A tale of two Higgs
aa r X i v : . [ h e p - ph ] F e b A tale of two Higgs
Aielet Efrati, ∗ Daniel Grossman, † and Yonit Hochberg ‡ Department of Particle Physics and Astrophysics,Weizmann Institute of Science, Rehovot 76100, Israel
A new boson with mass ∼
125 GeV and properties similar to the Standard Model Higgs hasbeen discovered by both the ATLAS and CMS collaborations, with significant observation in the ZZ ∗ → ℓ and γγ channels. In this work we ask whether the signals in these two channels can be dueprimarily to two distinct resonances, each contributing dominantly to one channel. We investigatethis question in the framework of a 2HDM and several of its extensions. We conservatively find thatsuch a scenario is not possible in a pure 2HDM, nor under the addition of vector-like quarks, butis allowed when adding one or two top-like scalars, if one allows for sub-one tan β . The resonancesin the diboson and diphoton channels can then be two scalars, or a scalar and a pseudoscalar,respectively. In each viable case, we further find the expected future deviations in the diboson,diphoton, b ¯ b and τ τ rates, which will be useful in excluding the two-resonance scenario. Introduction.
The ATLAS [1] and CMS [2] collab-orations have recently announced the discovery of a newboson with mass in the vicinity of 125 GeV and propertiesresembling that of a Standard Model (SM) Higgs. Thecleanest search channels for the Higgs are the h → γγ and h → ZZ ∗ → ℓ modes, where until very recently goodagreement between the mass of the resonance in eachchannel was observed. The latest ATLAS data for thesetwo channels exhibits a mass discrepancy [3], and thoughit is likely a statistical feature that may soon disappear,it is interesting to ask the following question: Can theresonance observed in the diphoton channel be differentfrom that observed in the ZZ ∗ channel? Namely, canthe two signals observed in these modes be due primarilyto two separate particles that are close in mass? This isthe question we aim to address in this work, within thecontext of a 2 Higgs Doublet Model (2HDM). Thoughinspired by the current trend in the ATLAS data, wedo not attempt to explain, reproduce or fit to the fullHiggs data set under the assumption of a two particlehypothesis. Rather, we are interested in addressing thequalitative question of whether the Higgs data could bedue to two resonances; a question which is relevant evenif the current mass discrepancy disappears. Preliminaries.
We start by setting the notation to beused along this paper. Assuming two distinct particlesare observed in the latest LHC results, we denote theparticles observed in the ZZ ∗ and the diphoton channelsas φ and φ , respectively. We define the normalizedproduction rate times branching ratio of a given channelby R iX = σ i tot × BR (cid:0) φ i → X (cid:1) σ SMtot × BR SM ( h → X ) , (1)where X = ZZ ∗ , γγ , i = 1 , σ SMtot and BR SM are the production cross section andbranching ratios of a 125 GeV SM Higgs boson. As-suming the mass splitting between the two resonances is larger than their width, interference effects are sup-pressed, and the total production rate times branchingratio in each channel is the sum of the two contributions, R X = R X + R X .We ask whether the resonances observed in the dif-ferent channels can be a result of two different particlesof mass close to 125 GeV. For this to be the case, thefollowing conditions should hold:1. In each channel a different particle is responsiblefor the major contribution to the production ratetimes branching ratio, while the contribution of theother particle is minor;2. Together, the two resonances give the observedrates for the two channels.The rates in additional measured channels, such as the b ¯ b and τ τ modes, should also be accommodated by thetwo particles combined.We quantify these conditions by the following (mild)set of requirements: R ZZ ∗ ≥ R ZZ ∗ ,R γγ ≥ R γγ , . ≤ R ZZ ∗ ≤ . , . ≤ R γγ ≤ . . (2)We (conservatively) consider a parameter region to bedisfavored if it fails any of the four conditions of Eq. (2),and take a model to be ruled out if there is no pointin its parameter space that can satisfy all four of theseconditions. In what follows, we refer to the first andlast two lines of Eq. (2) as the ‘ratio’ and ‘range’ con-ditions, respectively. The use of such a moderate set ofrequirements allows us to be conservative: A model thatfails in accommodating the range conditions cannot bethe source of the Higgs measurements in the ZZ ∗ anddiphoton channels, regardless