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Published for SISSA by Springer

Received: October 19, 2012 Accepted: December 11, 2012

Published: January 9, 2013

Genevive Blanger,a Ulrich Ellwanger,b John F. Gunion,c Yun Jiang,c Sabine Kramld and John H. Schwarze

aLAPTH, Universit de Savoie,

CNRS, B.P.110, F-74941 Annecy-le-Vieux Cedex, France

bLaboratoire de Physique Thorique, Universit Paris-Sud,

Centre dOrsay, F-91405 Orsay-Cedex, France

cDepartment of Physics, University of California,

Davis, CA 95616, U.S.A.

dLaboratoire de Physique Subatomique et de Cosmologie, UJF Grenoble 1, CNRS/IN2P3, INPG,53 Avenue des Martyrs, F-38026 Grenoble, France

eDepartment of Physics, California Institute of Technology,

Pasadena, CA 91125, U.S.A.

E-mail: mailto:[email protected]

Web End [email protected] , mailto:[email protected]

Web End [email protected]

Abstract: We discuss NMSSM scenarios in which the lightest Higgs boson h1 is consistent with the small LEP excess at 98 GeV in e+e ! Zh with h ! bb and the heavier Higgs

boson h2 has the primary features of the LHC Higgs-like signals at 125 GeV, including an enhanced rate. Verication or falsication of the 98 GeV h1 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.

Keywords: Higgs Physics, Beyond Standard Model

ArXiv ePrint: 1210.1976

Open Access doi:http://dx.doi.org/10.1007/JHEP01(2013)069

Web End =10.1007/JHEP01(2013)069

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

JHEP01(2013)069

Contents

1 Introduction 1

2 Higgs boson production and decay 2

3 Other NMSSM particles and parameters 5

4 Dark matter, including LSP and light chargino compositions 7

5 Future tests of the 98+125 GeV Higgs scenario 105.1 Direct Higgs production and decay at the LHC 115.2 Higgses from neutralino decays 135.3 Linear collider and photon collider tests 145.4 A [notdef]+[notdef] collider 18

6 Conclusions 19

1 Introduction

Data from the ATLAS and CMS collaborations [1, 2] provide an essentially 5 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 12 from predictions for the hSM. One

of the most signicant deviations in the current data is the enhancement in the nal 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[prime], thereby enhancing the branching ratio of the h [49]. In such models, a particularly interesting question is whether one could simultaneously explain the LHC signal and the small ( 2) LEP excess in e+e ! Zbb in the vicinity of Mbb 98 GeV [10, 11] using

the h[prime] with mh[prime] 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

hSM. Consistency with such a result for the h[prime] is natural if the h[prime] 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.

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In this paper we demonstrate that the two lightest CP-even Higgs bosons,1 h1 and h2, of the Next-to-Minimal Supersymmetric Model (NMSSM) could have properties such that the h1 ts the LEP excess at 98 GeV while the h2 is reasonably consistent with the

Higgs-like LHC signals at 125 GeV, including in particular the larger-than-SM signal in

the channel. The NMSSM [12] is very attractive since it solves the [notdef] problem of the minimal supersymmetric extension of the SM (MSSM): the ad hoc parameter [notdef] appearing in the MSSM superpotential term [notdef]ud is generated in the NMSSM from the ud superpotential term when the scalar component S of develops a VEV [angbracketleft]S[angbracketright] = s: [notdef]e = s.

The three CP-even Higgs elds, contained in Hu, Hd and S, mix and yield the mass eigenstates h1, h2 and h3. A 125 GeV Higgs state with enhanced signal rate is easily obtained for large and small tan [5] (see also [7, 8]). To describe the LEP and LHC data the h1 and h2 must have mh1 98 GeV and mh2 125 GeV, respectively, with the

h1 being largely singlet and the h2 being primarily doublet (mainly Hu for the scenarios we consider). In addition to the CP-even states, there are also two CP-odd states, a1 and a2, and a charged Higgs boson, H[notdef]. Verication of the presence of the three CP-even Higgs bosons and/or two CP-odd Higgs bosons would establish a Higgs eld structure that goes beyond the two-doublet structure of the MSSM.

