]>PLB30848S03702693(15)00153710.1016/j.physletb.2015.02.062The AuthorsPhenomenologyFig. 1Numerical values of the parameters ri in (4) for 600 benchmarks that fulfill the above mentioned requirements.Fig. 2The cross section values (2) for the diHiggs production processes for the 600 benchmarks used previously. The solid lines correspond to the SM cross sections.Fig. 3The ratios ξ given in (5) for the diHiggs production processes for the 600 benchmark used previously. The green benchmarks correspond to the large mixing case where 0.35<cos2θ<0.65, and the blue point represents the SM; and the solid curve represents the case of a SM extension, where the new physics affects the triple Higgs coupling as λhhh=λhhhSM(1+Δ); and the value of the relative enhancement Δ can be read from the palette. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)Fig. 4Normalized diHiggs invariant mass distribution for the process e−e+→hh+Emiss for the background (BG) and the considered benchmarks in Table 2.Table 1Different contributions to the considered processes cross sections. Numbers for LHC are taken from [16] at NLO.σaa (fb)σab (fb)σbb (fb)σSM (fb)
hh9.66−49.970.129.86
hh+tt¯3.3164×10−20.139520.847311.02
hh+Z9.0206×10−34.6999×10−29.005×10−20.14607
hh+Emiss5.1631×10−2−0.208670.297080.14004
Table 2Different values of the ratios (4) and (5) for the three chosen benchmarks.B1B2B3
sinθ0.535550.90126−0.39802
r12.953862.884665.62286
r21.316340.28189−1.26011
ξ(hh)1.103452.809756.27248
ξ(hh+tt¯)2.697282.518214.66603
ξ(hh+Z)1.222430.885320.55827
ξ(hh+Emiss)1.249002.764886.07213
Table 3The events number for the different processes within the luminosity values mentioned above for the SM and the benchmarks shown in Table 2.Events numberChannelSMB1B2B3
pp→hh4b966.751066.82716.36063.9
2b2τ106.70117.74299.8669.27
2b2γ3.894.2910.9324.4

pp→hh+tt¯4b33.0289.0683.15154.07

e−e+→hh+Z4b23.6528.9120.9413.2

e−e+→hh+Emiss4b45.3456.63125.36275.31
Triple Higgs coupling as a probe of the twinpeak scenarioAmineAhricheabc⁎aahriche@ictp.itAbdesslamArhribdaarhrib@ictp.itSalahNasriesnasri@uaeu.ac.aeaDepartment of Physics, University of Jijel, PB 98 Ouled Aissa, DZ18000 Jijel, AlgeriaDepartment of PhysicsUniversity of JijelPB 98 Ouled AissaJijelDZ18000AlgeriabThe Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, I34014, Trieste, ItalyThe Abdus Salam International Centre for Theoretical PhysicsStrada Costiera 11TriesteI34014ItalycFakultät für Physik, Universität Bielefeld, 33501 Bielefeld, GermanyFakultät für PhysikUniversität BielefeldBielefeld33501GermanydUniversité AbdelMalek Essaadi, Faculté des Sciences et Techniques, B.P 416, Tangier, MoroccoUniversité AbdelMalek EssaadiFaculté des Sciences et TechniquesB.P 416TangierMoroccoePhysics Department, UAE University, POB 17551, Al Ain, United Arab EmiratesPhysics DepartmentUAE UniversityPOB 17551Al AinUnited Arab Emirates⁎Corresponding author.Editor: J. HisanoAbstractIn this letter, we investigate the case of a twin peak around the observed 125 GeV scalar resonance, using diHiggs production processes at both LHC and e+e− Linear Colliders. We have shown that both at LHC and Linear Collider the triple Higgs couplings play an important role to identify this scenario; and also that this scenario can be distinguishable from any Standard Model extension by extra massive particles which might modify the triple Higgs coupling. We also introduce a criterion that can be used to rule out the twin peak scenario.KeywordsHiggsSingletsdiHiggs productionIn July 2012, ATLAS and CMS Collaborations [1,2] have shown the existence of a Higgslike resonance around 125 GeV confirming the cornerstone of the Higgs mechanism that predicted such particle long time ago. All Higgs couplings measured so far seem to be consistent, to some extent, with the Standard Model (SM) predictions. Moreover, in order to establish the Higgs mechanism as responsible for the phenomena of electroweak symmetry breaking one still needs to measure the self couplings of the Higgs and therefore to reconstruct its scalar potential.Recent measurements at the LHC show that there is still uncertainty on the Higgs mass; mh=125.3±0.4(stat.)±0.5(syst.) GeV for CMS [3] and mh=125.0±0.5 GeV for ATLAS [4] from the diphoton channel and mh=125.5±0.37(stat.)