Two Higgs doublet models augmented by a scalar colour octet

Journal of High Energy Physics, Sep 2016

The LHC is now studying in detail the couplings of the Higgs boson in order to determine if there is new physics. Many recent studies have examined the available fits to Higgs couplings from the perspective of constraining two Higgs doublet models (2HDM). In this paper we extend those studies to include constraints on the one loop couplings of the Higgs to gluons and photons. These couplings are particularly sensitive to the existence of new coloured particles that are hard to detect otherwise and we use them to constrain a 2HDM augmented with a colour-octet scalar, a possibility motivated by minimal flavour violation. We first study theoretical constraints on this model and then compare them with LHC measurements.

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Two Higgs doublet models augmented by a scalar colour octet

HJE Two Higgs doublet models augmented by a scalar Li Cheng 0 2 4 German Valencia 0 1 2 3 0 Wellington Road , Melbourne, Victoria 3800 , Australia 1 On leave from Department of Physics, Iowa State University , Ames, IA 50011 , U.S.A. 2 Osborn Dr , Ames, IA 50011 , U.S.A 3 School of Physics and Astronomy, Monash University 4 Department of Physics and Astronomy, Iowa State University , USA The LHC is now studying in detail the couplings of the Higgs boson in order to determine if there is new physics. Many recent studies have examined the available ts to Higgs couplings from the perspective of constraining two Higgs doublet models (2HDM). In this paper we extend those studies to include constraints on the one loop couplings of the Higgs to gluons and photons. These couplings are particularly sensitive to the existence of new coloured particles that are hard to detect otherwise and we use them to constrain a 2HDM augmented with a colour-octet scalar, a possibility motivated by minimal avour violation. We rst study theoretical constraints on this model and then compare them with LHC measurements. Higgs Physics; Beyond Standard Model 1 Introduction The model Unitarity and stability constraints Existing LHC constraints Tree-level Higgs decay Direct bounds on the colour octet 2 3 4 5 6 7 1 2.1 2.2 4.1 4.2 6.1 6.2 6.3 One-loop decays of neutral colour-singlet scalars to gg and Numerical study Two Higgs doublet model parameters Parameters that mix the 2HDM sector with the colour-octet sector Loop-induced Higgs decay Summary and conclusions Introduction h ! Following up on their discovery of the Higgs boson with mass near 125 GeV [1, 2], the ATLAS and CMS collaborations continue the detailed study of its properties. For example, the Higgs couplings to top, bottom and tau have been measured to be in agreement with the standard model (SM) although the errors are still large. Couplings to W W , ZZ as well as e ective one-loop couplings h ! gg and h ! are also well described by the SM [3]. However, present day uncertainties still allow for a variety of new physics possibilities. For example, when compared with two Higgs doublet models (2HDM), these measurements constrain the parameter space but do not exclude the possibility of additional scalars below 1 TeV [4{14]. Two Higgs doublet models can also be confronted with h ! gg and ts and this comparison restricts the allowed parameter space. Manohar and Wise (MW) [15] introduced a model consisting of the SM augmented by a colour octet electroweak doublet of scalars. The addition was motivated by minimal avour violation: assuming that the scalars transform trivially under the avour group, only electroweak doublets which are colour singlets or octets are allowed. These coloured scalars are very weakly constrained by direct searches at LHC but they can a ect the loop induced Higgs couplings by factors of two. The model has been constrained theoretically and also using the h ! gg and h ! phenomenological studies in the literature [18{38]. ts with comparable results, and there are many { 1 { violation. More complicated models exist that contain both of these ingredients [39, 40], but our approach here is purely phenomenological. Our main goal is to explore the oneloop e ective couplings h ! gg and h ! of the SM-like Higgs in two Higgs doublet models in the presence of the additional scalar S transforming as (8; 2; 1=2) under the SM gauge group SU(3)C SU(2)L U(1)Y . The model contains a large number of parameters that we rst reduce by imposing standard theoretical constraints such as minimal avour violation [41, 42], custodial symmetry [43{45], and perturbative unitarity [31, 46{50]. The question of vacuum stability [51{70] is more complicated and will be discussed elsewhere. 