is typically quite substantial, at least 35 GeV for the low-m χ 0 1 points, so that for these points the above difficulty would not arise. Of particular interest is the very large range of mt 1 that arises in the 98 + 125 GeV LEP-LHC Higgs scenarios. For lighter values of mt 1 , as typical of the WMAP-window points in region A, thet 1 always decays viat 1 → χ + 1 b ort 1 → χ 0 1 t, the latter being absent when mt 1 < m χ 0 1 + m t . At high mt 1 , these same channels are present but alsot 1 → χ 0 2,3,4,5 t can be important, which channels being present depending upon whether It is interesting to survey the GUT scale parameters that lead to the scenarios of interest.
Relevant plots are shown in Fig. 5. No particular regions of these parameters appear to be singled out aside from some preference for negative values of A 0 . These plots show clearly that scenarios A and B correspond to distinct regions in the parameter space. Note however that the density of red points in these plots is purely due to our scan procedures which have some focus on region A.

IV. DARK MATTER, INCLUDING LSP AND LIGHT CHARGINO COMPOSITIONS
The composition of the χ 0 1 and the χ ± 1 are crucial when it comes to the relic density of the χ 0 1 . For those points in the WMAP window in region A (red diamonds), the χ 0 1 can have a large Higgsino fraction since the χ 0 1 χ 0 1 → W + W − annihilation mode (mainly via t-channel exchange of the light Higgsino-like -see second plot of Fig. 6 -chargino) is below threshold; the group of points with m χ 0 1 > 93 GeV (region B, orange diamonds) can lie in the WMAP window only if the χ 0 1 does not have a large Higgsino fraction. This division is clearly seen in Fig. 6. We note that to a reasonable approximation the singlino fraction of the χ 0 1 is given by 1 minus the Higgsino fraction plotted in the left-hand window of the figure.
Dark matter (DM) properties for the surviving NMSSM parameter points are summarized in The main mechanism at work to make Ωh 2 too small for many points is rapid χ 0 1 χ 0 1 annihilation to W + W − due to a substantial Higgsino component of the χ 0 1 (see third plot of Fig. 7). Indeed, the relic density of a Higgsino LSP is typically of order Ωh 2 ≈ 10 −3 −10 −2 . As the Higgsino component declines Ωh 2 increases and (except for the strongly overlapping points with m χ 0 1 < m W , for which χ 0 1 χ 0 1 → W + W − is below threshold) it is the points for which the LSP is dominantly singlino that have large enough Ωh 2 to fall in the WMAP window.
Also plotted in Fig. 7 is the spin-independent direct detection cross section, σ SI , as a function of  [18]. We recall that the observation requires σv ( χ 0 1 χ 0 1 → γγ) ∼ 10 −27 cm 3 /sec (this quoted value assumes standard dark matter density, ρ ∼ 0.3). 5 The situation is illustrated in Fig. 8 where we plot σv ( χ 0 1 χ 0 1 → a 1 → γγ) vs. Ωh 2 for just those points with m χ 0 1 ∈ [125, 135] GeV. (It is the schannel a 1 diagram that can give a large σv .) We observe that points with Ωh 2 in the WMAP window have values of σv four orders of magnitude below that required to explain the excess.
Those points with the largest σv always have quite small Ωh 2 and hence ρ DM . Incidentally, we have checked that all the points in our plots are fully consistent with the current bounds from the continuum γ spectrum as measured by Fermi-LAT [19,20].
If the 130 GeV gamma ray line is confirmed, then the above questions will need to be explored more carefully. That a fully general NMSSM model (no GUT scale unifications) can be consistent simultaneously with the WMAP window, σv ( χ 0 1 χ 0 1 → a 1 → γγ) ∼ 10 −27 cm 3 /sec, a Higgs mass close to 125 GeV and 2011 XENON100 constraints was demonstrated in [21]. However, the value of 5 Here, and below, v is the very small velocity typical of dark matter in the current epoch, v ∼ 10 −3 c, as relevant for indirect detection of the χ 0 1 through χ 0 1 χ 0 1 annihilations. This, of course, differs from the velocity at the time of freeze out, which is substantially higher.