of the ratio conditions. Amodel that fails the ratio conditions cannot explain theHiggs measurements in the ZZ ∗ and diphoton channelsby means of two separate particles. A model that passesthe criteria of Eq. (2) can then be scrutinized in order tolearn whether the various rates are enhanced, suppressedor similar to that of the SM. We further restrict to simi-lar range conditions in the b ¯ b and τ τ channels, requiringthat a model that passes the conditions of Eq. (2) alsoobeys 0 . ≤ R b ¯ b ≤ . , . ≤ R ττ ≤ . , (3)in order to be viable.A comment is in order regarding existing literature onthe presence of multiple resonances in the Higgs data.This topic was discussed in [4] in the context of theNMSSM, in [5] in the context of a 2HDM, and most re-cently in [6] where general conditions for detection ofsuch resonances were derived (see also [7]). However,these works do not require the signals in each channel tobe predominantly a result of a distinct particle and thusaddress a different qualitative question than that posedin this work.We follow the notations of [8], and write the La-grangian of the two scalars ( i = 1 ,
2) as follows: L φ i ⊃ c iW m W v φ i W + µ W − µ + c iZ m Z v φ i Z µ Z µ − c it m t v φ i ¯ tt − c ib m b v φ i ¯ bb − c iτ m τ v φ i ¯ τ τ − c ic m c v φ i ¯ cc − c if m f v φ i ¯ f f − c is m s v φ i S † S , (4)where custodial symmetry implies c iW = c iZ ≡ c iV , andwe assume the invisible branching ratios to be negligi-ble. f ( S ) symbols any new fermion (scalar) added tothe theory, and we do not consider the addition of vectorbosons. The effective couplings to gluons and photonsare obtained via one loop processes, defined such thatΓ igg = | ˆ c ig | | ˆ c SM g | Γ SM gg , Γ iγγ = | ˆ c iγ | | ˆ c SM γ | Γ SM γγ , (5)where Γ iX denotes the partial width into X , and are givenby:ˆ c ig = c it A f ( τ it ) + c ib A f ( τ ib ) + c ic A f ( τ ic )+ 2 C ( r f ) c if A f ( τ if ) + C ( r s )2 c is A s ( τ is ) , ˆ c iγ = 29 c it A f ( τ it ) − c iV A f ( τ iW ) + 118 c ib A f ( τ ib ) + 16 c iτ A f ( τ iτ )+ N ( r f )6 Q f c if A f ( τ if ) + N ( r s )24 Q s c is A s ( τ is ) . (6)Here Tr (cid:0) T a T b (cid:1) = C ( r ) δ ab , N ( r ) is the dimension of therepresentation r , τ ix = m φ i / m x and A f,s are the fermionand scalar loop functions given by [8, 9]: A f ( τ ) = ξ + 22 τ [ ξτ + ( τ − ξ ) f ( τ )] ,A s ( τ ) = 3 τ [ f ( τ ) − τ ] , (7) with ξ = 1 (0) for scalars (pseudoscalars) and f ( τ ) = ( [sin − ( p /τ )] , if τ ≥ , − [ln( η + /η − ) − iπ ] , if τ < . (8)For heavy particles, τ ix ≪
1, and one finds A x ≃
1. Inthe SM with a 125 GeV Higgs, c t, SM = c b, SM = c c, SM = c τ, SM = c V, SM = 1, ˆ c g, SM ≃ . c γ, SM ≃ − . i tot = | C i tot | Γ SMtot , (9)with [10] | C i tot | ≃ . | c ib | + 0 . | c iV | + 0 . | ˆ c ig | | ˆ c SM g | + 0 . | c iτ | + 0 . | c ic | , (10)one finds the following approximate expressions: R iZZ ∗ ≃ (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) ˆ c ig c iV ˆ c SM g C i tot (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) ,R iγγ ≃ (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) ˆ c ig ˆ c iγ ˆ c SM g ˆ c SM γ C i tot (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) , (11)where in the above we have assumed that the productionis dominated by the gluon fusion process. Expressions forthe b ¯ b rate with an associated vector boson, R b ¯ b , as wellas the τ τ rate R ττ , and the dijet category in the diphotonchannel R jj γγ , can be found in or deduced from [8], withthe efficiencies in the diphoton channel, both inclusiveand dijet categories, taken from [11]. In the τ τ channel,we consider the vector boson fusion category, and use theefficiency numbers of the semi-leptonic channel as givenin [12].In what follows we use the full expressions for the pro-duction cross section times branching ratios, Eq. (1), andask whether the conditions detailed in Eq. (2) can be sat-isfied by two bosons within the 2HDM framework. Weconsider four different scenarios: Pure 2HDM withoutadditional particles, 2HDM plus vector-like quarks in the(3 , / and (3 , − / representations, and 2HDM plusadditional one or two top-like scalars.Throughout this paper we use the leading order con-tributions to the relevant production and decay pro-cesses. In all models considered, the QCD next-to-leading-order (NLO) corrections are either small or fac-tored out (see e.g. [13, 14]), and thus cancel in the ratiosto the SM. The electroweak NLO corrections are smallin the discussed models (see e.g. [15]). In this context,a