2 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 or ZZ ! 4[lscript]. 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! +. We compute the ratio of the gg or VBF induced

Higgs cross section times the Higgs branching ratio to a given nal state X, relative to the corresponding value for the SM Higgs boson, as

Rhigg(X)

(hi ! gg) BR(hi ! X)

(hSM ! gg) BR(hSM ! X)

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, RhiVBF(X)

(hi ! W W ) BR(hi ! X)

(hSM ! W W ) BR(hSM ! X)

(2.1)

where hi is the ith NMSSM scalar Higgs, and hSM is the SM Higgs boson, taking mhSM = mhi. In the context of any two-Higgs-doublet plus singlets model, not all the Rhi are independent. For example, RhiVH(X) = RhiVBF (X), RhiY() = RhiY(bb)2 and RhiY(ZZ) =

RhiY(W W ). A complete independent set of Rhis can be taken to be (with h = h1 or h = h2)

Rhgg(W W ), Rhgg(bb), Rhgg( ), RhV BF (W W ), RhV BF (bb), RhV BF ( ) . (2.2)

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-unied GUT scale soft-SUSY-breaking. By semi-unied we mean universal gaugino mass parameter m1/2, scalar

1We assume absence of CP-violating phases in the Higgs sector.

2This equality is altered by radiative corrections at large tan ; however, these are small in our scenarios all of which have small to moderate tan values.

0.3

0.25

0.2

0.15

0.1

0.05

Figure 1. Signal strengths (relative to SM) Rh1VBF (bb) versus Rh2gg( ) for mh1 2 [96, 100] GeV and

mh2 2 [123, 128] GeV. In this and all subsequent plots, points with h2 < 0.094 are represented

by blue circles and points with h2 2 [0.094, 0.136] (the WMAP window) are represented by

red/orange diamonds.

(sfermion) mass parameter m0, and trilinear coupling A0 At = Ab = A at the GUT

scale, but m2Hu, m2Hd and m2S as well as A and A are taken as non-universal at MGUT. Specically, we use points from scans performed using NMSSMTools 3.2.0 [1315], 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 avor constraints as implemented in NMSSMTools, h2 < 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, a[notdef], is too

small to explain the discrepancy between the observed value of a[notdef] [16] and that predicted by the SM. For a full discussion of the kind of NMSSM model employed see [7, 8, 17].

We rst display in gure 1 the crucial plot that shows Rh1VBF (bb) versus Rh2gg( ) when mh1 2 [96, 100] GeV and mh2 2 [123, 128] GeV are imposed in addition to the above

mentioned experimental constraints.3 (In this and all subsequent plots, points with h2 < 0.094 are represented by blue circles and points with h2 2 [0.094, 0.136] (the WMAP

window) are represented by red and orange diamonds. These two colors are associated with di erent LSP masses as will be discussed below.) Note that Rh1VBF (bb) values are required to be smaller than 0.3 by virtue of the fact that the LEP constraint on the e+e ! Zbb channel with Mbb 98 GeV is included in the NMSSMTools program.

Those points with Rh1VBF (bb) between about 0.1 and 0.25 would provide the best t to the LEP excess. (We note again that Rh1VBF (bb) is equivalent to Rh1Vh1(bb) as relevant for

LEP.) A large portion of such points have Rh2gg( ) > 1 as preferred by LHC data. In

3Here the Higgs mass windows are designed to allow for theoretical errors in the computation of the Higgs masses.

Rh VBF ( bb )

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RhVBF (bb)

Figure 2. For the h1 and h2, we plot (top) Rhgg( ) and RhV BF ( ) and (bottom) Rhgg(bb) and RhV BF (bb) for NMSSM scenarios consistent with the LEP and LHC Higgs excesses. More specically, in this and all subsequent plots we only show points that satisfy all the basic constraints specied in the text and that also satisfy mh1 2 [96, 100] GeV, mh2 2 [123, 128] GeV, Rh2gg( ) > 1 and

Rh1VBF (bb) 2 [0.1, 0.25]. These we have termed the 98 + 125 GeV Higgs scenarios. Regarding

the WMAP-window points, we refer to the red diamonds as region A and to the orange ones as region B.

all the remaining plots we will impose the additional requirements: Rh2gg( ) > 1 and 0.1 Rh1VBF (bb) 0.25. In the following, we will refer to these NMSSM scenarios as the

98 + 125 GeV Higgs scenarios. To repeat, the Rh2gg( ) > 1 requirement is such as to focus on points that could be consistent (within errors) with the enhanced Higgs signal at the LHC of order 1.5 times the SM. The 0.1 Rh1VBF (bb) 0.25 window is designed to

reproduce the small excess seen in LEP data at Mbb 98 GeV in the Zbb nal state.

In gure 2, we plot (upper row) Rh1gg( ) vs. Rh2gg( ) and Rh1VBF ( ) vs. Rh2VBF ( ) and (lower row) Rh1gg(bb) vs. Rh2gg(bb) and Rh1VBF (bb) vs. Rh2VBF (bb). In these and all subsequent plots, we only show points that satisfy all the basic constraints specied earlier and that also satisfy mh1 2 [96, 100] GeV, mh2 2 [123, 128] GeV, Rh2gg( ) > 1 and Rh1VBF (bb) 2 [0.1, 0.25].

