One or more Higgs bosons?
Riccardo Barbieri, Dario Buttazzo, Kristjan Kannike, Filippo Sala, Andrea Tesi
CCERN-PH-TH-2013-170
One or more Higgs bosons?
Riccardo Barbieri a , Dario Buttazzo a,b , Kristjan Kannike a,c , Filippo Sala a,d , Andrea Tesi aa Scuola Normale Superiore and INFN, Piazza dei Cavalieri 7, 56126 Pisa, Italy b CERN Theory Division, CH-1211 Geneva 23, Switzerland c National Institute of Chemical Physics and Biophysics, R¨avala 10, Tallinn 10143, Estonia d Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720
Abstract
Now that one has been found, the search for signs of more scalars is a primary taskof current and future experiments. In the motivated hypothesis that the extraHiggs bosons of the next-to-minimal supersymmetric Standard Model (NMSSM)be the lightest new particles around, we outline a possible overall strategy tosearch for signs of the CP -even states. This work complements Ref. [1]. E-mail: [email protected], [email protected], [email protected], [email protected], [email protected] a r X i v : . [ h e p - ph ] S e p Introduction
The discovery of the/a Higgs boson, h LHC , with a mass of about 126 GeV and Standard-Model-like properties [2–6] raises a clear question: Is it the coronation of the Standard Model(SM) or a first step into yet largely unexplored territory? The answer to this question, whoserelation with the absence so far of any signal of new physics does not need to be illustrated,is in some sense paradoxical. While the newly found resonance completes the SM spectrum,thus representing a major milestone in the entire history of particle physics, there are stillgood reasons to think that its discovery may not be the end of the story. The many well-known problems that the finding of the resonance, viewed as the Higgs boson of the SM,leaves unresolved are one order of reasons. Quite independently and in fact on more generalgrounds, now that a scalar particle has been found, one may wonder if and why it shouldbe alone and not part of an extended Higgs system. Since we know of no strong argumentin favour of a single scalar particle, it is justified to think that the search for signs of extrascalars is a primary task of current and future experiments.A motivated example of an extended Higgs system is the one of the next-to-minimal su-persymmetric Standard Model (NMSSM), which adds to a usual Higgs doublet one furtherdoublet and one complex singlet under the SU(2) × U(1) gauge group, all parts of correspond-ing chiral super-multiplets, so that to allow a supersymmetric gauge-invariant Yukawa-likecoupling λSH u H d [7] (see [8] for a review and references). In spite of the presence of (broken)supersymmetry, the Higgs sector of the NMSSM is not free from the problem common to theintroduction of a scalar sector in any gauge theory: the significant number of free parame-ters that describe their masses and interactions, of which the Yukawa couplings in the SMare a prototype example. In turn this explains the difficulty of a simple enough descriptionof the related phenomenology as well as the extended literature on the subject. The pur-pose of this work is to outline a possible overall strategy to search for signs of the CP -evenextra-states of the NMSSM Higgs sector. This paper must be viewed as a complement of [1],to which we add: i) the consideration of the case in which one state exists below h LHC ; ii)the expected sensitivity on the overall parameter space of the measurements of the signalstrengths of h LHC at LHC14 with their projected errors; iii) the consideration of the impactof the EWPT on the different situations. To keep things comprehensive we will have to makesome simplifying assumptions, that we shall be careful to specify whenever needed.
