On the impact of the LHC Run2 data on general Composite Higgs scenarios
PPrepared for submission to JHEP
On the impact of the LHC Run2 data on generalComposite Higgs scenarios
Charanjit K. Khosa a and Veronica Sanz b,c a Dipartimento di Fisica, Università di Genova and INFN, Sezione di Genova,Via Dodecaneso 33, 16146, Italy b Department of Physics and Astronomy, University of Sussex,BN1 9QH Brighton, UK c Instituto de Física Corpuscular (IFIC), Universidad de Valencia-CSIC,E-46980, Valencia, Spain
E-mail: [email protected] , [email protected] Abstract:
We study the the impact of Run2 LHC data on general Composite Higgs sce-narios, where non-linear effects, mixing with additional scalars and new fermionic degrees offreedom could simultaneously contribute to the modification of Higgs properties. We obtainnew experimental limits on the scale of compositeness, the mixing with singlets and doubletswith the Higgs, and the mass and mixing angle of top-partners. We also show that for sce-narios where new fermionic degrees of freedom are involved in electroweak symmetry break-ing, there is an interesting interplay among Higgs coupling measurements, boosted Higgsproperties, SMEFT global analyses, and direct searches for single- and double-productionof vector-like quarks. a r X i v : . [ h e p - ph ] F e b ontents The true origin of the Higgs mechanism is still an open question in Particle Physics, despitethe discovery of its key element, the Higgs particle [1, 2], and the observation of the SM-likenature of its couplings to massive particles [3].The main reason to doubt a purely SM Higgs sector can be traced back its quantumbehaviour, a problem often expressed in the context of naturalness : how can a fundamentalscalar be so light, yet so sensitive to UV effects. And this is not the only suspicious aspect ofthe SM Higgs. The hierarchy among its Yukawa couplings, or its inability to produce enoughbaryon asymmetry during the electroweak phase transition also add to the unsatisfactoryaspects of the SM Higgs sector.However, these shortcomings also open opportunities for new physics. The Higgs, due toits scalar nature, could connect to other sectors via mixing with scalars, participate in phasetransitions and inflation. Among the theories bringing the Higgs into a new framework,one particularly appealing proposal is the concept of compositeness, leading to CompositeHiggs Models (CHMs). In CHMs, the Higgs is not a truly fundamental particle but a boundstate of other, more fundamental, particles.Primitive proposals for a Composite Higgs [4] were replaced by more realistic realisa-tions based on the idea that a Higgs is not just any composite state from strong dynamics,but a pseudo-Goldstone boson [5]. Pseudo-Goldstone bosons appear when approximateglobal symmetries are spontaneously broken. The size of the symmetry and what it breaksdown to determines the amount of scalar degrees of freedom one will have in CHMs. Thepartial gauging of some of these global symmetries sets what kinds of quantum numbers– 1 –easurement Reference
Higgs Measurements
Run 1 ATLAS and CMS combined Higgs signal strength measurements [7]Run 2 ATLAS Higgs signal strength measurements [8, 9]Run 2 CMS Higgs signal strength measurements [10–15]ATLAS Higgs+jet differential measurement [16]
LHC direct searches for VLQ
ATLAS T → Wb channel [17]ATLAS T → top+MET channel [18]CMS T → Wb channel [19]CMS T → Zt final state [20]
Table 1 . Experimental measurements considered in this work. the scalars have. The minimal framework to achieve successful Electroweak SymmetryBreaking (EWSB), i.e. leading to a Higgs doublet of SU (2) L with a m h ∼ v , was foundin Ref. [4]. In this setup, the Higgs originated from the breaking SO (5) → SO (4) , and itsradiative potential had to be supplemented with a new vector-like fermion with the samequantum numbers as the top, called top-partner and denoted by T . This minimal set-upand its phenomenological consequences has been thoroughly explored in the literature, seee.g. Ref. [6] for a review.Typically one would assume the main manifestation of the composite nature of theHiggs would be the non-linear origin of its couplings, leading to very specific types of Higgscoupling deviations. Yet Composite Higgs scenarios could exhibit a richer phenomenology,such as the presence of new scalars or fermions which would also modify the Higgs