V. FUTURE TESTS OF THE 98 + 125 GeV HIGGS SCENARIO
A critical issue is what other observations would either confirm or rule out the 98 + 125 GeV LEP-LHC Higgs scenarios. We first discuss possibilities at the LHC and then turn to future colliders, including a future e + e − collider, a possible γγ collider and a future µ + µ − collider.

A. Direct Higgs production and decay at the LHC
We have already noted in the discussion of Fig. 2 that gg and VBF production of the h 1 with h 1 → bb provide event rates that might eventually be observable at the LHC once much higher integrated luminosity is attained. Other possibilities include production and decay of the a 1 , a 2 , and h 3 . Decay branching ratios and LHC cross sections in the gg fusion mode for a 1 , a 2 and h 3 are shown in Fig. 9. Since the a 1 is dominantly singlet in nature, its production rates at the LHC are rather small. The largest σBR(X) values are in the X = bb final state, but this final state will have huge backgrounds. When allowed, σBR(X) for X = χ 0 1 χ 0 1 can be significant, but observation of this invisible final state would require a jet or photon tag that would further decrease the cross section. The a 2 is dominantly doublet and provides better discovery prospects. If m a 2 > 2m t , the tt final state has σ(gg → a 2 )BR(a 2 → tt) > 0.01 pb for m a 2 < 550 GeV, implying > 200 events for L = 20 fb −1 . A study is needed to determine if this would be observable in the presence of the tt continuum background. No doubt, efficient b tagging and reconstruction of the tt invariant mass in, say, the single lepton final state would be needed. For m a 2 < 2m t , the X = a 1 h 2 final state with both a 1 and h 2 decaying to bb might be visible above backgrounds. However, a dedicated study of this particular decay mode is still lacking. Similar remarks apply in the case of the h 3 where the possibly visible final states are tt for m h 3 > 2m t and h 1 h 2 for m h 3 < 2m t . For both the a 2 and h 3 , σBR(X) is substantial for X = χ 0 1 χ 0 1 , but to isolate this invisible final state would require an additional photon or jet tag which would reduce the cross section from the level shown.
A final possible detection mode is gg → a 2 , h 3 → τ + τ − . For this case we plot in Fig. 10 the effective down-quark coupling, C a 2 ,h 3 d (eff) vs. m a 2 and m h 3 , where we define and where 0.1 is a reference value of BR(H, A → τ + τ − ) implicit in the MSSM limit plots discussed below. Noting that m a 2 m h 3 and the fact that the two plots are nearly identical shows that we may sum the a 2 and h 3 signals together in the same manner as the H and A signals are summed together in the case of the analogous plot of tan β vs. m A m H in the case of the MSSM. Limits from CMS 4.6 fb −1 data [24] are of order C a 2 ,h 3 d (eff) < ∼ 7 − 8 for m a 2 m h 3 ∈ [150, 220] GeV rising rapidly to reach ∼ 50 at degenerate mass of order 500 GeV. A dedicated study is needed to determine the precise luminosity for which LHC detection or meaningful limits will become possible for C a 2 ,h 3 d (eff) < ∼ 1 (as relevant for m a 2 , m h 3 < 550 GeV). Even though Higgs cross sections from gg fusion increase, relative to √ s = 8 TeV, for √ s = 14 TeV quite high luminosity will be needed.
Currently, for example, the CMS limit from 10 fb −1 of data at m a 2 m h 3 ∼ 300 GeV is of order 18, and this amplitude level limit will only improve statistically by 1/L 1/4 . Even accounting for the √ s = 14 TeV cross section increase, very significant improvements in the sensitivity of this analysis will be needed.
The branching ratios for the H ± are plotted in Fig. 11, Prospects for its discovery at masses for which H + H − production has substantial cross section appear to be promising in the bt final state provided reconstruction of the bt mass is possible with good efficiency and one or more b tags are sufficient to reject SM background. Also very interesting would be detection of H ± → h 1 W ± in the h 1 → bb final state using mass reconstruction for the bb and a leptonic trigger from the W ± to reject backgrounds. This channel could prove especially essential in order to detect the m h 1 ∼ 98 GeV Higgs at the LHC and verify the 98 + 125 GeV Higgs scenario.  11. Decay branching ratios of the charged Higgs bosons.