For ease of the reader we summarize in this Section the definitions and the reference equationsthat we shall use to describe the relation between the physical observables and the parametersof a generic NMSSM.Assuming a negligibly small CP -violation in the Higgs sector, the original scalar fields H =( H d , H u , S ) T are related to the three CP -even physical mass eigenstates H ph = ( h , h , h ) T by H = R α R γ R σ H ph ≡ R H ph , (2.1)where R ijθ is the rotation matrix in the ij sector by the angle θ = α, γ, σ . We shall identify For a partial list of recent references, see [9–25]. h .In full generality the mixing angles δ ≡ α − β + π/ , γ, σ can be expressed in terms of themasses m h ,h ,h and m H ± , the charged Higgs boson mass, as [1] s γ = det M + m h ( m h − tr M )( m h − m h )( m h − m h ) , (2.2) s σ = m h − m h m h − m h det M + m h ( m h − tr M )det M − m h m h + m h ( m h + m h − tr M ) , (2.3) s δ = (cid:104) s σ c σ s γ (cid:0) m h − m h (cid:1) (cid:16) M − m h c γ − m h ( s γ + s σ c γ ) − m h ( c σ + s γ s σ ) (cid:17) + 2 ˜ M (cid:0) m h (cid:0) c σ − s γ s σ (cid:1) + m h (cid:0) s σ − s γ c σ (cid:1) − m h c γ (cid:1) (cid:105) × (cid:104) (cid:0) m h − m h s γ − m h c γ (cid:1) + (cid:0) m h − m h (cid:1) c γ s σ + 2 (cid:0) m h − m h (cid:1) (cid:0) m h + m h s γ − m h (cid:0) s γ (cid:1)(cid:1) c γ s σ (cid:105) − , (2.4)where s θ = sin θ, c θ = cos θ , M is the 2 × × M of the neutral CP -even scalars in the H basis M = (cid:18) m Z c β + m A s β (2 v λ − m A − m Z ) c β s β (2 v λ − m A − m Z ) c β s β m A c β + m Z s β + δ t (cid:19) (2.5)and ˜ M = R β − π/ M R tβ − π/ in Eq. (2.4). In Eq. (2.5) m A = m H ± − m W + λ v , (2.6)where v (cid:39)
174 GeV, and δ t ≡ ∆ t /s β (2.7)is the well-known effect of the top-stop loop corrections to the quartic coupling of H u . Weneglect the analogous correction to Eq. (2.6), which lowers m H ± by less than 3 GeV for stopmasses below 1 TeV. More importantly we have also not included in Eq. (2.5) the one loopcorrections to the 12 and 11 entries, respectively proportional to the first and second powerof ( µA t ) / (cid:104) m t (cid:105) , to which we shall return.We shall in particular be interested in two limiting cases: • H decoupled: m h (cid:29) m h ,h and σ, δ ≡ α − β + π/ → • Singlet decoupled: m h (cid:29) m h ,h and σ, γ → • H decoupled: s γ = m hh − m h m h − m h , (2.8)where m hh = m Z c β + λ v s β + ∆ t ; (2.9) Notice that Eq. (2.4) is completely equivalent to the expression for sin 2 α in Eq. (2.10) of Ref. [1]. .6 0.7 0.81002 4 6 8 10020406080100120 tan Β m h (cid:72) G e V (cid:76) tan Β m h (cid:72) G e V (cid:76) Figure 1.
Singlet decoupled. Isolines of λ (solid) and m H ± (dashed). Left: h LHC > h . Right: h LHC < h . The orange region is excluded at 95%C.L. by the experimental data for the signalstrengths of h = h LHC . The blue region is unphysical. • Singlet decoupled: s α = s β λ v − m Z − m A | m h m A | m h + m Z + δ t − m h , (2.10) m h = m A | m h + m Z + δ t − m h , (2.11)where m A (cid:12)(cid:12) m h = λ v ( λ v − m Z ) s β − m h ( m h − m Z − δ t ) − m Z δ t c β m hh − m h . (2.12)All the equations in this section are valid in a generic NMSSM. Specific versions of it maylimit the range of the physical parameters m h , , , m H ± and α, γ, σ but cannot affect any ofthese equations. From Eqs. (2.10)-(2.12) and (2.6), since m h is known, m h , m H + and the angle δ are functionsof (tan β, λ, ∆ t ). From our point of view the main motivation for considering the NMSSMis in the possibility to account for the mass of h LHC with not too big values of the stopmasses. For this reason we take ∆ t = 75 GeV, which can be obtained, e.g., for an averagestop mass of about 700 GeV. In turn, as it will be seen momentarily, the consistency of Eqs.(2.10)-(2.12) requires not too small values of the coupling λ . It turns out in fact that forany value of ∆ t (cid:46)
85 GeV, the dependence on ∆ t itself can be neglected, so that m h , m H ± and δ are determined by tan β and λ only. For the same reason it is legitimate to neglect4 .6 0.7 0.81002 4 6 8 10020406080100120 tan Β m h (cid:72) G e V (cid:76) tan Β m h (cid:72) G e V (cid:76) Figure 2.