properties.The focus of this paper is the study of the rich patterns which arise in general CompositeHiggs scenarios and what the Run2 LHC data can tell us about them. The data we willuse for this analysis is summarised in Table 1.The paper is organised as follows. In section 2, we describe the different patternsarising in Composite Higgs scenarios: non-linear effects (Sec. 2.1), extended scalar sectors(Sec. 2.2) and new fermionic degrees of freedom (Sec. 2.3). In these section we examine theimpact that Higgs measurements and direct top-partner searches have on these patternsand in combinations of them, e.g. how non-linearities and mixing with new scalars docontribute on the same direction to reduce Higgs couplings to massive particles. Hence, asone switches on more than one of these effects, each individual limit becomes stronger. Thelast Section 3 is devoted to conclusions. The idea of the Higgs as a composite state could be realised in many ways. Consideringtheoretical constraints and precision measurements substantially reduces the possible sce-– 2 – omposite Higgs scenariosMore scalars singlets/doublets non-standard Higgs Fermionic Top-partners
Higgs inclusive cross-sections Higgs differential cross-sections Single and double VLQ searches N on - m i n i m a l c o s e t e m b e dd i ng s Non-linear realisation of EWSB s u cce s f u l E W S B Figure 1 . Different realisations of composite Higgs scenario and the relevant experimental mea-surements. narios, yet there are still many possibilities to contemplate. Nevertheless, one can describemodern Composite Higgs scenarios as exhibiting one or more of the following patterns:1. A Composite Higgs sector would be able to trigger Electroweak Symmetry in a non-linear fashion. This leads to new possibilities for the light Higgs boson. Its couplings,and even quantum numbers, could be different from the SM expectation. Indeed, inthe SM the Higgs is a SU (2) L -doublet, and the way it induces EWSB completelydetermines how it couples to fermions and bosons, including couplings to more thanone Higgs. On the other hand, in CHMs these couplings would be more general, evenopening the possibility of a SU (2) L singlet Higgs [21]. This additional freedom leadsto the expectation that the SM-like Higgs, the 125 GeV state observed by the CERNcollaborations, should exhibit non-standard interactions. We will discuss this firstComposite Higgs pattern in Sec. 2.1.2. The second set of patterns found in CHMs refers to the origin of the CompositeHiggs in the spontaneous breaking of an approximate global symmetry. This breakingcould lead to just the right amount of degrees of freedom to match one single lightHiggs particle and the three missing polarisations of the W ± and Z bosons. Butmore generically, this breaking would lead to new scalar degrees of freedom which,after partially gauging the global symmetry, could be identified as SU (2) L singlets,doublets, or even higher representations. These non-minimal coset embeddings wouldlead to additional degrees of freedom which could also develop their own potential,– 3 –articipate in EWSB, and typically mix with the SM-like Higgs. These additionalscalars would be typically required to be heavier than the Higgs, and their effectscould appear at leading-order at tree-level in the effective theory via e.g., mixing withthe SM-like Higgs. The study of the Run2 limits on these extensions of the SM scalarsector can be found on Sec . 2.2.3. The third set of patterns found in CHMs refers to the presence of new, fermionic de-grees of freedom which would assist the SM-like Higgs in its job of triggering EWSB.These fermions, often called top-partners, should be relatively light to efficiently mod-ify the Higgs potential. They can be searched for directly, via their production at theLHC through couplings to the strong or electroweak sector, or indirectly, as theymodify the Higgs properties. The discussion on direct and indirect searches for top-partners will be developed in Sec 2.3.4. In each section we also discuss situations where more than one dominant patterncould be at play in the LHC measurements. We will explain how in this case, theireffect in the Higgs couplings would go in the same direction, ruling out cancellationswhich could invalidate the limits from the previous sections.These patterns are summarised in Fig. 1. In CHM one assumes the