±0.18(syst.) GeV from combined channels. Despite this relatively large uncertainty, a scenario of two degenerate scalars around 125.5 GeV resonance is neither excluded nor confirmed [5].In the twin peak scenario (TPS); it is assumed that there are two scalars h1,2 with almost degenerate masses around 125 GeV. To our knowledge, there is no indication from experimental data which disfavor this scenario. The couplings of the twin peak Higgs to SM particles ghiXX are simply scaled with respect to SM rate by cosθ (for h1) and sinθ (for h2), where θ is a mixing angle, such that we have the following approximate sum rule:(1)gh1ff¯2+gh2ff¯2≃ghSMff¯2,gh1VV2+gh2VV2≃ghSMVV2, where f can be any of the SM fermions and V=W,Z vector boson. In fact, the branching ratios of the Higgs to SM particles are SMlike only if the Higgs invisible is very suppressed or kinematically forbidden as will be considered in our example. Consequently, the single Higgs production such as gluon–gluon fusion at LHC, Higgsstrahlung, Vector Boson Fusions, and tt¯H at LHC and e+e− Linear Colliders (LC) will obey the same sum rule. The summation of event numbers (both for production and decay) of the two possible cases will be identical to SM case since cos2θ+sin2θ=1. However, for processes with diHiggs final states (pp(e−e+)→hh+X), the triple Higgs couplings may play an important role, and therefore these processes can be useful to distinguish between the cases of one scalar or two degenerate ones around the observed 125 GeV resonance.It is well known that the triple Higgs couplings can be, in principle, measured directly at the LHC with high luminosity option through double Higgs production pp→gg→hh [6]. Such measurement is rather challenging at the LHC, and for this purpose several parton level analysis have been devoted to this process. It turns out that hh→bb¯γγ [7], hh→bb¯τ+τ− [7,8] and hh→bb¯W+W− [8,9] final states are very promising for High luminosity. Recently, CMS reported a preliminary result on the search for resonant diHiggs production in bb¯γγ channel [10].The LC has also the capability of measuring with better precision: the Higgs mass and some of the Higgs couplings together with the self coupling of the Higgs [11]. Using recoil technique for the Higgsstrahlung process, the Higgs mass can be measured with an accuracy of about 40 MeV [11]. We note that at LHC with high luminosity we can measure the Higgs mass with about 100 MeV uncertainty which is quite comparable to e+e− colliders. The triple Higgs coupling can be extracted from e+e−→Zh⁎→Zhh at 500 GeV and even better from e+e−→νν‾h⁎→νν‾hh at s>800 GeV. In this regard, the LHC and e+e− LC measurements are complementary [12].In Ref. [13], the authors have provided a tool to distinguish the twodegenerate states scenario from the single Higgs one. The approach of [13] applies only to models which enjoy modifications of h→γγ rate with respect to the SM. However, according to the latest experimental results, both for ATLAS and CMS the diphoton channel seem to be rather consistent with the SM [3,4]. In this work we propose a new approach to distinguish the TPS. This approach is based on the diHiggs production which is sensitive to the triple Higgs coupling, that is modified in the majority of SM extensions.Here, as an example, we consider, the TwoSinglets Model proposed in [14], where the SM is extended with two real scalar fields S0 and χ1; each one is odd under a discrete symmetry Z2(0) and Z2(1) respectively. The field χ1 has a nonvanishing vacuum expectation value, which breaks Z2(1) spontaneously, whereas, 〈S0〉=0; and hence, S0 is a dark matter candidate. Both fields are SM gauge singlets and hence can interact with the ‘visible’ particles only via the Higgs doublet H. The spontaneous breaking of the electroweak and the Z2(1) symmetries introduces the two vacuum expectation values υ and υ1 respectively. The physical Higgs h1 and h2, with masses m1 and m2≳m1, are related to the excitations of the neutral component of the SM Higgs doublet field, Re(H(0)), and the field χ1 through rotation with a mixing angle θ and, with a specific choice in the parameter space, could give rise to two degenerate scalars around 125 GeV. In what follows, we denote by c=cosθ and s=sinθ. The quartic and triple couplings of the physical fields hi are given in the appendices in [15].In our analysis we require that 11Actually, we considered that all quartic couplings to be of order unity; and the singlet vev υ1=〈χ1〉=20∼2000 GeV.: (i) all the dimensionless