comment is in order regarding addition of heavy chi-ral fermions which are not included in this work. Sincechiral fermions acquire mass from electroweak symmetrybreaking (EWSB), their loop contributions to the rel-evant production and decay channels do not decouple TABLE I: The dependence on α, β of the couplings of theneutral scalars to different particles [9].Type I φV V φ ¯ uu φ ¯ dd and φℓ + ℓ − h sin( β − α ) cos α sin β cos α sin β H cos( β − α ) sin α sin β sin α sin β A c I AV V cot β − cot β Type II φV V φ ¯ uu φ ¯ dd and φℓ + ℓ − h sin( β − α ) cos α sin β − sin α cos β H cos( β − α ) sin α sin β cos α cos β A c II AV V cot β tan β as their masses increase. The electroweak NLO contri-butions can then induce O (1) corrections to all decaymodes [15], and are important. The proper treatment ofadditional heavy chiral fermions is beyond the scope ofthis work, and is hence omitted from further discussion. We now study the pure CP-conserving 2HDMscheme with no additional particles, considering bothtype I and type II couplings. The dependence of the re-sults on the lepton couplings in the pure 2HDM is highlysuppressed, allowing us to extend our conclusions to theother natural flavor conserving 2HDM types. We con-ventionally define the ratio between the VEVs of the twoHiggs doublets by tan β and the rotation angle to theneutral mass eigenstates by α . The neutral spectrum ofthe 2HDM contains two scalars h and H with m h < m H ,and one pseudoscalar A .The couplings of h, H and A to vector bosons, upquarks, down quarks and charged leptons are presentedin Table I. We define an effective coupling between thepseudoscalar and two massive gauge bosons, | c iAV V | ≡ Γ iA → V V / Γ SM h → V V , where Γ iA → V V is the appropriate par-tial width of the pseudoscalar in type i =I, II [16–18],arising from the dimension 5 operator AV µν ˜ V µν which isgenerated at the loop level, where V µν is the field strengthof the vector boson. Throughout we neglect the contribu-tion of the charged Higgs loops to the diphoton channel(see e.g. [19]). We have verified numerically that subjectto electroweak precision data [20] and perturbativity con-straints on the trilinear couplings, the inclusion of sucheffects does not alter our results.In the following we consider all possible pairs amongst h, H and A as the potential resonances. The exchange ofthe two scalars produces almost identical results under ashift of α → α ± π/
2. Additionally, while the parity of theobserved particle in the ZZ ∗ channel is currently underscrutiny [21], we have included the possibility that φ isthe pseudoscalar A . In all the explored scenarios we findhowever that the pseudoscalar cannot successfully serveas the resonance in ZZ ∗ channel due to its suppressedcoupling. We thus quote our results only for the cases of (cid:0) φ , φ (cid:1) = ( h, H ) and ( h, A ).Given that φ is the resonance seen in the ZZ ∗ channel,the data suggests that this particle should have, to someextent, SM-like couplings, namely c V should be of orderone. In contrast, the φ contribution to the diphotonchannel is required to be small. The effective couplingto two photons arises at one loop, primarily via internal W and t contributions which interfere destructively witheach other, ˆ c iγ ∝ c it − c iV . Thus, it is difficult to find aparameter space in which φ dominates the ZZ ∗ chan-nel but has only a moderate contribution to the γγ finalstate, unless a delicate cancelation occurs. The comple-mentary demand that φ contributes significantly onlyto the γγ channel is easily achieved if φ is the pseu-doscalar A , since its coupling to two heavy gauge bosonsis loop-induced and thus highly suppressed.We learn that the four conditions of Eq. (2) are dif-ficult to accommodate generically in a 2HDM. In whatfollows we identify the scenarios and regions of parameterspace in which the appropriate cancelations do occur andthe conditions are met. We note that a combination ofseveral effects determines whether a scenario or parame-ter space is viable or not. Whenever possible, we explainthese effects.We consider 0 . ≤ tan β ≤
65 and | α | ≤ π/
2, andfirst ask whether a parameter space exists in which theobserved resonances are a result of two different particles,namely the ratio conditions in Eq. (2) are satisfied. Wethen further seek the parameter space in which all theconditions are met. Our results are as follows: • The two scalars, h and H , cannot provide the ob-served signals. In type II the ratio conditions canbe achieved only for tan β ∼ < .