existence of a global symmetry G , spontaneously broken to asmaller subgroup H . The Higgs particle and the would-be Goldstone bosons for the W ± and Z originate from this breaking. Part of H is then weakly gauged to provide the Higgsand massive gauge bosons with the correct properties under the SM.To go beyond the SM structure of EWSB, it is useful to follow the Callan, Coleman,Wess and Zumino prescription [22]. Within this prescription, one aims to build objectswith definite transformation properties under SU (2) × U (1) . In CHMs the object thatcontains the Goldstones from the global breaking G → H is Σ = exp iφ a X a /f , where φ a are the Goldstones, X a generators in the coset G / H and f is the scale associated withthe spontaneous breaking. At low energies, below f , one can write an effective Lagrangianinvolving Σ L eff kinetic = f D µ Σ † D µ Σ] , (2.1)which, after making a choice for weakly gauging H , determines the Higgs and vector bosoninteractions. Assuming the Higgs is a doublet of SU (2) L , similarly as in the SM, thestructure that arises from this kinetic term is g f sin (cid:18) hf (cid:19) . (2.2)One could also allow the Higgs to be a singlet under SU (2) L , but that would lead to theneed to impose a tuning in the effective Lagrangian to explain the specific relations betweenthe Z and W masses [23, 24]. We will not follow this path in this paper, and embed the– 4 –HM global symmetry structure in a way that preserves the custodial symmetry presentin the SM.Expanding around the physical Higgs boson vacuum expectation value (VEV), onefinds clear predictions of the structure of the Higgs-vector boson couplings κ V = g CHV V h g SMV V h = (cid:112) − ξ ≈ − ξ , (2.3)where ξ = v /f .Turning now to the Higgs-fermion couplings, we note that the predictions are notunique. In particular, the fermion mass generation mechanism in CHMs usually relies onthe concept of partial compositeness [23, 25], i.e. the idea that SM fermions feel EWSBvia mixing with fermionic bound states. To build structures leading to fermion couplingsto the Higgs, one needs to specify the embedding of the fermionic degrees of freedom inthe global symmetry structure G . As an example, in the minimal composite Higgs models,based on SO (5) /SO (4) coset group, Σ will transform as 5-plet of SO (5) which could forma SO (5) invariant either with two 5-plets or pair of 5 and 10-plets.More general CHMs lead to very different patterns of breaking and types of embeddingsfor the fermion content of the model. Yes, despite spanning many model building options,it was noted in Ref. [26] that the Yukawa couplings usually fall into two choices, κ AF = (cid:112) − ξ ≈ − ξ, (2.4)and κ BF = 1 − ξ √ − ξ ≈ − ξ. (2.5)For example, the models based on coset groups SO (5) /SO (4) [27, 28], SO (6) /SO (4) × SO (2) [29–31], SU (5) /SU (4) [32], SO (8) /SO (7) [33, 34] have fermions-Higgs couplingsmodified by κ AF . On the other hand, κ BF -type couplings could exist in SO (5) /SO (4) [28, 35–37], SU (4) /Sp (4) [38], SU (5) /SO (5) [39], SO (6) /SO (4) × SO (2) [29–31] groups basedmodels. In all these models the Higgs doublet lies within the unbroken subgroup, but insome of those there could be an extra singlet or Higgs doublet.A Composite Higgs, with non-standard couplings to massive fermions and bosons,would also exhibit non-standard loop-level couplings to gluons and photons ( κ g,γ ) [7, 40] κ g = 1 . κ t + 0 . κ b − . κ b κ t (2.6) κ γ = 1 . κ V + 0 . κ t − . κ V κ t , (2.7)as well as deviations on the Higgs width ( κ H ) κ H ≈ . κ b + 0 . κ V + 0 . κ g . (2.8)Note that κ t , κ b do not have to be equal (see Eqs. 2.4 and 2.5) depending on howfermions are embedded within the global symmetry group.– 5 –
00 600 800 1000 1200 14000246810 ( GeV ) χ - χ m i n LHC Run1 + ABB f min BAA