The upper plots show that the h2 can easily have an enhanced signal for both gg and VBF production whereas the signal arising from the h1 for both production mechanisms is quite small and unlikely to be observable. Note the two di erent Rh2gg( ) regions for which h2 lies in the WMAP window, one with Rh2gg( ) 1.6 (region A, red diamonds)

and the other with Rh2gg( ) 1.1 (region B, orange diamonds). As we will show later,

2000

1800

1600

1400

1200

1000

800

600

400

Figure 3. Scatter plot of ma2 versus ma1 for the 98+125 GeV scenario; note that ma2 [similarequal] mh3 [similarequal]

mH . Note that in this gure there is a dense region, located at (ma1, ma2) (130, 330) GeV,

of strongly overlapping red diamond points. These are the points associated with the low-m[tildewide][notdef]

WMAP-window region of parameter space. Corresponding dense regions appear in gures 47 and 10.

region A corresponds to m[tildewide][notdef]

01 77 GeV and m~t1 between 197 GeV and 1 TeV, while the

01 > 93 GeV and m~t1 > 1.8 TeV. These same two regions will emerge in many subsequent gures. If Rh2gg( ) 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 gure focuses on the bb nal state. We observe the reduced Rh2gg(bb) and Rh2VBF (bb) values that are associated with reduced bb width (relative to the SM)

needed to have enhanced Rh2gg( ) and Rh2VBF ( ). Meanwhile, the Rh1gg(bb) and Rh1VBF (bb) values are such that the h1 could not yet have been seen at the Tevatron or LHC. Sensitivity to Rh1gg(bb) (Rh1VBF (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 ps = 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 fb1. 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 Rh1VBF (bb) values occur for region A described above for which supersymmetric particle masses are as small as possible.

3 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. gure 3 displays the pseudoscalar masses in the ma1ma2 plane. We do not plot mh3 nor mH[notdef] since their masses are such that

4Here, we have used gure 12 of [2] extrapolated to a Higgs mass near 98 GeV and assumed L = 20 fb1 each for ATLAS and CMS.

region B corresponds to m[tildewide][notdef]

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m n

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mt~1 [GeV]

Figure 4. Plots showing m[tildewide][notdef]

1 , m[tildewide][notdef]

1 , m~t1, m~t2, m~q, m~g, and the mixing parameter (At

[notdef] cot )/pm~t1 m~t2. Also shown are m[tildewide][lscript]R

, m[tildewide] [lscript]

, m[tildewide]1

and m[tildewide]

, where [lscript] = e, [notdef].

mh3 [similarequal] mH[notdef] [similarequal] ma2 for the scenarios considered. We note that small ma1 is typical of the

WMAP-window points. We discuss discovery prospects for the a1 later in the paper. The masses of some crucial SUSY particles are displayed in gure 4. We observe the typically low values of m[tildewide][notdef]

01 and m[tildewide][notdef]

[notdef]

1 , the possibility of m~t1 as small as 197 GeV, the mostly modest values of the mixing parameter (At [notdef] cot )/pm~t1m~t2, and the fact that the predicted

m~q and m~g are beyond current experimental limits, although the lowest values (as found in particular in region A) may soon be probed. Note that m~g can be below m[tildewide][lscript]R

(as common

in constrained models when m0 is large) for some points, including the points in region A.

Low values of m[tildewide][notdef]

01 are typical for the scan points, but more particular to this model are the rather low values of m[tildewide][notdef]

[notdef]

1 . ATLAS and CMS are currently performing analyses that could in principle be sensitive to the m[tildewide][notdef]

[notdef]

1 values predicted in this model. For some points,

m[tildewide][notdef]

[notdef]

m[tildewide][notdef]

01 can be rather small, implying some di culty in isolating the leptons or jets associated with

e[notdef][notdef]1 !

e[notdef]01 + X decays. However, it should be noted that for the WMAP-window points m[tildewide][notdef]

[notdef]1 m[tildewide][notdef]01 is typically quite substantial, at least 35 GeV for the low-m[tildewide][notdef]01

points, so that for these points the above di culty would not arise. Of particular interest is the very large range of m~t1 that arises in the 98 + 125 GeV LEP-LHC Higgs scenarios. For lighter values of m~t1, as typical of the WMAP-window points in region A, the ~t1 always decays via ~t1 !

e[notdef]+1b or ~t1 ! e[notdef]01t, the latter being absent when m~t1 < m[tildewide][notdef]01 + mt. At

high m~t1, these same channels are present but also ~t1 !

e[notdef]02,3,4,5t can be important, which channels being present depending upon whether m~t1 m[notdef]02,3,4,5 mt > 0 or not.

It is interesting to survey the GUT scale parameters that lead to the scenarios of interest. Relevant plots are shown in gure 5. No particular regions of these parameters appear to be singled out aside from some preference for negative values of A0. 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.