Singlet decoupled. Isolines of λ (solid) and m H ± (dashed). Left: h LHC > h . Right: h LHC < h . The orange region would be excluded at 95%C.L. by the experimental data for thesignal strengths of h = h LHC with SM central values and projected errors at the LHC14 as discussedin the text. The blue region is unphysical. the one loop corrections to the 11 and 12 entries of the mass matrix, Eq. (2.5), as long as( µA t ) / (cid:104) m t (cid:105) (cid:46)
1, which is again motivated by naturalness.From all this we can represent in Fig. 1 the allowed regions in the plane (tan β, m h ) andthe isolines of λ and m H ± both for h < h LHC ( < h (= S )) and for h LHC < h ( < h (= S )),already considered in Ref. [1]. At the same time the knowledge of δ in every point of the same(tan β, m h ) plane fixes the couplings of h and h LHC , which allows to draw the currentlyexcluded regions from the measurements of the signal strengths of h LHC . We do not includeany supersymmetric loop effect other than the ones that give rise to Eq. (2.5). As in Ref. [1],to make the fit of all the data collected so far from ATLAS, CMS and Tevatron, we adaptthe code provided by the authors of Ref. [26]. Negative searches at LHC of h → ¯ τ τ mayalso exclude a further portion of the parameter space for h > h LHC . Note, as anticipated,that in every case λ is bound to be above about 0 .
6. To go to lower values of λ would requireconsidering ∆ t (cid:38)
85 GeV, i.e. heavier stops. On the other hand in this singlet-decoupled caselowering λ and raising ∆ t makes the NMSSM close to the minimal supersymmetric StandardModel (MSSM), to which we shall return.When drawing the currently excluded regions in Fig. 1, we are not considering the pos-sible decays of h LHC and/or of h into invisible particles, such as dark matter, or into anyundetected final state, because of background, like, e.g., a pair of light pseudo-scalars. Theexistence of such decays, however, would not alter in any significant way the excluded regionsfrom the measurements of the signal strengths of h LHC , which would all be modified by acommon factor (1 + Γ inv / Γ vis ) − . This is because the inclusion in the fit of the LHC data ofan invisible branching ratio of h LHC , BR inv , leaves essentially unchanged the allowed rangefor δ at different tan β values, provided BR inv (cid:46) . h LHC suggests that an improvement of such measurements, as foreseen in the coming stage5 .20.32 4 6 8 10 12 14020406080100120 tan Β m h (cid:72) G e V (cid:76) tan Β m h (cid:72) G e V (cid:76) Figure 3. H -decoupled. Isolines of s γ . λ = 0 . v S = v . Left: ∆ t = 75 GeV. Right: ∆ t = 85GeV. Orange and blue regions as in Fig. 1. The red region is excluded by LEP direct searches for h → b ¯ b . of LHC, could lead to an effective exploration of most of the relevant parameter space. Toquantify this we have considered the impact on the fit of the measurements of the signalstrengths of h LHC with the projected errors at LHC14 with 300 fb − by ATLAS [27] and CMS[28], shown in Table 1. The result is shown in Fig. 2, again both for h < h LHC ( < h (= S ))and for h LHC < h ( < h (= S )), assuming SM central values for the signal strengths.ATLAS CMS h → γγ h → ZZ h → W W
V h → V b ¯ b – 0.17 h → τ τ h → µµ Table 1.