Figure 2 . ∆ χ = χ ( f ) − χ min for the combination of Run 1 and 2 LHC data (signal strengthmeasurements). The different grey lines correspond to different choices of fermion couplings κ A,BF for ( κ t , κ b , κ τ ) . The vertical line is the lowest allowed value (95 % C.L.) of the compositeness scale( f min ) within a model where fermion couplings are of the ABB type i.e. top quark have κ A , bottomand tau have κ B factor with the Higgs couplings. Green and yellow are the 1 σ and 2 σ regions,respectively. Putting all this together, we are ready to compare measurements of the Higgs proper-ties with expectations from a non-linear realisation of EWSB via a Composite Higgs. Theexperimental inputs, described in Appendix A, are Higgs signal strengths for different pro-duction and decay channels. We compare these measurements with theoretical predictionsas a function of the κ modifiers κ f , κ V , κ g , κ γ , and κ H . For example, for the gluon fusion ggH ( H → γγ ) channel, it adopts the form: µ CH = κ g κ γ κ H . To compare the CHM predictionswith Higgs signal strength measurements from CMS and ATLAS experiments, we evaluatethe χ statistic test χ ( f ) = Run ,Run (cid:88) i (cid:32) µ i ( κ ( f )) CH − µ Expi ∆ µ i (cid:33) . (2.9)Here µ ( κ ( f )) CH , µ Exp and ∆ µ denote the model prediction of the signal strength, ex-perimental measurement, and error for the experimental measurement, respectively. Theindex i runs over all the measurements from Run 1 and Run 2. Note that the correlationsamong the different experimental measurements are not considered as they are subdominantrespect to the model uncertainties introduced by the choices of κ F .In this section we only focus on non-linear effects, hence the rates µ ( κ ( f )) CH are– 6 –ensitive to one parameter, the ξ = v /f ratio, and choices for the fermion couplings fromEqs. 2.4 and 2.5.In Figure 2, we show the χ fit of different choices for κ F to the combined LHC Run1 and Run 2 data. Run 1 data is taken from the combined CMS and ATLAS analysis [7].For Run 2 data, individual measurements from CMS [10–15] (see table 3) and ATLAS [8, 9](see table 4) are considered. For H → b ¯ b decay channel, both CMS and ATLAS havecombined Run 1 and Run 2 data measurements so we have not considered the single Run1 measurements.In Figure 2 we show the 1- and 2-sigma limits on χ − χ min in green and yellow,respectively. The values of ∆ χ depend on whether the top, bottom and tau κ modifiersare of type A or B . Following Ref. [26], we plot all the lines with all combinations anddenote which combination is less constrained (ABB) and which one is constrained morestrongly by LHC data, BAA. Comparing with Ref. [26], we obtain a stronger lower boundon the scale of compositeness of f min =
780 GeV. The different curves highlight the factthat there is roughly 500 GeV variation in the f min scale, reaching f min ∼ . TeV for themost tightly bound scenario.
When the group G breaks down to H , light degrees of freedom are generated. Only in specificconfigurations one would expect exactly four Goldstones, to match the SM needs. Hencegeneric Composite Higgs scenarios would typically exhibit a pattern of Extended HiggsSectors, with more light scalars involved in EWSB . In the simplest of such extensions, onewould consider an additional singlet, see e.g. [41], which could mix with the SM-like Higgsdoublet. The next simplest iteration would introduce new doublets, as is the case in e.g.the coset group SO (6) /SO (4) × SO (2) [31], where the light degrees of freedom organise asa Two-Higgs Doublet Model (2HDMs) [42].Doublets and singlets are not the only model-building possibilities which CompositeHiggs models offer, e.g. on the SU (6) /SO (6) coset one has two Higgs doublets but also acustodial bi-triplet [43]. Generically speaking, a Composite Higgs scenario leading to onesingle doublet at low-energies is minimal but not typical, and one should consider the effectof more scalars involved in EWSB.Moreover, this pattern opens new, interesting possibilities for model building beyondEWSB. These extra singlet or doublet pseudo-Goldstones could play a role in Inflation [44]or act as Dark Matter candidates [43]. In Composite Higgs scenarios, these new scalars couldhelp on enhancing the strength of the electroweak phase transition [45] by introducing newsources of CP violation and more interesting phase diagram structures, and even play somerole in the QCD CP problem [46].In this section, we explore what the Run2 LHC data can tell us about these extensions.We will discuss the modification of the gauge boson and fermions couplings to the SM-likeHiggs boson when the additional scalars mix with the SM-like Higgs. Their effect couldalso be felt at loop-level, even in the absence of a mixing, but these contributions would besuppressed by loop factors respect to mixing. Both possibilities, mixing and loop effects,– 7 –ere computed and explored in Ref. [47] and here we make use of these