2 The model The model we discuss in this paper is an extension of the type I and type II two Higgs doublet models. In this extension we add a colour octet electroweak doublet of scalars as in the MW [15] extension of the SM. The scalar content is chosen to satisfy desirable properties: minimal avour violation which naturally suppresses avour changing neutral currents and custodial symmetry which naturally preserves the relation 1. As observed in ref. [15], the only possible extensions of the scalar sector that do not transform under the avour group and that satisfy minimal avour violation are electroweak doublets that are colour singlets or colour octets and this motivates our choice for this model. The scalar content of the model consists of two SU(2) scalars ( 1 ; 2) and one colouroctet scalar S. The general potential for ( 1 ; 2) is well known from the literature [71, 72]. Our starting point will be more modest, consisting of the CP conserving, two Higgs doublet 1 that is only violated softly by dimension model with a discrete symmetry two terms1 1 ! V ( 1; 2) = m121 y1 1 + m222 y2 2 1 2 + 1This is more restrictive than MFV and we comment on this later on. follow ref. [15] but using 1 5 for 1 or !1 5 for 2 in place of 1 5, V ( 1; S) = 1 y1i 1iTrSyj Sj + 2 y1i 1j TrSyj Si V ( 2; S) = !1 y2i 2iTrSyj Sj + !2 y2i 2j TrSyj Si + 3 y1i y1j TrSiSj + 4 y1iTrSyj Sj Si + 5 y1iTrSyj SiSj + h:c: + !3 y2i y2j TrSiSj + !4 y2iTrSyj Sj Si + !5 y2iTrSyj SiSj + h:c: (2.3) Some of the couplings 3;4;5 and !3;4;5 can be complex and violate CP, but we will restrict our study to the CP conserving case. Finally, we have terms that involve both 1 and 2 as well as S,2 VN ( 1; 2; S) = 1 y1i 2iTrSyj Sj + 2 y1i 2j TrSyj Si + 3 y1i y2j TrSj Si + h:c: (2.4) in all cases we have explicitly shown the SU(2) indices i; j, Si = T ASiA, and the trace is taken over colour indices. The complete potential is thus, V ( 1; 2; S) = V ( 1; 2) + V (S) + V ( 1; S) + V ( 2; S) + VN ( 1; 2; S) : (2.5) After symmetry breaking, this potential implies the following relations between couplings and scalar masses m2H = m2h = m2H = where 345 = 3 + 4 + 5, and v2 = v12 +v22 with v1;2 the vevs of 1;2 respectively. Similarly, for the colour octet sector we obtain m2S = m2S + m2S0 = m2S + R m2S0 = m2S + I v 2 4 v 2 4 v 2 4 + ( 1 + 2 + 3) sin 2 + ( 1 + 2 3) sin 2 1 cos2 + !1 sin2 + 1 sin 2 ; ( 1 + 2 + 2 3) cos2 + (!1 + !2 + 2!3) sin2 ( 1 + 2 2 3) cos2 + (!1 + !2 2!3) sin2 2Note that these terms are allowed by MFV but not by the discrete symmetry commonly used to restrict the 2HDM potential. ; fermions with the colour octet. In the avour eigenstate basis, they are S = T ASA, and ; are avour indices. where we have de ned as usual H~i = "ij Hj for all three scalar doublets H = 2.1 Minimal Flavour Violation To suppress avour changing neutral currents in two Higgs doublet models, it is conventional to introduce discrete symmetries. For the Type I model, g1D;U = 0, while in the Type II model, g1U = g2D = 0. In the Yukawa terms, the type I model can be enforced with the discrete symmetry 1 ! symmetry 1 ! 1, dR ! requiring that there be only two 1, whereas the type II model can be enforced with the discrete dR [71]. We will instead follow ref. [15] and enforce MFV, avour symmetry breaking matrices GU transforming as (3U ; 3Q) under the avour group and GD transforming as (3D; 3Q) under the avour group. The matrices appearing in eq. (2.9) must satisfy g 1D = 1DGD; g 2D = 2DGD; g 3D = 3DGD g 1U = 1U GU ; g 2U = 2U GU ; g 3U = 3U GU ; where i under consideration are then de ned by D;U , i = 1; 2; 3, are complex scalars. The two types of two Higgs doublet model (2.8) (2.9) 1;2; S, (2.10) Type I: 1D = 1U = 0 Type II: 1U = 2D = 0 instead of the usual discrete symmetries. Requiring MFV instead of a discrete symmetry to de ne the models allows quartic terms in the scalar potential that are odd in either of the doublets. This justi es including the terms with coe cients 4;5, !4;5 and 1;2;3 in eqs. (2.3) and (2.4). One should note that in general, this also allows the additional terms in eq. (2.1), V 0( 1; 2) = 6 To impose custodial symmetry conveniently, we follow the matrix formulation of ref. [44] in which the scalar doublets are written as follows, Mab = ~ a; b S A = S~A; SA = = 0 a a SA0 SA +! b 0 b SA+! SA0 ; ; a; b = 1; 2; and the custodial symmetry is imposed by writing the scalar potential directly in terms of O(4) invariants such as y 1 i 2iSyj Sj ! Tr M1y1M22 Tr SyS . There are two methods proposed