Projected uncertainties of the measurements of the signal strengths of h LHC , normalizedto the SM, at the 14 TeV LHC with 300 fb − . Needless to say, the direct search of the extra CP -even states will be essential eitherin presence of a possible indirect evidence from the signal strengths or to fully cover theparameter space for h > h LHC . To this end, under the stated assumptions, all productioncross sections and branching ratios for the h state are determined in every point of the(tan β, m h ) plane. 6 .0250.05 0.10.22 4 6 8 10 12 14020406080100120 tan Β m h (cid:72) G e V (cid:76) tan Β m h (cid:72) G e V (cid:76) Figure 4. H -decoupled. Isolines of s γ . ∆ t = 75 GeV and v S = v . Left: λ = 0 .
8. Right: λ = 1 . h → b ¯ b . H -decoupled As we are going to see, the situation changes significantly when considering the H -decoupledcase where the singlet S mixes with the doublet with SM couplings. By comparing Eqs. (2.8)with Eqs.(2.10), note first that in this case there is only a single relation between the mixingangle γ and the mass of the extra CP -even state m h , involving tan β, λ and ∆ t . Since thecase h LHC < h ( < h (= H )) has been extensively discussed in Ref. [1], here we concentrateon the case of h < h LHC ( < h (= H )) and we consider both the low and the large λ case.The low λ case ( λ = 0 .
1) is shown in Fig. 3 for two values of ∆ t together with theisolines of s γ . Due to the singlet nature of S it is straightforward to see that the couplingsof h = h LHC and h to fermions or to vector-boson pairs, V V = W W, ZZ , normalized tothe same couplings of the SM Higgs boson, are given by g h ff g SM hff = g h V V g SM hV V = c γ , g h ff g SM hff = g h V V g SM hV V = − s γ . (4.1)As a consequence for m h > m h LHC / h = h LHC and h get modified with respect to the ones of the SM Higgs boson with the corresponding mass,whereas their production cross sections are reduced by a common factor c γ or s γ respectivelyfor h = h LHC and h . The current fit of the signal strengths measured at LHC constrain s γ < .
22 at 95% C.L., which explains the lighter excluded regions in Fig. 3. The red regionsare due to the negative searches of h → ¯ bb at LEP [29]. As in the previous case we do notinclude any invisible decay mode except for h LHC → h h when kinematically allowed. Here To include h LHC → h h we rely on the triple Higgs couplings as computed by retaining only the λ -contributions. This is a defendable approximation for λ close to unity, where h LHC → h h is important.In the low λ case the λ -approximation can only be taken as indicative, but there h LHC → h h is lessimportant. .2 0.3 0.42 4 6 8 10 12 14020406080100120 tan Β m h (cid:72) G e V (cid:76) tan Β m h (cid:72) G e V (cid:76) Figure 5. H -decoupled. Isolines of g h /g h (cid:12)(cid:12) SM . Left: λ = 0 .
1, ∆ t = 85 GeV and v S = v . Right: λ = 0 .
8, ∆ t = 75 GeV and v S = v . Orange and blue regions as in Fig. 1. The red region is excludedby LEP direct searches for h → b ¯ b . an invisible branching ratio of h LHC , BR inv , would strengthen the bound on the mixing angleto s γ < (0 . − . inv ).For λ close to unity we take as in the singlet-decoupled case ∆ t = 75 GeV, but any choicelower than this would not change the conclusions. The currently allowed region is shown inFig. 4 for two values of λ . Note that, for large λ , no solution is possible at low enough tan β ,since, before mixing, m hh in Eq. (2.9) has to be below the mass squared of h LHC .How will it be possible to explore the regions of parameter space currently still allowed inthis h < h LHC ( < h (= H )) case in view of the reduced couplings of the lighter state? Unlikein the singlet-decoupled case, the improvement in the measurements of the signal strengthsof h LHC is not going to play a major role. Based on the projected sensitivity of Table 1, thebound on the mixing angle will be reduced to s γ < .