theoretical calcu-lations and update the limits in the context of CHMs and the possible interplay betweenmixing and non-linearities. The presence of an extra singlet modifies the κ F/V by a factor of cos θ S , where θ S denotesthe mixing angle between the neutral scalar h and the extra singlet scalar field. This effectis simply due to linear mixing terms when both the singlet and the SM-like Higgs get theirVEVs. Non-linearities due to the origin of the SM-like Higgs as a Composite Higgs wouldstill be present, in exactly the same way we discussed in Sec. 2.1 . Therefore, the Higgscouplings to vector bosons would be doubly modified as κ V = cos θ S (cid:112) − ξ ≈ − ξ − θ S , (2.10)where we have expanded for small values of non-linearities and mixing to show how thesetwo effects work in the same direction, i.e. to reduce the coupling value from the SMexpectation.The non-linear part of the modification of the fermion couplings depends on the fermionembedding in representations of the global symmetry. As discussed before, we find two mainchoices for κ F , namely κ AF = cos θ S (cid:112) − ξ ≈ − ξ − θ S (2.11)or κ BF = cos θ S − ξ √ − ξ ≈ − ξ − θ S , (2.12)where again we expand for small modifications ξ and θ S to show explicitly the cooperativeeffort of both effects to lower the coupling.We perform the fit to the Higgs data as in Sec. 2.1 but now including the effect ofmixing, χ ( f, θ S ) . As shown in Figure 2, we vary options for the fermion couplings and findthe f min . We perform this fit for different values of the mixing angle, always finding theminimum f corresponding to a set of options for κ F . The result of this procedure is shownin Figure 3, where we plot ξ max = v /f min scale as a function of the singlet mixing. Onthe right side of the plot we see the effect of small mixing, where we recover the result fromthe previous section. As we move towards the left in the plot, the mixing becomes moreimportant and at some point ξ max → , we obtain the pure mixing limit of | cos θ S | (cid:39) m S ), singlet vev ( v S ) andquadratic coupling of light Higgs doublet and singlet scalar ( λ ), as given below cos θ S = cos (cid:32) v ( m effS ) (cid:33) ; m effS = m S (cid:112) λ ( v S /v ) (2.13)where v = 246 GeV. Therefore, the limit | cos θ S | (cid:39) m effS (cid:38) One could consider situations where the additional singlets or doublets do participate directly in themechanism for EWSB, as shown in the see-saw Composite Higgs [48], where this assumption would fail. – 8 – .96 0.97 0.98 0.99 1.000.000.020.040.060.080.100.12 | cos θ S | ξ m ax Singlet Mixing and Non - linearity Figure 3 . The bound on the ξ max as a function of cos θ S in case of singlet mixing scenario for theABB type model. Model κ V κ F Type − I s β − α κ u = κ d = κ (cid:96) = c β − α /t β + s β − α Type − II s β − α κ u = c β − α /t β + s β − α κ d = κ (cid:96) = s β − α − t β c β − α (cid:96) − Specific s β − α κ u = κ d = c β − α /t β + s β − α κ (cid:96) = s β − α − t β c β − α Flipped s β − α κ u = κ (cid:96) = c β − α /t β + s β − α κ d = s β − α − t β c β − α Table 2 . The κ V and κ F expressions in Two Higgs doublet models. Here s x /c x /t x =sin x/ cos x/ tan x . In between these two asymptotic limits, the constraints on the scales f and m effS become stronger, as both mixing and non-linearities work together to reduce the Higgscouplings. As discussed in the previous section, the mixing effect due the additional Higgses in aComposite Higgs model does not typically couple with the non-linear effects at leadingorder. Hence, in composite two Higgs doublet models the vector and femion couplings tothe Higgs, κ V/f , would still adopt this factorisable form κ HDMV/F × κ CHV/F , where κ CHV/F hasbeen discussed in Sec. 2.1 and κ HDMV/F correspond to the modifications of the SM-like Higgscouplings in 2HDM models.The explicit form of κ HDMV/F is given in Table 2 for various types of 2HDM models. Inthese scenarios, vector and fermion modifiers are determined by two parameters, the ratio– 9 – - cos ( β - α ) t an β - - cos ( β - α ) t an β Figure 4 . The 68 % (green), 95 % (yellow) and 98 % (red) C.L. limits in the cos( β − α ) − tan β planefor 2HDM Type I (left plot) and Type II (right plot) with ξ = 0 . - - cos ( β - α ) t an β Type I 2HDM vs Non - linearity - - ξ c o s ( β - α ) Type I 2HDM vs Non - linearity Figure 5 . Type I 2HDM results.