quartic couplings to be ≪4π for the theory to remain perturbative, (ii) the two scalar eigenmasses should be in agreement with recent measurements [3,4]: we have checked that for the TwoSinglets model, the splitting between m1 and m2 could be of the order of 40 MeV. (iii) the ground state stability to be ensured; and (iv) we allow the DM mass m0 to be as large as 1 TeV.In our work, we consider diHiggs production processes at the LHC and e+e− LC, whose values of the cross section could be significant, namely, σLHC(hh) and σLHC(hh+tt¯) at 14 TeV; σLC(hh+Z) at 500 GeV and σLC(hh+Emiss) at 1 TeV. All these processes include, at least, one Feynman diagram with triple Higgs coupling. For the TPS, the total cross section gets contributions from the final states h1h1, h1h2 and h2h2. Therefore the quantity to be compared with the standard scenario can be expressed as:(2)σTPS(hh+X)=σ(h1h1+X)+2σ(h1h2+X)+σ(h2h2+X), which can be parameterized as:(3)σTPS=σaar1+σabr2+σbb, with σaa+σab+σbb=σSM(hh+X) and σaa, σbb and σab correspond to the cross section contributions coming from triple Higgs diagrams (a), nontriple Higgs diagrams (b) and the interference term in the amplitude, respectively. The coefficients ri are dimensionless parameters, that receive contributions from the final states hihj, which depend on the mixing angle θ and the Higgs triple couplings λijk(3).In the TPS, the amplitudes for diHiggs production processes have SM Feynman diagrams where theHiggs field h is replaced by hi. To compute the parameters ri, we first estimate how does each amplitude get modified with respect to the corresponding SM one for each case hihj. For example, in the case of h1h1 production, there are two types of diagrams: (1) The ones that involve triple scalar interactions h1h1h1 and h2h1h1, with couplings equal to the one of a SM times a factor of cλ111(3)/λhhhSM and sλ112(3)/λhhhSM, respectively. We denote the total amplitude of these two contributions by M(a). (2) The ones with no triple Higgs couplings. Their amplitude, denoted by M(b), is given by the one of the SM scaled by a factor of c2. Therefore, the amplitudes M(a,b) (where a (b) stand for triple Higgs (nontriple Higgs) Feynman diagrams) for the diHiggs production can be written in terms of their corresponding SM values as:h1h1:M(a)=[(cλ111(3)+sλ112(3))/λhhhSM]M(a)SM,
M(b)=c2M(b)SM,

h2h2:M(a)=[(cλ122(3)+sλ222(3))/λhhhSM]M(a)SM,
M(b)=s2M(b)SM,

h1h2:M(a)=[(cλ112(3)+sλ122(3))/λhhhSM]M(a)SM,
M(b)=csM(b)SM,
where λhhhSM is the SM triple Higgs coupling calculated at oneloop. Then the parameters ri are given by:(4)r1={c2[λ111(3)2+λ122(3)2+2λ112(3)2]+s2[λ112(3)2+λ222(3)2+2λ122(3)2]+2cs[λ111(3)λ112(3)+2λ112(3)λ122(3)+λ122(3)λ222(3)]}/(λhhhSM)2,r2={c3λ111(3)+3c2sλ112(3)+3cs2λ122(3)+s3λ222(3)}/λhhhSM. Thus, the values of ri quantify by how much each diHiggs process deviates from the SM case. In Fig. 1, we show the parameters ri as a function of sinθ for about 600 chosen sets of the model parameters within the condition (1). We see that for very small mixing angle ri's are approximately equal to unity, while for sinθ>0.8 and sinθ<−0.2, the parameter r1 becomes larger than unity and r2 acquires negative values. This behavior could lead to an enhancement/reduction to the cross section depending on the sign of the interference contribution, σab, to the total cross section. This means that the measurement of the following ratio:(5)ξ(hh+X)=σTPS(pp(e−e+)→hh+X)σSM(pp(e−e+)→hh+X), could be very useful to confirm or exclude this scenario based on the deviation of any of the parameters ri from unity. For instance, the ratio ξ(hh+X) can deviate from unity if the SM is extended with massive particles (SM+MP) that couple to the Higgs doublet and contribute to the triple Higgs coupling as well the Higgs mass. In this case, r1=(1+Δ)2 and r2=1+Δ, where Δ represents the relative enhancement of the triple Higgs coupling due to SM+MP. As we will show later, our considered scenario for small or large mixing could be distinguished from the case of SM+MP by combining the ratio (5) for different processes.In Table 1, we give the values of σaa, σab and σbb for the corresponding diHiggs production processes. We note that their contributions to the LHC process pp→hh and to the LC one e+e−→Zhh seem to be uncorrelated, which makes the Higgs triple coupling useful to probe this scenario and distinguish it from (SM+MP).For the