in the literature, HJEP09(216)7 Case 1. Construction using only M11 and M22. This yields the following constraints on the couplings of eqs. (2.1){(2.4): all the i are real and For the vacuum to be invariant as well one needs v1? = v2. An immediate consequence of custodial symmetry is that = 0 holds. The change induced in by the colour octet scalars is [15], / v1 2 + v22!2 + 2v1v2 2 2 2 2v12 3 + 2v22!3 + 2v1v2 3 2 : (2.16) Upon substitution of eqs. (2.14) and (2.15) we nd both sets of constraints result in = 0 as expected. As is known, both cases also in mass degeneracies mH = mA and from eqs. (2.6), (2.7) the rst method, eq. (2.14) for our numerical study. they also result in mS = mS0 . The constrain v1? = v2 is too restrictive so we will only use I It has been pointed out before that it is also possible to satisfy = 0 with = mS0 [ 18 ], and that this follows from `twisted' custo R mH = mH [ 73, 74 ] and with mS dial symmetry. 3 Unitarity and stability constraints In this section we consider high energy two-to-two scalar scattering to constrain the strength of the self interactions with the requirement of perturbative unitarity. The potential is renormalizable and the tree-level scattering amplitudes approach a constant value at high energy proportional to the quartic couplings. Perturbative unitarity then constrains their { 5 { jAai = jCai = jE1i = p2i jF+i = jS1i = jS3i = applied to two Higgs doublet models [47{50], and to the Manohar-Wise model [31]. We extend them here to the combined model as described in the previous section, considering only the neutral, colour singlet amplitudes. We begin by de ning the two particle state basis for the calculation of amplitudes, 2 a+ a + a a + a a ; a ai ; + The unitarity constraints for the 2HDM without the coloured scalars are known from refs. [47, 49]. The two-to-two scattering matrix is a 14 14 matrix that can be diagonalized exactly producing the following eigenvalues (which we have simpli ed by setting 5 = 4 as per custodial symmetry), 3 ( 1 + 2) to-two scattering amplitudes, by requiring that ja0j that the largest eigenvalue in eq. (3.2) be less than 8 . 1=2. This is equivalent to requiring In addition to the unitarity constraint, we also impose the known conditions for having a positive de nite Higgs potential with a Z2 symmetry [81], 1 > 0; 2 > 0; 3 > For phenomenological studies one prefers to control the scalar masses instead of the i couplings as input parameters via the relations eq. (2.6). We will always identify the lightest neutral scalar h with the 125.6 GeV state found at LHC [1, 2]. The other masses will be allowed to vary in ranges discussed later on, but we will always use 0s that ensure all the squared masses are positive and larger than around (400 GeV)2. { 6 { When we add the colour octet, the two-to-two scattering matrix becomes an 18 matrix which we diagonalize numerically. Unitarity constraints are obtained again from the J = 0 partial wave as in the case of the 2HDM. Approximate results in the custodial symmetry limit from 4 4 submatrices are, 8 3 ; The couplings that a ect only octet self-interactions at tree level, those in V (S) eq. (2.2), have identical constraints as already found in ref. [31]. In particular eq. 3.9 of that reference (translated to the notation of this paper) Recalling that in 2HDM-I t = b = = ) + sin( ) cos( tan { 7 { (3.4a) (3.4b) (3.4c) (3.5) (3.6) (4.1) (4.2) is reproduced in our numerical diagonalization of the 18 18 matrix. Additional constraints obtained in ref. [31] by studying unitarity in the colour octet channel are imposed on our entries and we quote them here for convenience, j 4 + 5j < p3215 ; j!4 + !5j < p3215 ; been presented recently for example in refs. [6, 7, 14, 68, 70] and we do not repeat this exercise. The reader interested in the results of that global t is referred to gure 1 in ref. [70], for example. There are a few relevant comments to be made that are not apparent from the global t. To this end we consider the results of the seven parameter t to the Higgs couplings as per the ATLAS-CMS combination of data. We further consider their second scenario, in which contributions from BSM particles are allowed both in the loops and in the Higgs decay but V 1 is assumed. Those results, as listed on table 14 of [3] are: -0.6 -0.3 panel we have the 2HDM-I and in the right panel we have the 2HDM-II. In both cases the blue cross marks the best t and the blue contour encloses the region allowed at 95% con dence level. The dashed green shows the 68% c.l. region. Superimposed is the red dotted area corresponding to points allowed