6, where the cancela-tion between the W and the t loops is increased dueto the enhanced top coupling. However, this pa-rameter range typically leads to a very small dipho-ton rate, since a large cancelation occurs for bothof the scalars. In type I, since c h,Ht = c h,Hb there isless freedom for α and β and the required cancela-tion cannot occur, yielding null results for the ratioconditions in the case of the two scalars. • For φ = h and φ = A in the type II 2HDM, allfour conditions of Eq. (2) are satisfied for tan β ∼ < .
6, in which case R γγ ∼ < .
2. The reason is that forsuch small tan β , the coupling of the scalar to thetop is enhanced and suppresses R γγ , while R ZZ ∗ is naturally small. The pseudoscalar contributionto the diphoton signal, R γγ , is further enhanced atsuch small tan β . However, in the relevant param-eter space, the normalized production rate timesbranching ratio in the b ¯ b channel, R b ¯ b , is suppressedto the level of a few percent, disfavoring this sce-nario. In type I these particles can obey the desiredratios, but the relevant parameter space yields toosmall a signal in both channels.We learn that a pure 2HDM of type II can accountfor the conditions of Eq. (2) if φ = h and φ = A ,for tan β ∼ < .
6, but cannot accommodate a reasonablerate in the b ¯ b mode, Eq. (3), disfavoring the pure 2HDMscenario. We note that in 2HDM, a bound exists on therate of the associated production of b ¯ b , stemming fromEq. (10) and Table I, of R b ¯ b ∼ < . Next weconsider the addition of two vector-like top quarks, trans-forming as T ∼ (3 , / and T c ∼ (¯3 , − / . Assumingsmall mixing between these heavy fields and the first twogenerations, the most general renormalizable interactionsare: L = L − M T T c − λQ h u T c − mT t c + h . c ., (12)where the last term in Eq. (12) can be rotated away by aredefinition of T and t without loss of generality, and h u is the up-type Higgs of the 2HDM with h h u i = v u / √ Q and t c , yieldingtwo physical states with masses m t and m T ≃ M ≫ m t (see experimental bounds on m T below). The mass eigen-states are linear combinations of the heavy and light tops,and the mixing angle for the left-handed components isgiven by tan 2 θ L ≃ m t m T λy t . (13)Denoting the physical mass eigenstates by ˜ t, ˜ t c , ˜ T and ˜ T c ,we write the Yukawa Lagrangian in terms of these fields: L Y = − cos θ L m t v u h u ˜ t ˜ t c − sin θ L m T v u h u ˜ T ˜ T c − sin 2 θ L m T v u h u ˜ t ˜ T c − sin 2 θ L m t v u h u ˜ T ˜ t c + h . c . (14)The couplings of the light and heavy tops to the physicalHiggs fields are given by: c i ˜ t = cos θ L (cid:0) c it (cid:1) ,c i ˜ T = sin θ L (cid:0) c it (cid:1) , (15)resulting in the following changes to the effective cou-plings to gluons and photons: δ ˆ c ig = 92 δ ˆ c iγ = sin θ L [ A f ( τ T ) − A f ( τ t )] (cid:0) c it (cid:1) . (16)Existing bounds on vector-like top quarks give M T &
475 GeV, whether its primary decay channel is viacharged-current [22] or neutral-current [23] interactions,or if the branching ratios in these channels are 1/2 and1/4, respectively (as predicted by the equivalence prin-ciple in the large mass limit [24]). We thus can safelyuse A f ( τ T ) ≃
1. Since the difference between the loop function of the light and heavy top particles is of ordera percent, we find as expected that the results of a pure2HDM are virtually unaffected by the presence of thenew vector-like top.Alternatively, one can add vector-like quarks in therepresentations B ∼ (3 , − / and B c ∼ (¯3 , / , whichmix with the SM bottom quark. The couplings of theHiggs fields to the light and heavy mass eigenstates, ˜ b and ˜ B , as well as the shift to the effective coupling togluons and photons, can be straightforwardly deducedfrom Eqs. (15) and (16). Experimental bounds on vector-like bottom quarks yield M B &
480 [25, 26], resultingagain in A f ( τ B ) ≃ B alters thecoupling of the Z boson to the left-handed component ofthe light state ˜ b by δg b L = g sin θ L / (2 cos θ W ). This, inturn, changes the partial width of the Z boson into two b quarks: δR b R b ≃ . δg b L g b L . (17)The experimental 2 σ bound gives − . ∼ < δR b /R b ∼ < .