B. Higgses from neutralino decays
Given that cascades from gluinos/squarks will have low event rate as a result of the large mg and mq masses predicted and the rather low χ ± 1 and χ 0 1 masses typical of the NMSSM scenarios we discuss, prospects for detecting chargino pair production and neutralino+chargino production would appear to be better, although one is faced with cross sections that are electroweak in size. Of particular interest is whether some of the Higgs bosons can be detected via ino-pair production. To assess the possibilities, we present in Fig. 12 the branching ratios for the decay of the neutralinos and [GeV]   charginos to lighter inos plus a Higgs boson. A brief summary of the results shown is in order. First, decays to the a 1 are not shown since they have very low branching ratios due to the singlet nature of the a 1 . The only decay with branching ratio to the a 2 above 0.1 is χ ± 2 → χ ± 1 a 2 with m χ ± 2 > ∼ 1.4 TeV (beyond LHC reach via electroweak production). In contrast, prospects for the all important h 1 are quite good, with BR( χ 0 3 , χ 0 4 → χ 0 1 h 1 ) and BR( χ ± 2 → χ ± 1 h 1 ) being quite substantial (i.e. > 0.1) at lower values of m χ 0 3 , m χ 0 4 and m χ ± 2 , respectively. Decays of χ 0 3 , χ 0 4 , χ 0 5 to χ 0 1 h 2 all have BR > 0.1 once m χ 0 3 , m χ 0 4 , m χ 0 5 are > ∼ 250, 400, 500 GeV, respectively. Similarly, BR( χ ± 2 → χ ± 1 h 2 ) > 0.1 for m χ ± 2 > ∼ 500 GeV. Since the charged Higgs has m H ± > 300 GeV, decays to it, although present for 1.1, 1.3, 1.3 TeV, respectively.