15 at 95% C.L. A significant deviationfrom the case of the SM can occur in the cubic h LHC -coupling, g h , as shown in Fig. 5. TheLHC14 in the high-luminosity regime is expected to get enough sensitivity to be able tosee such deviations [27, 30, 31]. At that point, on the other hand, the searches for directlyproduced s-partners should have already given some clear indications on the relevance of theentire picture.For completeness we recall from Ref. [1] that the parameter space in the case h LHC < h ( 1. Most promising in this case are the directsearches of h with gluon-fusion production cross-sections at LHC14 in the picobarn rangeand a large branching ratio, when allowed by phase space, into a pair of h LHC . Furthermorehere as well large deviations from the SM value can occur in the cubic h LHC -coupling.8 .3 0.61 11.5 2 4 6 8 10 12 14020406080100120 tan Β m h (cid:72) G e V (cid:76) tan Β m h (cid:72) G e V (cid:76) Figure 6. Fully mixed situation. Isolines of the signal strength of h → γγ normalized to the SM.We take m h = 500 GeV, s σ = 0 . 001 and v s = v . Left: λ = 0 . 1, ∆ t = 85 GeV. Right: λ = 0 . t = 75 GeV. Orange and blue regions as in Fig. 1. The red and dark red regions are excluded byLEP direct searches for h → b ¯ b and h → hadrons respectively. γ γ signal The phenomenological exploration of the situation considered in the previous section couldbe significantly influenced if the third state, i.e. the doublet H , were not fully decoupled. Asan example we still consider the case of a state h lighter than h LHC , lowering m h to 500GeV, to see if it could have an enhanced signal strength into γγ . Using Eqs. (2.2)-(2.4), forfixed values of σ , λ and ∆ t , the two remaining angles α (or δ = α − β + π/ 2) and γ aredetermined in any point of the (tan β, m h ) plane and so are all the branching ratios of h and of h LHC . More precisely δ is fixed up to the sign of s σ c σ s γ (see first line of Eq. (2.4)),which is the only physical sign that enters the observables we are considering.The corresponding situation is represented in Fig. 6, for two choices of λ and ∆ t (thechoice λ = 0 . s σ c σ s γ has been taken negativein order to suppress BR( h → b ¯ b ). This constrains s σ to be very small in order to leave aregion still not excluded by the signal strengths of h LHC , with δ small and negative. To get asignal strength for h → γγ close to the SM one for the corresponding mass is possible for asmall enough value of s γ , while the dependence on m h is weak for values of m h greater than500 GeV. Note that the suppression of the coupling of h to b -quarks makes it necessary toconsider the negative LEP searches for h → hadrons [32], which have been performed downto m h = 60 GeV.Looking at the similar problem when h > h LHC , we find it harder to get a signal strengthclose to the SM one, although this might be possible for a rather special choice of theparameters. Our purpose here is more to show that in the fully mixed situation the role of An increasing significance of the excess found by the CMS [33] at 136 GeV would motivate such specialchoice. h LHC , either current or foreseen, plays a crucial role. One may ask if the electro-weak precision tests (EWPT) set some further constraint on theparameter space explored so far. We have directly checked that this is not the case in anyof the different situations illustrated in the various figures. The reason is different in thesinglet-decoupled and in the H -decoupled cases.In the H -decoupled case the