benchmarks considered previously in Fig. 1, we illustrate in Fig. 2 the production cross section of diHiggs at e+e− LC and LHC and in Fig. 3 the ratio ξ. As it can be seen, in the TPS, the cross section of the processes pp→hh, pp→hh+tt¯ and e−e+→hh+Emiss are mostly enhanced, while for e−e+→hh+Z it is enhanced just for the mixing values 0.5<sinθ<0.8.Now let us discuss the possibility of disentangling the TPS from the SM+MP. It is clear from Fig. 3 that for both LHC and LC processes with large mixing, 0.35<cos2θ<0.65, the TPS may coincide with SM+MP. However, for nonmaximal mixing values the TPS is clearly different than SM+MP where all benchmarks have the following feature(6)ξ1TPS+ξ2TPS>ξ1SM+MP(Δ)+ξ2SM+MP(Δ), where ξiTPS the ratio in (5) for any LHC or LC processes and ξiSM+MP(Δ) is the same ratio due the existence of massive particles. Therefore, when measuring the quantities (5) for both the LHC and e+e− LC processes, and one finds that the criterion (6) is not fulfilled, then it is a certain exclusion for this scenario. In case where the criterion (6) is fulfilled, detailed analysis is required for in order to identify the mixing angle, the parameters ri and therefore the Higgs triple couplings. In fact, by studying all the diHiggs production channels at both LHC and e+e− LC one not only confirm/exclude this scenario, but also distinguished it from models where only one type of processes gets modified by new physics such as: it manifests as new sources of missing energy in e−e+→hh+Emiss [17], new colored scalar singlets contribution to pp→hh (or hh+tt¯) [18], or the presence of a heavy resonant Higgs [19].In order to show whether this scenario can be tested at colliders, we consider three benchmarks that may be distinguished from SM+MP (i.e., three red points from Fig. 3), and compare the diHiggs distribution (of the diHiggs invariant mass as an example) with the SM one. The corresponding values of ratios ri and ξi are given in Table 2, and in Table 3, we present the expected number of events at both the LHC and LC. We see that for benchmark B2, the events number is significantly larger than the SM for the channels pp→2b2τ at the LHC and e−e+→4b+Emiss at LC's, while it is reduced for the processes pp→4b+tt¯ and e−e+→4b+Z. For benchmark B1, the events number of the processes pp→2b2τ and e−e+→4b+Emiss is SMlike but it is reduced for the processes pp→4b+tt¯ and e−e+→4b+Z. For benchmark B3, the events number is reduced for the considered processes.In Fig. 4, we illustrate the diHiggs invariant mass distribution (Mh,h) for the process e−e+→hh+Emiss. Clearly, the TPS can be easily distinguished from the SM, especially in the case of nonmaximal mixing. However, the full confirmation of the TPS requires the enlargement of the investigation by taking into account other diHiggs production channels such as hhjj, hhW±, hhZ and hhtj at the LHC [20] and the e+e− LC [11].In conclusion, we have investigated the case of twinpeak at the 125 GeV observed scalar resonance by considering different diHiggs production processes at both LHC and e+e− LC. We have introduced a criterion whose violation excludes the TPS scenario, otherwise this scenario can be surely distinguished from the SM and SM extended by massive fields in case of nonmaximal mixing.Last but not least, we should note that this scenario could be realized within SM+(real/complex) singlet scalar, or any larger scalar field content. This includes neutral or charged scalars that are members any multiplets, where two degenerate scalar eigenstates h1,2 at 125 GeV, do couple to the SM gauge fields and fermions by more than ∼90%, i.e., the sum rule (1) is fulfilled.22In the 2HDM, twin pick scenario has been studied in [21], but the study concentrated only on the diphoton channel. According to this study [21], this scenario is not ruled out. If the measurement of diHiggs processes at LHC and/or e+e− LC turn out to be consistent with SM predictions, then it will be very challenging to distinguish the TPS scenario.If the measurement of the couplings hff¯ and hVV become much more precise from the future experiment data, it may be possible that one could be sensitive to the radiative corrections effect to these couplings. Such radiative corrections to hff¯ and hVV couplings in a variety of extended Higgs sector have been evaluated in [22–24]. 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