Left plot:
The 95 % C.L. limit including non-linear effects. Theblack, red and green lines correspond to choices of the parameter ξ = 0 , 0.05 and 0.07, respectively. Right plot:
The 68 % (green), 95 % (yellow) and 98 % (red) C.L. limits in the ξ - c β − α plane for tan β = 6 . of symmetry breaking VEVs of Higgs doublets ( tan β ) and neutral Higgs mixing angle ( α ).In our analysis, we only consider the main scenarios, Type I and Type II. The χ CHM statistical test for a Composite Higgs with possible mixing with another doublet becomesa function of three parameters: f, cos( β − α ) , and tan β .First we discuss the information that Run2 LHC data provides on type I and II 2HDMs,– 10 –ithout considering the non-linear effects. This information is shown in Figure 4, wherethe coloured regions green, yellow and red represent 68 % , 95 % and 98 % C.L. limits inthe cos( β − α ) − tan β plane, respectively. As expected, the SM-like Higgs prefers a regionwith cos β − α (cid:39)
0, the alignment limit [49].The alignment limit can be understood in terms of the potential parameters in the2HDM, couplings between the two doublets ˜ λ i and masses ˜ µ , , see Ref. [47] for more details.In terms of these parameters, the deviation from the alignment limit can be parametrisedas cos β − α ∼ λ v / ˜ µ .Next we introduce the additional non-linear effects in the left panel in Figure 5, wherewe show how the 95 % C.L. regions are modified with non-linear effects. The non-lineareffects, as in the case of the singlet add up to the doublet mixing. Larger non-linearitiesrestrict further the parameter space of 2HDMs.Finally, as the tan β dependence is rather mild for tan β (cid:38)
2, we fix the value of tan β = cos β − α and ξ . In the right panel of Figure 5, we plotthe one-, two- and three- σ contours in this plane. In the alignment limit, cos β − α (cid:39) ξ (cid:39) . at 95%C.L.. As we move from the alignmentlimit, and allow a larger amount of doublet mixing, the limit on ξ becomes milder, leadingto a stronger bound on the compositeness scale f . On the left side of the plot where ξ →
0, we find the limit on non-decoupling effects cos β − α (cid:39) ˜ µ ∼
500 GeV for ˜ λ ∼ O (1) . We finish this section on patterns, analysing a typical building block in Composite Higgsscenarios: the presence of new fermionic degrees of freedom, not too far from the electroweakscale. These fermionic degrees of freedom are usually coming along as top partners, newvector-like fermions which mix with the SM top quark and modify its couplings with theHiggs.We first focus on the mixing, and present results for the SU (2) L -singlet top partnerscenario T L,R . We calculate the indirect bound on these states from measurements onthe differential distributions of the the boosted Higgs in association with an energetic jet.The methodology used here was developed in Ref. [50] and further expanded in Refs. [51]and [52]. We will then evaluate other sources of experimental constraints, including directsearches for the new state.To describe the effect of the top-partner in the Higgs behaviour we need to specify themixing parameters between the top-partner and the SM top quark. For the singlet case,the mass matrix of the SM top quark and Dirac fermion top partner T = ( T L , T R ) can bewritten as (cid:16) ¯ t L ¯ T L (cid:17) (cid:32) y t h √ ∆0 M (cid:33) (cid:32) t R T R (cid:33) , (2.14)where ∆ describes the mixing between t and T , and M is the Dirac mass of the top partner.After diagonalising this matrix by a bi-unitary transformation, we can calculate the mass– 11 –igenstates M T and m t and the mixing angle θ R = 12 sin − (cid:18) m t M T ∆( M T − m t ) M (cid:19) . (2.15)Note that θ R and θ L are related in a simple way, tan θ L = M T m t tan θ R . (2.16) Contrary to the previous sections, total Higgs rates and their respective limits on vectorand fermion couplings κ V/F would not be sensitive to the presence of the top partner.On the other hand, high- p T probes would access the top partner mixing and mass scaleindirectly [50, 51].To analyse the effect of T in the Higgs production in association with radiation, itis useful to define a quantity which depends on M T and θ R based on semi-differentialmeasurements, σ ( p T > p cutT ) = (cid:90) ∞ p cutT dp T dσdp T . (2.17)In particular, we define a quantity based on these differential measurements, δ ( p cutT , M t , sin θ R ) = σ t + T ( p cutT , M T , sin θ R ) − σ t ( p cutT ) σ t ( p cutT ) , (2.18)which exhibits good properties from the point of view of systematic and statistical fluctu-ations, see Ref. [50] for more details.With this observable as an indirect probe for fermionic top-partners, we calculated σ t and σ t + T for √ s =