by tree-level unitarity. one sees that the b and t couplings to the Higgs from eq. (4.1) are in tension within the 2HDM-1, being a bit more than 3 away if one adds the two errors in quadrature. To connect with the usual plot presented in the literature [14, 68, 70], we can do a simple t to the 5 couplings in eq. (4.1), which we show in gure 1. The left panel illustrates the same point as the best t is closer to b and so is the 68% c.l. region enclosing the best t point. The second dashed-green region is closer to t and one needs to go to a 95% c.l. to obtain a connected region which covers most of the parameter space. The addition of the colour octet cannot help address this problem as it does not a ect the fermion Yukawa couplings at tree-level. On the right panel we repeat the comparison for the type-II 2HDM. In this case there is a much smaller allowed region of parameter space but the goodness of the t (as measured by 2min) is better than that for 2HDM-I. The blue contour is similar, but not identical, to that obtained in the literature from a direct global t to LHC measurements. The slight shift of this region towards larger values of cos( ) is due to the small value of b and its small error in eq. (4.1). The values of Z = 1:00 0:08 and W = 0:90 0:09 in eq. (4.1) prefer the region cos( ) near one, the so called alignment limit. In addition there are constraints from the non-observation of the additional Higgs bosons that are shown in ref. [14], for example, and that we do not reproduce here. The constraints shown gure 1 are not a ected by the additional coloured scalars and should be identical to those obtained in the 2HDM if the same constraints are used. For this reason, they are not directly the concern of this paper. 4.2 Direct bounds on the colour octet One would expect that the LHC can place stringent constraints on the existence of the additional colour scalars from their non-observation. It turns out however that the existing bounds are not very restrictive for this model, depending on the values of the couplings in the scalar potential the masses. The main reason is that the cross-sections for production of one or two such scalars are below current LHC sensitivity as can be ascertained by a { 8 { quick glance at theoretical predictions [ 16, 24 ] compared to those for coloured scalars that are currently constrained [ 82 ] and vis-a-vis LHC results [83, 84]. Indirect constraints allow masses as low as The most important decays of the neutral scalars for example, would be into two jets or a tt pair. CMS limits on a colour-octet scalar S0 from dijet nal state quote MS < 3:1 TeV [83]. However, this is a gross overestimate for the MW model where the S0 production cross-section is a few thousand times smaller than the model used by CMS. Similarly, bounds on Z0 resonances decaying to tt pairs [84] can be interpreted as posing no signi cant constraint for these scalars where SB(S ! tt) 50{100 fb since their best sensitivity is to SB(S ! tt) > 200 fb for the mass range studied (up to 2 TeV for narrow resonances and 3 TeV for wide resonances). As already mentioned in refs. [ 15, 16 ] the cross sections for producing pairs of coloured scalars are larger than those for single scalar production for much of the parameter space. In this case the relevant constraints would arise from searches for dijet pairs and four topquarks. Again the relevant quantity SBr2 for this model is measured in fb whereas the published constraints are above this. Nonetheless, the dijet pair channel appears to be the most promising one to constrain this model and a detailed study will be forthcoming. For our numerical study we will use two examples, one in which MS is set at 1 TeV and another one at 800 GeV. The couplings in the potential a ecting eq. (2.7) are constrained so that 725 MS0 R 1200 GeV, and the custodial symmetry will ensure that MSI0 = MS . 5 One-loop decays of neutral colour-singlet scalars to gg and Finally we discuss the loop induced Higgs couplings where the colour-octet can play its most important role. Fits to the LHC Higgs data already exist in the literature and we use ref. [80] for our discussion. It is standard to parameterize the one-loop results with e ective operators for hgg and h 2 N (rf )Qf2 8 { 9 { Le = cg 12 v s hGa G a v + c hF F : A general parametrization for couplings to the Higgs of di erent kinds of new particles such as a complex scalar S, a Dirac fermion f , and a charged and colourless vector V are L = cs 2MS2 hSyS v cf v Mf hf f + cV 2MV2 hV yV : v They contribute to the e ective Higgs coupling to gluons and to