009 [20], leading to sin θ L ∼ < . θ L , they are highly suppressed under this constraint,and we find no deviation in the results from the pure2HDM scenario. We now discuss theaddition of one top-like scalar ˜ t to the 2HDM scenario: L = L − | ˜ t | (cid:0) M + λ | h u | (cid:1) , (18)which, in the language of (4), with S = ˜ t , gives˜ m t = M + m t λy t ,c i ˜ t = m t ˜ m t λy t (cid:0) c it (cid:1) , (19)resulting in a shift to the effective coupling to gluons andphotons: δ ˆ c ig = 92 δ ˆ c iγ = 14 m t ˜ m t λy t A s ( τ ˜ t ) (cid:0) c it (cid:1) . (20)There are thus 2 additional parameters compared to thepure 2HDM case, r ≡ λ/y t and ˜ m t . The quadratic di-vergences in the Higgs mass are canceled for r = 2. Weconsider all values of r up to the perturbative limit of ± π , and allow ˜ m t ∼ >
80 GeV. The pure 2HDM case isreproduced in the large ˜ m t limit. We find the following: • The two scalars h and H can provide for the condi-tions Eq. (2) for positive r and small tan β ∼ < . ∼ r = 2 the allowed mass range is200 −
400 GeV.) In this case, we find R ZZ ∗ ∼ > . R γγ ∼ > . R b ¯ b ∼ . R ττ ∼ > .
2. Intype II, larger tan β of order a few can be reachedfor low ˜ m t , but the τ τ rate is strongly enhanced to R ττ ∼ >
8, excluding this scenario [12]. • If φ = h and φ = A , the conditions of Eq. (2)can be met in type I for tan β ∼ <
10 for positive r and ˜ m t ∼ <
750 GeV, but then either R ττ ∼ > . R b ¯ b ∼ < .
5, disfavoring this scenario. The conditionsEq. (2) are also met for r <
0, but then R b ¯ b is toolow, disfavoring this scenario as well. In type II,Eq. (2) holds for tan β ∼ < . r , andcombining the conditions of Eq. (3) gives an en-hanced diphton rate R γγ ∼ >
2, suppressed dibosonrate R ZZ ∗ ∼ < . τ τ rate of R ττ ∼ . R b ¯ b close to the SM value. For negative r , the allowedregion yields a b ¯ b rate of order a percent. The con-ditions Eq. (2) can be met in type II for tan β oforder a few as well, but then R ττ ∼ > .
5, disfavoringthis scenario.We learn that in a 2HDM with one additional top-likescalar, satisfying the conditions of Eq. (2), while keepingthe b ¯ b and τ τ rates at the reasonable levels of Eq. (3), ispossible with the two scalars h and H in type I, or with φ = h and φ = A in type II, where both cases requiresmall tan β below one. In the former case, enhanced ratesare expected in the diboson, diphoton and τ τ channels,with the b ¯ b channel proceeding slightly above the SM rateand ˜ m t ∼ < τ τ rates are enhanced, the diboson rate is suppressed and R b ¯ b ∼