reduced couplings of h LHC to the weak bosons lead to well-known asymptotic formulae for the corrections to the ˆ S and ˆ T parameters [34]∆ ˆ S = + α πs w s γ log m h m h LHC , ∆ ˆ T = − α πc w s γ log m h m h LHC (6.1)valid for m h sufficiently heavier that h LHC . The correlation of s γ with m h given in Eq. (2.8)leads therefore to a rapid decoupling of these effects. The one loop effect on ˆ S and ˆ T becomesalso vanishingly small as m h and h LHC get close to each other, since in the degenerate limitany mixing can be redefined away and only the standard doublet contributes as in the SM.In the singlet-decoupled case the mixing between the two doublets can in principle leadto more important effects, which are however limited by the constraint on the mixing angle α or the closeness to zero of δ = α − β + π/ h LHC . Since in the δ = 0 limit every extra effect on ˆ S and ˆ T vanishes,this explains why the EWPT do not impose further constraints on the parameter space thatwe have considered. As recalled in section 3, it is interesting to consider the MSSM, i.e. the λ = 0 limit of theNMSSM in the singlet-decoupled case, using as much as possible the same language. Theanalogue of Fig. 1 are shown in Fig. 7. From the point of view of the parameter space themain difference is that instead of λ we use ∆ t as an effective parameter. As expected, boththe left and right panel of Fig. 7 make clear that a large value of ∆ t is needed to make theMSSM consistent with a 125 GeV Higgs boson.At the same time, and even more than in the NMSSM case, the projection of the measure-ments of the signal strengths of h LHC is expected to scrutinize most of the parameter space.We have checked that this is indeed the case with the indirect sensitivity to m h in the rightpanel of Fig. 7, which will be excluded up to about 1 TeV, as well as with the closure ofthe white region in the left side of the same Figure. Notice that a similar exclusion will holdalso for the CP-odd and charged Higgs bosons, whose masses are fixed in terms of the oneof h . A warning should be kept in mind, however, relevant to the case h < h LHC : the oneloop corrections to the mass matrix controlled by ( µA t ) / (cid:104) m t (cid:105) modify the left side of Fig. 7for ( µA t ) / (cid:104) m t (cid:105) (cid:38) 1, changing in particular the currently and projected allowed regions. Notice that in the fully mixed situation there may be relevant regions of the parameter space still allowedby the fit with a largish δ (see e.g. Fig. 1 of Ref. [1]). This could further constrain the small allowedregions, but the precise contributions to the EWPT depend on the value of the masses of the CP -oddscalars, which in the generic NMSSM are controlled by further parameters. 085 100120 1402 4 6 8 10 12 14020406080100120 tan Β m h (cid:72) G e V (cid:76) tan Β m h (cid:72) G e V (cid:76) Figure 7. MSSM. Isolines of ∆ t (solid) and m H ± (dashed) at ( µA t ) / (cid:104) m t (cid:105) (cid:28) 1. Left: h LHC > h ,red region is excluded by LEP direct searches for h → b ¯ b . Right: h LHC < h , red region is excludedby CMS direct searches for A, H → τ + τ − [35]. Orange and blue regions as in Fig. 1. Given the current experimental informations, the Higgs sector of the NMSSM appears toallow a minimally fine-tuned description of electro-weak symmetry breaking, at least in thecontext of supersymmetric extensions of the SM. Motivated by this fact and complementingRef. [1], we have outlined a possible overall strategy to search for signs