4 Dark matter, including LSP and light chargino compositions

The composition of the

e[notdef]01 and the e[notdef][notdef]1 are crucial when it comes to the relic density of

the

JHEP01(2013)069

e[notdef]01. For those points in the WMAP window in region A (red diamonds), the

e[notdef]01 can

e[notdef]01 ! W +W annihilation mode (mainly via t-channel exchange of the light Higgsino-like see second plot of gure 6 chargino)

is below threshold; the group of points with m[tildewide][notdef]

have a large Higgsino fraction since the

e[notdef]01

01 > 93 GeV (region B, orange diamonds) can lie in the WMAP window only if the

e[notdef]01 does not have a large Higgsino fraction. This division is clearly seen in gure 6. We note that to a reasonable approximation the singlino fraction of the

e[notdef]01 is given by 1 minus the Higgsino fraction plotted in the left-hand window of the gure.

Dark matter (DM) properties for the surviving NMSSM parameter points are summarized in gure 7. Referring to the gure, we see a mixture of blue circle points (those with h2 < 0.094) and red/orange diamond points (those with 0.094 h2 0.136, i.e.

in the WMAP window). The main mechanism at work to make h2 too small for many points is rapid

e[notdef]01 e[notdef]01 annihilation to W +W due to a substantial Higgsino component of

the

e[notdef]01 (see third plot of gure 7). Indeed, the relic density of a Higgsino LSP is typically of order h2 103 102. As the Higgsino component declines h2 increases and (except

for the strongly overlapping points with m[tildewide][notdef]

01 < mW , for which

e[notdef]01 ! W +W is below threshold) it is the points for which the LSP is dominantly singlino that have large enough h2 to fall in the WMAP window.

Also plotted in gure 7 is the spin-independent direct detection cross section, SI,

as a function of m[tildewide][notdef]

e[notdef]01

01 . First of all, we note that the 2012 XENON100 limits on SI are obeyed by all the points that have h2 in the WMAP window, even though our scans

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Figure 5. GUT scale and SUSY scale parameters leading to the 98 + 125 GeV LEP-LHC Higgs scenarios.

only implemented the 2011 XENON100 limits indeed only a modest number of the h2 < 0.094 points are inconsistent with the 2012 limits. The SI plot also shows that experiments probing the spin-independent cross section will reach sensitivities that will probe some of the SI values that survive the 2012 XENON100 limits relatively soon, especially the m[tildewide][notdef]

01 > 93 GeV points that are in the WMAP window (region B). However, it is also noteworthy that the m[tildewide][notdef]

01 75 GeV points in region A can have very small SI.

The fourth plot of gure 7 and fth plot of gure 5 illustrate clearly the two categories of WMAP-window points. The rst category (A) of points is that for which the

e[notdef]01 has

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Figure 6. Neutralino and chargino compositions for the 98 + 125 GeV LEP-LHC Higgs scenarios.

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Figure 7. Dark matter properties for the 98 + 125 GeV LEP-LHC Higgs scenarios.

low mass and large Higgsino component with tan 2 [2, 2.6] and 2 [0.53, 0.6]; the second

category (B) is that for which m[tildewide][notdef]

01 > 93 GeV, tan 2 [5, 7] and 2 [0.37, 0.48] .

It is interesting to discuss whether or not any of the 98+125 GeV Higgs scenario points are such as to describe the monochromatic signal at 130 GeV observed in the Fermi-LAT data [18]. We recall that the observation requires [angbracketleft]v[angbracketright](

e[notdef]01

e[notdef]01 ! ) 1027cm3/sec (this

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125 GeV<mc1<135 GeV

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3 /sec]

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JHEP01(2013)069

e[notdef]01 ! a1 ! ) vs. h2 for just those points with m[tildewide][notdef]012 [125, 135] GeV.

quoted value assumes standard dark matter density, 0.3).5 The situation is illustrated

in gure 8 where we plot [angbracketleft]v[angbracketright](

e[notdef]01

Figure 8. We plot [angbracketleft]v[angbracketright](

e[notdef]01

e[notdef]01 ! a1 ! ) vs. h2 for just those points with

m[tildewide][notdef]01 2 [125, 135] GeV. (It is the s-channel a1 diagram that can give a large [angbracketleft]v[angbracketright].) We

observe that points with h2 in the WMAP window have values of [angbracketleft]v[angbracketright] four orders of

magnitude below that required to explain the excess. Those points with the largest [angbracketleft]v[angbracketright]

always have quite small h2 and hence DM. Incidentally, we have checked that all the points in our plots are fully consistent with the current bounds from the continuum spectrum as measured by Fermi-LAT [19, 20].