13 TeV by varying M T and sin θ R . The results can be seen in Figure 6,where we plot the relative change in the Higgs+jet cross-section as a function of p cutT fordifferent combinations of the mixing angle and M T . For this plot, M T is varied from 500GeV to 1500 GeV, and one can see that δ has a weak dependence on M T . We can thenuse the experimental measurements in this channel to put a bound on the mixing angle. Inparticular, we used the ATLAS Higgs differential cross-section analysis [16], which reportsan 8 % deviation at 95 % C.L. in the 250-350 GeV (diphoton) p T bin from the SM cross-section. We can then look back at our Fig. 6 and note the variation of δ as a function of sin θ R for p cutT =250 GeV.In Fig. 7 we show the variation of δ as a function of sin θ R for a fixed p cutT = 250 GeV.The green band corresponds to varying M T from 500 GeV to 1500 GeV. The 8% limit isnoted with a hashed black line, which allows us to set a limit on sin θ R (cid:46) . .Another source of constraints from a singlet VLQ top-partner would come from a SMEffective Field Theory (SMEFT) global analysis of Run2 LHC and LEP measurements.The singlet top-partner would produce a SMEFT pattern characterised by relations amongsome SMEFT operators, whereas all the other operators would be zero at tree-level, seeRef. [53] for a dictionary between many extensions of the SM and their SMEFT matching.– 12 –
00 200 300 cut (GeV)
T,j p0102030 ( % ) d = 0.5 R q sin = 0.4 R q sin = 0.3 R q sin = 0.2 R q sin = 0.1 R q sin=500 GeV T M =700 GeV T M =900 GeV T M =1100 GeV T M =1300 GeV T M =1500 GeV T M Figure 6 . Percentage enhancement in the Higgs + jet cross-section by the top partner contributionas a function of p cutT for different values of mixing angle and M T . θ R δ ( % ) M T : 500 - p T cut =
250 GeV
Figure 7 . Percentage enhancement in the Higgs+jet cross-section by the top partner contribution( δ ) as a function of the top-partner mixing angle for p cutT =250 GeV. The horizontal hashed linecorresponds to the experimental bound [16], and the band width to the variation in M T ∈ [500,1500]GeV. See also the discussion in Ref. [54] on the top-partners and the SMEFT framework. Usingthis dictionary and a global SMEFT analysis, in Ref. [55] the parameters of the singlettop-partner were bound to sin θ L (cid:46) . for M T (cid:39)
00 800 1000 1200 1400 1600 M T (GeV) | s i n L | Top Partner Limits: SMEFT, EW and QCD Couplings
SMEFT (T VLQ)TTHiggs+jet t + MET(ATLAS)Wb(ATLAS)Zt(CMS)Wb(CMS) Figure 8 . Direct searches bounds on singlet top-partners from single and double production ofVLQs, and indirect bounds from the Higgs+jet final state. Blue, orange, green and violet curvescorrespond to the ATLAS single VLQ bound from
W b channel [17], ATLAS bound from top+METfinal state [18], CMS
W b final state [19] and CMS Zt final state [20], respectively. The vertical linecorresponds to the ATLAS pair production bound [56]. The SMEFT bound is taken from Ref. [55]and the red line indicates the limit from Higgs+jet differential distributions discussed in Sec. 2.3.1. Boosted Higgs measurements provide one handle on top-partners. The LHC New Physicssearch programme includes very mature analyses looking for single and pair production ofVector-Like Quarks (VLQ). Pair production of VLQs is a dominantly strong interactionprocess, whereas single production relies on electroweak couplings.A singlet up-type VLQ (T) is excluded up to 1.31 TeV by the ATLAS √ s = 13 TeV(36.1 fb − ) search for pair produced VLQs [56] after considering all decay modes. Thislimit is a combined limit from several searches for the pair production of VLQs.From the CMS side, there are separate limits from each analysis of pair production ofVLQs. The exclusion limit on singlet T from dilepton final state of VLQs decaying to Zboson is 1280 GeV [57]. The CMS analysis for all leptonic final states excludes M T in therange 1140-1300 GeV corresponding to different branching fractions [58], and the analysisof the bW ¯ bW final state excludes singlet T up to 1295 GeV [59]. The analysis targetingfully hadronic final states provides a bound up to 1.3 TeV for a specific combination of thebranching fractions of VLQs [60].The single VLQs production process is mediated by its coupling with SM particles,hence it provides a bound on the mixing as a function of the mass of VLQs [17–19]. Boththe production cross-section and decay branching ratios are sensitive to mixing effects. Thecommunication of the single-production results is a bit more cumbersome than for double-– 14 –roduction. In some analyses, this mixing is directly parametrised by the mixing angle( sin θ L,R ) and sometimes by the coupling c bw where c bwL/R = √ | sin θ L/R | [61] is just a re-scaling of the mixing angle. ATLAS analysis cross-section limits are interpreted in termsof either | sin θ L | , or