of the CP -even statesby suggesting a relatively simple analytic description of four different situations: • Singlet-decoupled, h < h LHC < h (= S ) • Singlet-decoupled, h LHC < h < h (= S ) • H -decoupled, h < h LHC < h (= H ) • H -decoupled, h LHC < h < h (= H )To make this possible at all we have made some simplifying assumptions on the parameterspace, which are motivated by naturalness requirements and have been in any case specifiedwhenever needed. In our view the advantages of having an overall coherent analytic picturejustify the introduction of these assumptions.Not surprisingly, a clear difference emerges between the singlet-decoupled and the H -decoupled cases: the influence on the signal strengths of h LHC of the mixing with a doubletor with a singlet makes the relative effects visible at different levels. A quantitative estimateof the sensitivity of the foreseen measurements at LHC14 with 300 fb − makes it likely thatthe singlet-decoupled case will be thoroughly explored, while the singlet-mixing effects couldremain hidden. We also found that, in the MSSM with ( µA t ) / (cid:104) m t (cid:105) (cid:46) 1, the absence ofdeviations in the h LHC signal strengths would push the mass of the other Higgs bosons upto a TeV. Needless to say, in any case the direct searches will be essential with a variety of11ossibilities discussed in the literature. As an example we have underlined the significanceof h → h LHC h LHC in the h LHC < h < h (= H ) case. It is also interesting that, in the H -decoupled case, large deviations from the SM value are possible in the triple Higgs coupling g h LHC , contrary to the S -decoupled and MSSM cases. More in general it is useful to observethat the framework outlined in this work makes possible to describe the impact of the variousdirect searches in a systematic way, together with the indirect ones in the h LHC couplings.Finally, in case of a positive signal, direct or indirect, it may be important to try to interpretit in a fully mixed scheme, involving all the three CP -even states. To this end the analyticrelations of the mixing angles to the physical masses given in Eqs. (2.2)-(2.4) offer a usefultool, as illustrated in the examples of a γγ signal of Fig. 6.It will be interesting to follow the progression of the searches of the Higgs system of theNMSSM, directly or indirectly through the more precise measurements of the properties ofthe state already found at the LHC. Acknowledgments We would like to thank Pietro Slavich for useful discussions. This work is supported in part bythe European Programme “Unification in the LHC Era”, contract PITN-GA-2009-237920(UNILHC), MIUR under the contract 2010YJ2NYW-010, the ESF grants 8943, MJD140and MTT8, by the recurrent financing SF0690030s09 project and by the European Unionthrough the European Regional Development Fund. We would like to thank the GalileoGalilei Institute in Florence for hospitality during the completion of this work. References [1] R. Barbieri, D. Buttazzo, K. Kannike, F. Sala, and A. Tesi, Phys. Rev. D87 (2013) 115018, arXiv:1304.3670 [hep-ph] .[2] ATLAS Collaboration , G. Aad et al., Phys.Lett. B716 (2012) 1–29, arXiv:1207.7214[hep-ex] .[3] CMS Collaboration , S. Chatrchyan et al., Phys.Lett. B716 (2012) 30–61, arXiv:1207.7235 [hep-ex] .