1, with ˜ m t ∼ <
700 GeV. The results are summa-rized in Table II.
We now moveto the addition of two top-like scalars to the 2HDM. Wedenote by ˜ t the up-component of an SU(2) doublet inthe representation (3 , / and ˜ t c ∼ (¯3 , − / . In thespirit of the MSSM, we consider the following stops-HiggsLagrangian: L stop = − | ˜ t | (cid:0) ˜ m + y t | h u | (cid:1) − | ˜ t c | (cid:0) ˜ m c + y t | h u | (cid:1) − (cid:0) y t h u X t ˜ t ˜ t c + h . c . (cid:1) + D − terms , (21)where in the MSSM X t = A t − µ cot β , and we do notwrite the D -terms explicitly. In the following we assume X t real. After EWSB, the two mass eigenstates, ˜ t and˜ t , are linear combinations of ˜ t and ˜ t c with m ≤ m andmixing angle 0 ≤ θ t ≤ π , given bysin 2 θ t = 2 m t X t m − m . (22)In the language of Eq. (4), c i ˜ t = m t m ( c it ) (cid:20) − X t m t sin 2 θ t + D − terms (cid:21) ,c i ˜ t = m t m ( c it ) (cid:20) X t m t sin 2 θ t + D − terms (cid:21) , (23) È X t È(cid:144) m m @ G e V D FIG. 1: Parameter space of a 2HDM with 2 top-like scalarsin which Eqs. (2) and (3) hold, for ( φ , φ ) = ( h, H ) type I(entire colored area) and ( h, A ) type II (purple/lower). where the D -term contributions above can be found e.g. in [27]. The effective couplings to gluons and photons arechanged according to: δ ˆ c ig = 92 δ ˆ c iγ = 14 c i ˜ t A s (cid:0) τ ˜ t (cid:1) + 14 c i ˜ t A s (cid:0) τ ˜ t (cid:1) . (24)In the limit of m ≫ m , m t we find: δ ˆ c ig ≃ m t m ( c it ) A s ( τ ) (cid:20) − X t m + 0 . × cos 2 β (cid:21) . (25)The two top-like scalars contribution to the gluon effec-tive coupling can be mapped to the one obtained in thesingle scalar case, Eq. (20). However, in the one-scalarlanguage, only r . . D -terms does not qual-itatively affect the results.We find, as expected, that the same scenarios are vi-able when adding one or two top-like scalars, and givesimilar rates in all considered channels, since there existsa mapping between the one- and two-stop cases. In Fig. 1we present the two-stops parameter space in which all theconditions of Eq. (2) hold, and the τ τ and b ¯ b rates obeyEq. (3). As is evident, the light stop should be lighterthan ∼
310 GeV in all cases, and the mixing X t shouldobey | X t | /m ∼ < Conclusions.
A Higgs-like boson of mass ∼
125 GeVhas been discovered by the ATLAS and CMS collabo-rations, with significant observation in both the γγ and ZZ ∗ → ℓ channels. In this work we posed the quali-tative question of whether the signal seen in these twochannels could be the result of two distinct resonanceseach contributing dominantly to a single channel. Weinvestigated this idea in the context of a 2HDM as wellas in several of its extensions. The (mild) conditions weuse to quantify whether or not two separate particles canbe at play in each channel are given in Eq. (2) and in-clude ratio (first two lines) and range (bottom two lines)conditions. In addition, we demand that the b ¯ b and τ τ rates obey similar range conditions as the ZZ ∗ and γγ channels, Eq. (3). TABLE II: The viable scenarios of the 2HDM in which theconditions Eq. (2) and Eq. (3) hold. The scenarios with thereplacement h ↔ H are viable as well.2HDM + φ φ Type tan β R γγ R ZZ ∗ R b ¯ b R ττ R jjγγ h H I ∼ < ∼ > . ∼ > . ∼ . ∼ > ∼ < . h A II ∼ < ∼ > ∼ < . ∼ ∼ . ∼ . Table II summarizes our results of the viable scenar-ios: A 2HDM with one or two additional top-like scalars,where ( φ , φ ) = ( h, H ) in type I or ( h, A ) in type II.In each allowed case, we further detail the allowed rangeof tan β , and indicate whether the diphoton, diboson, b ¯ b and τ τ rates, as well as the dijet category in the dipho-ton channel, are enhanced, suppressed or similar to theirSM value. We find that a ratio larger than three be-tween the individual rates in the γγ , ZZ ∗ channels can-not be achieved subject to the range conditions. All theallowed cases require low tan β below unity and an en-hanced diphoton rate. The viable scenarios when addingone or two top-like scalars give similar rates in all consid-ered channels, since there exists a mapping of one caseto the other. The allowed two-stop parameter space isdepicted in Fig. 1.As the Higgs data continues to accumulate, our knowl-edge of the rates in the γγ , ZZ ∗ , b ¯ b and τ τ channels, aswell as in others, will improve significantly, further re-stricting the allowed cases and parameter space of thetwo-resonance scenario. Determining the parity of theboson in the ZZ ∗ and γγ channels will also provide usefulinformation in this context, as will improved constraintson masses of top-like scalars.In the future, the two-resonance possibility studied inthis work can result in two distinct outcomes. If themass difference between the resonances is larger than theexperimental resolution, with increased data two distinctresonances will be seen in the ZZ ∗ and γγ channels, witha different resonance dominant in each channel. This isin contrast to a two resonance case where one particleis dominant in both channels [4, 5]. On the other hand,if the mass difference between the resonances is smallerthan the experimental resolution, a double peak structurein the invariant mass distribution will not be detectable,and non-traditional methods, e.g. [6], will need to be em-ployed. Acknowledgments.