If the 130 GeV gamma ray line is conrmed, then the above questions will need to be explored more carefully. That a fully general NMSSM model (no GUT scale unications) can be consistent simultaneously with the WMAP window, [angbracketleft]v[angbracketright](

e[notdef]01

e[notdef]01 ! a1 ! ) 1027cm3/sec, a Higgs mass close to 125 GeV and 2011 XENON100 constraints was

demonstrated in [21]. However, the value of ma1 has to be carefully tuned and the 125 GeV Higgs couplings to all particles (including photons) must be within 5% of those for a SM

Higgs boson of this mass, implying di culty in describing the enhanced LHC rates in this channel. Some general (non-NMSSM) theoretical discussions of the 130 GeV line in the context of DM appear in [22, 23].

5 Future tests of the 98+125 GeV Higgs scenario

A critical issue is what other observations would either conrm or rule out the 98+125 GeV LEP-LHC Higgs scenarios. We rst discuss possibilities at the LHC and then turn to future colliders, including a future e+e collider, a possible collider and a future [notdef]+[notdef] collider.

5Here, and below, v is the very small velocity typical of dark matter in the current epoch, v 103c,

as relevant for indirect detection of the

e~01 through e~01 e~01 annihilations. This, of course, di ers from the velocity at the time of freeze out, which is substantially higher.

5.1 Direct Higgs production and decay at the LHC

We have already noted in the discussion of gure 2 that gg and VBF production of the h1 with h1 ! 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 a1, a2, and h3. Decay branching ratios and LHC cross sections in the gg fusion mode for a1, a2 and h3 are shown in gure 9. Since the a1 is dominantly singlet in nature, its production rates at the LHC are rather small. The largest BR(X) values are in the X = bb nal state, but this nal state will have huge backgrounds. When allowed, BR(X) for X =

e[notdef]01 e[notdef]01 can be signicant, but observation of this invisible nal state would require a jet or photon tag that would further decrease the cross section. The a2 is dominantly doublet and provides better discovery prospects. If ma2 > 2mt, the tt nal state has (gg ! a2)BR(a2 ! tt) > 0.01 pb for ma2 < 550 GeV, implying > 200 events for

L = 20 fb1. A study is needed to determine if this would be observable in the presence of the tt continuum background. No doubt, e cient b tagging and reconstruction of the tt invariant mass in, say, the single lepton nal state would be needed. For ma2 < 2mt, the

X = a1h2 nal state with both a1 and h2 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 h3 where the possibly visible nal states are tt for mh3 > 2mt and h1h2 for mh3 < 2mt. For both the a2 and h3, BR(X) is substantial for X =

e[notdef]01 e[notdef]01, but to isolate this invisible nal state would require an additional photon or jet tag which would reduce the cross section from the level shown.

A nal possible detection mode is gg ! a2, h3 ! +. For this case we plot in

gure 10 the e ective down-quark coupling, Ca2,h3d(e ) vs. ma2 and mh3, where we dene

Ca2,h3d(e ) = [notdef]Ca2,h3d[notdef] [bracketleftbigg]

and where 0.1 is a reference value of BR(H, A ! +) implicit in the MSSM limit plots

discussed below. Noting that ma2 [similarequal] mh3 and the fact that the two plots are nearly identical

shows that we may sum the a2 and h3 signals together in the same manner as the H and A signals are summed together in the case of the analogous plot of tan vs. mA [similarequal] mH in the case of the MSSM. Limits from CMS 4.6 fb1 data [24] are of order Ca2,h3d(e ) <

for ma2 [similarequal] mh3 2 [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 Ca2,h3d(e ) <

1 (as relevant for ma2, mh3 < 550 GeV). Even though Higgs cross sections from gg fusion increase, relative to ps = 8 TeV, for ps = 14 TeV quite high luminosity will be needed. Currently, for example, the CMS limit from 10 fb1 of data at ma2 [similarequal] mh3 300 GeV is of order 18, and

this amplitude level limit will only improve statistically by 1/L1/4. Even accounting for the ps = 14 TeV cross section increase, very signicant improvements in the sensitivity of this analysis will be needed.

The branching ratios for the H[notdef] are plotted in gure 11. Prospects for its discovery at masses for which H+H production has substantial cross section appear to be promising

JHEP01(2013)069

BR(a2, h3 ! +) 0.1

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100

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c01c01

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s(gga 2)BR(a 2X) [pb]

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h1h2

Za1

c01c01

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BR(h 3X)

0.3

s(ggh 3)BR(h 3X) [pb]

10-2

0.2

10-3

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10-4

mh3 [GeV]

Figure 9. Branching ratios and LHC cross sections in the gg fusion mode (at ps = 8 TeV) for a1,

a2 and h3.