[4] ATLAS Collaboration , F. Hubaut. Talk at the Moriond 2013 EW session. ATLAS Collaboration , E. Mountricha. Talk at the Moriond 2013 QCD session. ATLAS Collaboration , V. Martin. Talk at the Moriond 2013 EW session. ATLAS Collaboration , ATLAS-CONF-2013-009. ATLAS Collaboration , ATLAS-CONF-2013-010. ATLAS Collaboration , ATLAS-CONF-2013-011. ATLAS Collaboration , ATLAS-CONF-2013-012. ATLAS Collaboration , ATLAS-CONF-2013-013. ATLAS Collaboration , ATLAS-CONF-2013-014. ATLAS Collaboration , ATLAS-CONF-2013-030. CMS Collaboration , G. Gomez-Ceballos. Talk at the Moriond 2013 EW session. CMS Collaboration , M. Shen. Talk at the Moriond 2013 QCD session. CMS Collaboration , B. Mansoulie. Talk at the Moriond 2013 EW session. CMS Collaboration , V. Dutta. Talk at the Moriond 2013 EW session. CMS Collaboration , CMS-PAS-HIG-13-001. CMS Collaboration , CMS-PAS-HIG-13-002. CMS Collaboration , CMS-PAS-HIG-13-003. CMS Collaboration , CMS-PAS-HIG-13-004. CMS Collaboration , CMS-PAS-HIG-13-006. CMS Collaboration , CMS-PAS-HIG-13-009.[6] CDF and D0 Collaborations , L. ˇZivkovi´c. Talk at the Moriond 2013 EW session.[7] P. Fayet Nucl.Phys. B90 (1975) 104–124.[8] U. Ellwanger, C. Hugonie, and A. M. Teixeira, Phys.Rept. (2010) 1–77, arXiv:0910.1785 [hep-ph] .[9] L. J. Hall, D. Pinner, and J. T. Ruderman, JHEP (2012) 131, arXiv:1112.2703[hep-ph] .[10] U. Ellwanger JHEP (2012) 044, arXiv:1112.3548 [hep-ph] .[11] J.-J. Cao, Z.-X. Heng, J. M. Yang, Y.-M. Zhang, and J.-Y. Zhu, JHEP (2012) 086, arXiv:1202.5821 [hep-ph] .[12] K. S. Jeong, Y. Shoji, and M. Yamaguchi, JHEP (2012) 007, arXiv:1205.2486[hep-ph] .[13] K. Agashe, Y. Cui, and R. Franceschini, JHEP (2013) 031, arXiv:1209.2115[hep-ph] .[14] G. Belanger, U. Ellwanger, J. F. Gunion, Y. Jiang, S. Kraml, et al., JHEP (2013) 069, arXiv:1210.1976 [hep-ph] .[15] K. Choi, S. H. Im, K. S. Jeong, and M. Yamaguchi, JHEP (2013) 090, arXiv:1211.0875 [hep-ph] .[16] S. F. King, M. Muhlleitner, R. Nevzorov, and K. Walz, Nucl.Phys. B870 (2013) 323–352, arXiv:1211.5074 [hep-ph] .[17] R. T. D’Agnolo, E. Kuflik, and M. Zanetti, arXiv:1212.1165 [hep-ph] .[18] R. S. Gupta, M. Montull, and F. Riva, arXiv:1212.5240 [hep-ph] .[19] T. Gherghetta, B. von Harling, A. D. Medina, and M. A. Schmidt, JHEP (2013) 032, arXiv:1212.5243 [hep-ph] .[20] Z. Kang, J. Li, T. Li, D. Liu, and J. Shu, arXiv:1301.0453 [hep-ph] .[21] C. Cheung, S. D. McDermott, and K. M. Zurek, arXiv:1302.0314 [hep-ph] . 22] T. Cheng, J. Li, T. Li, and Q.-S. Yan, arXiv:1304.3182 [hep-ph] .[23] M. Badziak, M. Olechowski, and S. Pokorski, JHEP (2013) 043, arXiv:1304.5437[hep-ph] .[24] B. Bhattacherjee, M. Chakraborti, A. Chakraborty, U. Chattopadhyay, D. Das, et al., arXiv:1305.4020 [hep-ph] .[25] U. Ellwanger arXiv:1306.5541 [hep-ph] .[26] P. P. Giardino, K. Kannike, I. Masina, M. Raidal, and A. Strumia, arXiv:1303.3570[hep-ph] .[27] ATLAS Collaboration , ATL-PHYS-PUB-2012-004.[28] CMS Collaboration . http://indico.cern.ch/contributionDisplay.py?contribId=144&confId=175067 . seefile CMS-EF-ESPG.pdf.[29] ALEPH Collaboration, DELPHI Collaboration, L3 Collaboration, OPALCollaboration, LEP Working Group for Higgs Boson Searches , S. Schael et al.,Eur.Phys.J. C47 (2006) 547–587, arXiv:hep-ex/0602042 [hep-ex] .[30] M. J. Dolan, C. Englert, and M. Spannowsky, JHEP (2012) 112, arXiv:1206.5001[hep-ph] .[31] F. Goertz, A. Papaefstathiou, L. L. Yang, and J. Zurita, JHEP (2013) 016, arXiv:1301.3492 [hep-ph] .[32] LEP Higgs Working Group for Higgs boson searches arXiv:hep-ex/0107034[hep-ex] .[33] CMS Collaboration , CMS-PAS-HIG-13-016.[34] R. Barbieri, B. Bellazzini, V. S. Rychkov, and A. Varagnolo, Phys.Rev. D76 (2007) 115008, arXiv:0706.0432 [hep-ph] .[35] CMS Collaboration . CMS-PAS-HIG-12-050.. CMS-PAS-HIG-12-050.