both C W = ( c bwL ) + ( c bwR ) and | sin θ L | . On the other hand, CMSexclusion limits on production cross-section times branching fraction are provided only as afunction of m V LQ . Additionally, the theoretical cross-section is provided for the fixed valueof BR and c bw = 0 . . We use this additional information to calculate the approximatebound on c bw as a function of m V LQ .We translate CMS bound in terms of mixing angle | sin θ L | by parametrizing the pro-duction cross-section as σ ( T ) × BR ( T → bW ) = ˜ σ ( T ) c bw × BR ( T → bW ) , where ˜ σ ( T ) is calculated from the theoretical cross-section with fixed c bw . Then using the bound oncross-section (including BR), we calculate the limit on c bw which we further translate to | sin θ L | using the relation c bwL/R = √ | sin θ L/R | . Note that we have not considered the effectof C W variation on the width of T . We also consider other decay channels of the singletvector-like top to ht and Zt . Note that CMS analyses for W b [19] and Zt [20] final statesdo assume 100 % branching ratio, and the ATLAS collaboration has considered W b andtop +MET final states [18] assuming BR( T → Zt ) = 0 . from the singlet model.In Figure 8 we show all these direct and indirect limits together in the plane of top-partner mass versus mixing angle. Double production of VLQs (dark-green vertical line)sets a limit on the mass M T (cid:38) M T (cid:62) v . The currentsensitivity of the other indirect probe for top-partners, the H +jet channel, is below theSMEFT fit, although it is worth noticing that our H +jet analysis is not at the same levelof sophistication as the SMEFT’s [55]. Note that for the ATLAS top+MET analysis (blackline) the | sin θ L | values covered by the closed contour are excluded. In this work we have studied the impact of the LHC Run 2 measurements on generalComposite Higgs scenarios.The dataset we used includes Higgs signal strength measurements from CMS and AT-LAS, differential properties of boosted Higgs production, several searches for single- anddouble-production of vector-like quarks, and a specific result from a global fit to SMEFTproperties obtained in Ref. [55].We have described the most significant deviations expected from Composite Higgs sce-narios, going from the simplest effects, non-linear couplings, to the most complex interplaybetween direct and indirect searches for additional fermionic degrees of freedom.We have shown how in general Composite Higgs scenarios one should expect simulta-neous effects from more than one source. Typically, the composite nature of the Higgs istied to the non-linear realisation of EWSB and the scale of compositeness f . But genericComposite Higgs scenarios exhibit a richer phenomenology, in particular new light scalarsor fermions are also typical predictions of these scenarios.– 15 –hese new degrees of freedom, if close enough to the electroweak scale, will also modifythe Higgs couplings. For example, mixing of additional scalars participating in EWSB willadd to non-linearities to reduce even further the couplings of the Higgs to massive particles,leading then to even stronger limits on the scale of compositeness f . Note that this scaleis tied to the mass of new vector resonances like W (cid:48) and Z (cid:48) , and to the degree of tuningof Higgs potential. The Run2 LHC data has pushed this scale into the TeV range, and wehave shown that more complex scenarios would push this tuning even further. Hence Run3and future LHC runs should have a good handle at natural Composite Higgs scenarios. Acknowledgments
The work of V.S. by the Science Technology and Facilities Council (STFC) under grantnumber ST/P000819/1. We want to thank Stephan Huber and Jack Setford for manyfruitful discussions during the early stages of this work. We thank Andrea Banfi for thehelp regarding running the Higgs+jet process in his code implementation.
A Data inputs – 16 –roduction Decay Channel Lumi[Reference] Signal StrengthggH H → ZZ − [10] . +0 . − . VBF . +0 . − . VH . +0 . − . t ¯ tH, tH . +1 . − . ggH H → γγ
137 fb − [11] . +0 . − . VBF . +0 . − . VH . +0 . − . t ¯ tH . +0 . − . ggF H → W W − [10] . +0 . − . VBF . +0 . − . WH . +2 . − . ZH . +1 . − . ttH . +0 . − . ggH H → b ¯ b upto 77.4 fb − [10] . +2 . − . WH . +0 . − . ZH . +0 . − . t ¯ tH . +0 . − . VBF H → b ¯ b upto 77.2fb − [12] . ± . ggH H → τ ¯ τ
137 fb − [13] . +0 . − . VBF+V(qq)H . +0 . − . t ¯ tH H → M L
137 fb − [14] . +0 . − . ggH H → µµ
137 fb − [15] . +0 . − . VBF . +0 . − . VH . +3 . − . t ¯ tH . +2 . − . Table 3 . Summary of CMS Run 2 Higgs signal strength measurements. – 17 –roduction Decay Channel Lumi[Reference] Signal StrengthggF H → ZZ
139 fb − [8] . +0 . − . VBF . +0 . − . VH . +1 . − . ggF H → γγ
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