4.5

0 200 300 400 500 600 700 800 900 1000

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0 200 300 400 500 600 700 800 900 1000

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2.5

|Ch d |[ BR ( h tt )/0.1]

2.5

1.5

0.5

ma [GeV]

mh [GeV]

Figure 10. Ca2,h3d(e ), see eq. (5.1), vs. ma2 and mh3 for gg ! a2, h3 ! +.

c03c1

h1W+

c01c1

a1W+

c01c2

c02c2

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0 200 400 600 800 1000 1200 1400

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0.4

0.2

mH [GeV]

Figure 11. Decay branching ratios of the charged Higgs bosons.

in the bt nal state provided reconstruction of the bt mass is possible with good e ciency and one or more b tags are su cient to reject SM background. Also very interesting would be detection of H[notdef] ! h1W [notdef] in the h1 ! bb nal state using mass reconstruction for the

bb and a leptonic trigger from the W [notdef] to reject backgrounds. This channel could prove especially essential in order to detect the mh1 98 GeV Higgs at the LHC and verify the

98 + 125 GeV Higgs scenario.

5.2 Higgses from neutralino decays

Given that cascades from gluinos/squarks will have low event rate as a result of the large m~g and m~q masses predicted and the rather low

e[notdef][notdef]1 and

e[notdef]01 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

0.3

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mc [GeV]

Figure 12. Branching ratios for neutralino and chargino decays into nal states containing a Higgs boson for the 98 + 125 GeV LEP-LHC Higgs scenarios.

bosons can be detected via ino-pair production. To assess the possibilities, we present in gure 12 the branching ratios for the decay of the neutralinos and charginos to lighter inos plus a Higgs boson. A brief summary of the results shown is in order. First, decays to the a1 are not shown since they have very low branching ratios due to the singlet nature of the a1. The only decay with branching ratio to the a2 above 0.1 is

e[notdef][notdef]2 !

e[notdef][notdef]1a2 with

m[tildewide][notdef]

[notdef]2 >

1.4 TeV (beyond LHC reach via electroweak production). In contrast, prospects for the all important h1 are quite good, with BR(

e[notdef]03,

e[notdef]04 !

e[notdef]01h1) and BR(

e[notdef][notdef]2 !

e[notdef][notdef]1h1)

being quite substantial (i.e. > 0.1) at lower values of m[tildewide][notdef]03 , m[tildewide][notdef]04 and m[tildewide][notdef]

[notdef]2 , respectively. De-

cays of

e[notdef]03,

e[notdef]04,

e[notdef]05 to

e[notdef]01h2 all have BR > 0.1 once m[tildewide][notdef]03 , m[tildewide][notdef]04 , m[tildewide][notdef]05 are >

250, 400, 500 GeV,

respectively. Similarly, BR(

e[notdef][notdef]1h2) > 0.1 for m[tildewide][notdef]

[notdef]2 >

500 GeV. Since the charged Higgs has mH[notdef] > 300 GeV, decays to it, although present for the

e[notdef]04,

e[notdef][notdef]2 !

e[notdef]05 and

e[notdef][notdef]2, do not

have BR > 0.1 until m[tildewide][notdef]04 , m[tildewide][notdef]05 , m[tildewide][notdef]

[notdef]2 >

1.1, 1.3, 1.3 TeV, respectively.

5.3 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 nal states are shown in gure 13 for the three illustrative scenarios specied in table 1 taken from our NMSSM

Scenario mh1 mh2 mh3 ma1 ma2 mH[notdef] m[tildewide][notdef]

01 h2 LSP singlino LSP Higgsino Rh2gg( )

I 99 124 311 140 302 295 76 0.099 18% 75% 1.62

II 97 124 481 217 473 466 92 0.026 20% 74 % 1.53 III 99 126 993 147 991 989 115 0.099 75% 25% 1.14

Table 1. Higgs masses and LSP mass in GeV for the three scenarios for which we plot e+e

cross sections in gure 13. Also given are h2, the singlino and Higgsino percentages and Rh2gg( ). Scenarios I) and III) have h2 in the WMAP window, with I) being typical of the low-m[tildewide][notdef]

1 scenarios

and III) being that with smallest mh3 in the large-m[tildewide][notdef]

1 group of points in the WMAP window.