C. Linear Collider and Photon Collider Tests
An e + e − collider would be the ideal machine to produce the additional Higgs states and resolve the scenario. Production cross sections for the various Higgs final states are shown in Fig. 13 for the three illustrative scenarios specified in Table I  In the e + e − collider case, it would be easy to isolate signals in many final states. For example, in the case of Higgs pairs, final states such as (tt)(tt), ( χ 0 1 χ 0 1 )(tt) and so forth could be readily identified above background. Observation of the ( χ 0 1 χ 0 1 )( χ 0 1 χ 0 1 ) final states would require a photon tag and would thus suffer from a reduced cross section. Associated Z+Higgs, with Higgs decaying to tt or χ 0 1 χ 0 1 would be even more readily observed.  Fig. 13. Also given are Ωh 2 , the singlino and Higgsino percentages and R h2 gg (γγ). Scenarios I) and III) have Ωh 2 in the WMAP window, with I) being typical of the low-m χ 0 1 scenarios and III) being that with smallest m h3 in the large-m  m Higgs /0.8.
In the present context, it is of interest to assess the extent to which a γγ collider would be able to study the neutral NMSSM Higgs bosons. This is determined by the ratio of the γγ coupling squared of the given Higgs boson to that of the SM Higgs. In Fig. 14 we present plots of (C h γγ ) 2 as a function of m h for h = h 1 , h 2 , h 3 , a 1 , a 2 for masses below 1 TeV. The fairly SM-like h 2 at ∼ 125 GeV can be studied easily at such a collider since its γγ coupling is close to SM strength. For example, at an e − e − collider with the optimal E ee = 206 GeV, a 125 GeV SM Higgs has a cross section of 200 fb.
Even though the h 1 and a 1 are largely singlet, both have γγ couplings-squared that are often of order 0.1×SM and above (at the same mass). In part, this is because even singlets couple to γγ through a Higgsino-like chargino loop using the singlet-Higgsino-Higgsino coupling that arises from the λ S H u H d term in the superpotential. Indeed, this coupling becomes stronger as λ is increased.
Of course, it is important to note that the modest values of µ eff (see Fig. 5) that characterize many of our scenarios imply that the lightest chargino is largely Higgsino-like and has low mass (see Fig. 6), for which the Higgsino-chargino loop is less suppressed. Even for γγ coupling-squared of order 0.1×SM, with sufficient integrated luminosity observation of the h 1 and a 1 would be possible. For example, for suitably chosen E ee , the above SM Higgs rates multiplied by 0.1 would roughly apply for m h 1 ∼ 98 GeV or m a 1 < 300 GeV, from which it is clear that the bb final state would be easily observable with L = 500 fb −1 and one could measure the partial width with an accuracy of order 5%. Even the h 3 and a 2 would be observable for m a 2 < 500 GeV, again assuming appropriately optimal E ee for the given m h 3 or m a 2 and L = 500 fb −1 .
This raises the question of whether or not a γγ collider with adjustable (as is straightforward) √ s γγ in the 98 GeV range would be a good next step for high energy physics. It would have the advantage of allowing important detailed studies of the h 2 (or any SM-like Higgs boson with mass of 125 GeV) while testing for the presence of the h 1 . With adjustable √ s γγ and L ≥ 500 fb −1 , the h 3 , a 1 , a 2 , or any other light Higgs boson with significant (even if somewhat suppressed) γγ coupling, would be observable as well.

D. A µ + µ − Collider
A muon-collider with √ s close to the Higgs mass in question would be a particularly ideal machine to study any Higgs boson with µ + µ − coupling that is not too different from that of a SM Higgs boson of similar mass. Thus, in Fig. 15 we present plots of (C h µ + µ − ) 2 as a function of m h for h = h 1 , h 2 , h 3 , a 1 , that for the a 2 being essentially identical to the h = h 3 case. We see that prospects are really quite good for the h 1 as well as the h 2 . In addition, the WMAP-window a 1 points, all of which lie at relatively low mass, can be probed as well. As for the h 3 (and the a 2 ), the low-m χ 0 1 region points with low m h 3 ( m a 2 ) have nicely enhanced (C h 3 µ + µ − ) 2 ( (C a 2 µ + µ − ) 2 ). A muon collider would be ideal for probing such scenarios. Additional experimental evidence for this 98 + 125 GeV Higgs scenario from other machines would provide strong motivation for the muon collider.

VI. CONCLUSIONS
To summarize, we have emphasized the possibility that both the LEP excess in the bb final state at M bb ∼ 98 GeV and the LHC Higgs-like signal at ∼ 125 GeV with an enhanced rate in the two-photon final state can be explained in the context of the NMSSM. The NMSSM scenarios of this type have many attractive features. We have particularly emphasized the fact that the h 1 could eventually be observed at the LHC in gg, VBF → h 1 → bb. We urge the ATLAS and CMS collaborations to give attention to this possibility.  1 ∈ [1.9, 2.8] TeV, mq, mg ∈ [3, 5] TeV and tan β ∈ [5,7]. Clearly this latter region leaves little hope for LHC detection of the colored particles and experimental probes would need to focus on the gauginos and lighter Higgs bosons.
It is further associated with rather modest values for the enhancement of the 125 GeV Higgs signal in the γγ channel. Information related to the prospects for Higgs and superparticle detection for the two regions (A) and (B) at an e + e − , γγ or µ + µ − collider are summarized.