We thank Liron Barak, OfirGabizon, Oram Gedalia, Eric Kuflik, Yotam Soreq,Michael Spira and Tomer Volansky for useful discussions,and are grateful to Yossi Nir for early collaboration, manyhelpful conversations and comments on the manuscript. ∗ Electronic address: [email protected] † Electronic address: [email protected] ‡ Electronic address: [email protected][1] G. Aad et al. [ATLAS Collaboration], Phys. Lett. B ,1 (2012) [arXiv:1207.7214 [hep-ex]].[2] S. Chatrchyan et al. [CMS Collaboration], Phys. Lett. B , 30 (2012) [arXiv:1207.7235 [hep-ex]].[3] ATLAS Collaboration, ATLAS-CONF-2012-170, Decem-ber 14, 2012.[4] J. F. Gunion, Y. Jiang and S. Kraml, Phys. Rev. D ,071702 (2012) [arXiv:1207.1545 [hep-ph]].[5] P. M. Ferreira, H. E. Haber, R. Santos and J. P. Silva,arXiv:1211.3131 [hep-ph].[6] Y. Grossman, Z. ’e. Surujon and J. Zupan,arXiv:1301.0328 [hep-ph].[7] J. F. Gunion, Y. Jiang and S. Kraml, arXiv:1208.1817[hep-ph].[8] D. Carmi, A. Falkowski, E. Kuflik, T. Volansky andJ. Zupan, JHEP , 196 (2012) [arXiv:1207.1718 [hep-ph]].[9] J. F. Gunion, H. E. Haber, G. L. Kane and S. Dawson,Front. Phys. , 1 (2000).[10] S. Dittmaier et al. [LHC Higgs Cross Section WorkingGroup Collaboration], arXiv:1101.0593 [hep-ph].[11] ATLAS Collaboration, ATLAS-CONF-2012-091, July 6,2012.[12] ATLAS Collaboration, ATLAS-CONF-2012-160,November 13, 2012.[13] M. Spira, A. Djouadi, D. Graudenz and P. M. Zerwas,Nucl. Phys. B , 17 (1995) [hep-ph/9504378].[14] A. Djouadi and M. Spira, Phys. Rev. D , 014004 (2000)[hep-ph/9912476].[15] A. Djouadi, P. Gambino and B. A. Kniehl, Nucl. Phys.B , 17 (1998) [hep-ph/9712330].[16] A. Djouadi, Phys. Rept. , 1 (2008) [hep-ph/0503172].[17] A. Djouadi, Phys. Rept. , 1 (2008) [hep-ph/0503173].[18] G. C. Branco, P. M. Ferreira, L. Lavoura, M. N. Re-belo, M. Sher and J. P. Silva, Phys. Rept. , 1 (2012)[arXiv:1106.0034 [hep-ph]].[19] F. Boudjema and A. Semenov, Phys. Rev. D , 095007(2002) [hep-ph/0201219].[20] J. Beringer et al. (Particle Data Group), Phys. Rev. D86,010001 (2012).[21] S. Chatrchyan et al. [CMS Collaboration],arXiv:1212.6639 [hep-ex].[22] G. Aad et al. [ATLAS Collaboration], arXiv:1210.5468[hep-ex].[23] S. Chatrchyan et al. [CMS Collaboration], Phys. Rev.Lett. , 271802 (2011) [arXiv:1109.4985 [hep-ex]].[24] G. D. Kribs, A. Martin and T. S. Roy, Phys. Rev. D ,095024 (2011) [arXiv:1012.2866 [hep-ph]].[25] S. Chatrchyan et al. [CMS Collaboration], JHEP ,123 (2012) [arXiv:1204.1088 [hep-ex]].[26] [CMS Collaboration], CMS-PAS-EXO-11-066.[27] R. Dermisek and I. Low, Phys. Rev. D77