Scenario II) is chosen to have ma2 and mh3 intermediate between those for scenario I) and III), a region for which h2 is substantially below 0.1.

scans. The rst plot is for a WMAP-window scenario with m[tildewide][notdef]

JHEP01(2013)069

01 76 GeV and light

Higgs bosons. The third plot is for the point in region B with smallest mh3, for which ma2, mh3, mH[notdef] are all around 1 TeV. The second plot is for a sample scenario with Higgs masses that are intermediate, as only possible if h2 lies below the WMAP window. With an integrated luminosity of 1000 fb1, substantial event rates for many Z+Higgs and Higgs pair nal states are predicted. Of course, Zh1 and Zh2 production have the largest cross sections and lowest thresholds. The next lowest thresholds are for a1h1 production, but the cross sections are quite small, < 0.1, 0.01, 0.001 fb, respectively. The a1h2 cross sections are even smaller. Next in line are a1h3, a2h1 and a2h2, with a2h1 having thresholds > 400, 600, 1190 GeV for scenarios I), II) and III), respectively, as well as having the largest cross section, peaking at > 0.7, 0.2, 0.007 fb for the three respective scenarios. Production of a2h3 and H+H have thresholds > 620, 950, 2000 GeV, respectively, but have much larger cross sections, that for H+H being > 16.6, 6.3, 1.4 fb at the peak, for the three respective scenarios.

In the e+e collider case, it would be easy to isolate signals in many nal states. For example, in the case of Higgs pairs, nal states such as (tt)(tt), (

e[notdef]01 e[notdef]01)(tt) and so forth could be readily identied above background. Observation of the (

e[notdef]01 e[notdef]01)( e[notdef]01 e[notdef]01) nal states would require a photon tag and would thus su er from a reduced cross section. Associated

Z+Higgs, with Higgs decaying to tt or

e[notdef]01 e[notdef]01 would be even more readily observed.

Another future collider that would become possible if an e+e (or ee) collider is built is a collider where the s are obtained by backscattering of laser photons o the energetic es. For a recent summary see [25] and references therein. A huge range of energies is possible for such a collider, ranging from low to high center of mass energies depending upon the center of mass energy of the underlying electron collider. A collider based on ee collisions can even be considered as a stand-alone machine that could be built before an e+e collider, especially if high ps is not needed. Typically, the largest ps that is possible with large instantaneous luminosity is of order 0.8pse+e . That !Higgs is an e ective way to study a SM Higgs boson has been well established [2628].

For low Higgs masses, the required electron collider could have energy of order mHiggs/0.8.

In the present context, it is of interest to assess the extent to which a collider would be able to study the neutral NMSSM Higgs bosons. This is determined by the

scenario I scenario II

scenario III

Figure 13. Cross sections for Higgs production at an e+e collider, as functions of the center-of-mass energy ps, for three illustrative mass spectra as tabulated in table 1.

ratio of the coupling squared of the given Higgs boson to that of the SM Higgs. In gure 14 we present plots of (Ch )2 as a function of mh for h = h1, h2, h3, a1, a2 for masses below 1 TeV. The fairly SM-like h2 at 125 GeV can be studied easily at such a collider

since its coupling is close to SM strength. For example, at an ee collider with the optimal Eee = 206 GeV, a 125 GeV SM Higgs has a cross section of 200 fb. After two years of operation, equivalent to L = 500 fb1, one can measure the bb, W +W , partial widths with accuracies of (bb, W +W , )/ (bb, W +W , ) 0.015, 0.04, 0.06,

respectively [27] (see also [26, 28]).

Even though the h1 and a1 are largely singlet, both have couplings-squared that are often of order 0.1[notdef]SM and above (at the same mass). In part, this is because even

singlets couple to through a Higgsino-like chargino loop using the singlet-Higgsino-Higgsino coupling that arises from the

bS bHu bHd term in the superpotential. Indeed, this

coupling becomes stronger as is increased. Of course, it is important to note that the

JHEP01(2013)069

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96 96.5 97 97.5 98 98.5 99 99.5 100

0 0 100 200 300 400 500 600 700

mh [GeV]

ma [GeV]

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123 123.5 124 124.5 125 125.5 126 126.5 127 127.5 128

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0.95

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0.8

mh [GeV]

ma [GeV]

0 200 300 400 500 600 700 800 900 1000

2.5

(Ch gg )

1.5

0.5

mh [GeV]

Figure 14. (Ch )2 as a function of mh for h = h1, h2, h3, a1, a2.

modest values of [notdef]e (see gure 5) that characterize many of our scenarios imply that the lightest chargino is largely Higgsino-like and has low mass (see gure 6), for which the Higgsino-chargino loop is less suppressed. Even for coupling-squared of order 0.1[notdef]SM,

with su cient integrated luminosity observation of the h1 and a1 would be possible. For example, for suitably chosen Eee, the above SM Higgs rates multiplied by 0.1 would roughly apply for mh1 98 GeV or ma1 < 300 GeV, from which it is clear that the bb nal state

would be easily observable with L = 500 fb1 and one could measure the partial width with an accuracy of order 5%. Even the h3 and a2 would be observable for ma2 < 500 GeV, again assuming appropriately optimal Eee for the given mh3 or ma2 and L = 500 fb1.

1.6

0.35

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0.3

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0.25

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(Ch - )

(Ca - )

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0 0 100 200 300 400 500 600 700

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ma [GeV]

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0 200 300 400 500 600 700 800 900 1000

0.75

0.7

0.65

2 0.6

(Ch - )

0.55

(Ch - )

0.5

0.45

0.4

0.35

0.3

mh [GeV]

Figure 15. Reduced [notdef]+[notdef] couplings squared for h1, h2, h3, a1.

This raises the question of whether or not a collider with adjustable (as is straightforward) ps 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 h2 (or any SM-like Higgs boson with mass of 125 GeV) while testing for the presence of the h1. With adjustable ps and L 500 fb1, the h3, a1, a2, or any other light Higgs boson with

signicant (even if somewhat suppressed) coupling, would be observable as well.

5.4 A + collider

A muon-collider with ps close to the Higgs mass in question would be a particularly ideal machine to study any Higgs boson with [notdef]+[notdef] coupling that is not too di erent from that of a SM Higgs boson of similar mass. Thus, in gure 15 we present plots of (Ch[notdef]+[notdef])2 as a function of mh for h = h1, h2, h3, a1, that for the a2 being essentially identical to the h = h3 case. We see that prospects are really quite good for the h1 as well as the h2. In addition, the WMAP-window a1 points, all of which lie at relatively low mass, can be probed as well. As for the h3 (and the a2), the low-m[tildewide][notdef]

01 region points with low mh3 (and low ma2) have nicely enhanced (Ch3[notdef]+[notdef])2 (and (Ch3[notdef]+[notdef])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.

6 Conclusions

To summarize, we have emphasized the possibility that both the LEP excess in the bb nal state at Mbb 98 GeV and the LHC Higgs-like signal at 125 GeV with an enhanced rate

in the two-photon nal 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 h1 could eventually be observed at the LHC in gg, VBF ! h1 ! bb. We urge

the ATLAS and CMS collaborations to give attention to this possibility.

The 98 + 125 GeV Higgs scenarios have important implications for the other Higgs bosons and for supersymmetric particles. If we focus only on the subset of these scenarios that have relic density in the WMAP window, then there are two separate regions of NMSSM parameter space that emerge. One region (A) is characterized by small m[tildewide][notdef]

75 GeV and low masses for many of the Higgs bosons and superpartners, including m~t1 as low as 197 GeV. The second region (B) is characterized by larger m[tildewide][notdef]

01 2 [93, 150] GeV

and much larger mass scales for the heavier Higgs bosons and supersymmetric particles. For this latter region, one nds ma1 2 [100, 200] GeV, m[tildewide][notdef]

[notdef]

JHEP01(2013)069

1 2 [170, 230] GeV, ma2 [similarequal] mh3 [similarequal] mH[notdef] 2 [1, 1.4] TeV, m~t1 2 [1.9, 2.8] TeV, m~q, m~g 2 [3, 5] TeV and tan 2 [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 channel. Information related to the prospects for Higgs and superparticle detection for the two regions (A) and (B) at an e+e, or [notdef]+[notdef] collider are summarized.

Acknowledgments

The work of JFG and YJ was supported by US DOE grant DE-FG03-91ER40674, that of JHS the U.S. DOE grant No. DE-FG03-92-ER40701, and that of SK and GB by IN2P3 under contract PICS FRU.S.A. No. 5872. UE acknowledges partial support from the French ANR LFV-CPV-LHC, ANR STR-COSMO and the European Union FP7 ITN INVISIBLES (Marie Curie Actions, PITN-GA-2011-289442). GB, UE, JFG, SK, and JHS acknowledge the hospitality and the inspiring working atmosphere of the Aspen Center for Physics which is supported by the National Science Foundation Grant No. PHY-1066293.

Open Access. This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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JHEP01(2013)069

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SISSA, Trieste, Italy 2013

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(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image)

We discuss NMSSM scenarios in which the lightest Higgs boson h ^sub 1^ is consistent with the small LEP excess at ~ 98 GeV in e ^sup +^ e ^sup -^ [arrow right] Zh with ... and the heavier Higgs boson h ^sub 2^ has the primary features of the LHC Higgs-like signals at 125 GeV, including an enhanced γγ rate. Verification or falsification of the 98 GeV h ^sub 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.

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Title

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

Author

Bélanger, Geneviève; Ellwanger, Ulrich; Gunion, John F; Jiang, Yun; Kraml, Sabine; Schwarz, John H

Pages

1-22

Publication year

2013

Publication date

Jan 2013

Publisher

Springer Nature B.V.

e-ISSN

10298479

Source type

Scholarly Journal

Language of publication

English

DOI

https://doi.org/10.1007/JHEP01(2013)069

ProQuest document ID

1652941956

SISSA, Trieste, Italy 2013

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

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