photons at one-loop as [85{88] cg = c = 2 8 N (rs)Qs2 3C2(rs) csAs( s) + 3C2(rf ) cf Af ( f ); csAs( s) + cf Af ( f ) V cV AV ( V ); Q2 8 where ci = ci ci;SM, C2(r) is the quadratic Casimir of the colour representation r, and N (r) is the number of colours of the representation r. Ai (i = S; f; V , standing for scalar (5.1) (5.2) (5.3) (5.4) boson loop, fermion loop and vector boson loop, respectively) are loop functions, with AS( ) = Af ( ) = AV ( ) = 3 3 1 2 (f ( ) In terms of these general results and using ri = 4mi2 m2h ; Ri = m2H ; 4mi2 we can write the e ective one loop couplings. We begin quoting, for completeness, the amplitudes for these two processes within the SM [88], M (h ! gg)SM = Af (rt) and gg couplings for the 2HDM neutral scalars are given by where t1 = 1; t2 = 0 for Type-I and t1 = 0; t2 = 1 for Type-II and (5.5a) (5.5b) (5.5c) (5.6) (5.7) (5.8) cos sin sin sin Af (rb)t1 Af (Rb)t1 + sin cos cos cos Af (rt) + Af (rb)t1 Af (rb)t2 1 cos 18 sin 1 sin 18 sin )AV (rW ) + 48 ghH As(rH+ ) )AV (RW ) + 1 48 gHH As(RH+ ) Af (Rt) + Af (Rb)t1 + Af (Rb)t2 Af (rb)t2 Af (Rb)t2 1 sin 18 cos 1 cos 18 cos 1 sin sin2 cos + 2 cos sin cos2 3(cos sin3 sin cos3 ) 2 4 cos( + ) sin cos 1 cos sin2 cos + 2 sin sin cos2 3(cos cos3 + sin sin3 ) 2 4 sin( + ) sin cos (5.9) The top-quark and W -boson contributions to M (h ! gg) and M (h ! expressions for the 2HDM, reduce to the SM in the limit ) in the above scalars contribute the additional terms where we have shown our results in the custodial SU(2) limit, and the total contributions for the models in this work are M2HDM + MS. 6 Numerical study The model contains a large number of free parameters so we begin by presenting numbers for special values of masses to get a simple picture. We assume the lighter neutral CP-even Higgs h is the one discovered at LHC, and then compare the branching ratios to gg and to the t of ref. [80]. We rst set = 2 , mH = 600 GeV, mA = 500 GeV, mS = 800 GeV, !1;2 = 0, and use the Type II 2HDM. Ref. [14] provides a convenient form for scanning over input parameters for the 2HDM, which we adopt in this numerical study, we use input parameters Z5;7 in place of mA and m212 given by m2H sin2( ) + m2h cos2( ) + tan(2 )(Z6 Z7)v2 ; 1 2 Z7 parameter space for the example discussed in the text. Center panel: unitarity constraints in 1 2 for the same example (red points) and (blue points) allowed by h ! and h ! gg at 1 . Right panel: unitarity constraints in 1 example (red points) and (blue points) allowed by h ! and h ! gg at 1 . 1 for the same For this set of parameters we obtain the following constraints from unitarity, (6.2) Z7 0:42 < tan 24:5 < 1 2 1 In addition the parameters 1 and 2 as well as 1 and 1 exhibit the correlated unitarity constraint shown in gure 2. The allowed parameter region for this example in the tan plane is shown in the left panel in gure 2. From one-loop Higgs decays at 1 we nd j 1j < 12:4 as well as the blue dotted areas in gure 2. To illustrate the tree-level unitarity constraints implied by eq. (3.2) and the constraints from the LHC data t more generally, we randomly scanned the parameter space of the 2HDM (and its colour-octet extension) to nd a set of allowed points. To produce these gures we have used the custodial symmetry results by Method I as in eq. (2.14), including mH = mA. We have scanned over the range 600 MH 900 GeV. Our plots reproduce those of ref. [14] for mH = 300; 600 GeV and we also nd that the allowed region is reduced as mH increases. We further scan Z5;7 over the ranges 10 Z5 2:5, 10 Z7 The upper bound on Z5 arises from the requirement of mA being larger than about 400 GeV [89],3 and the lower bound keeps mA below around 1300 GeV. tan is scanned over the range 0:2; 50 and cos( ) is scanned over ( 0:5; 0:5). The charged Higgs mass is equal to mA and as calculated from eq. (2.6), is found to lie in the range (400; 1200) for these parameter values. The independent parameters that involve the colour octet scalars in the SU(2)C limit are allowed to vary in the range 5 1;2; !1;2; 1;2 5 , to cover the region implied by eq. (3.4c). The parameters that a ect only colour-octet self interactions at tree-level, i are constrained by eq. (3.5) (which we reproduce numerically by rst setting a slightly larger range) and eq. (3.6) which also constrains 4;5; !4;5 which do not a ect 3Taking at face value the constraint from B ! Xs : mH 0.5 0.1 h ! the text. 10 5 in the 2HDM (blue points) and the 2HDM plus a colour octet (green) as described in two-to-two scattering in the colour singlet zeroth partial wave. Finally, the mass MS is set to 1 TeV, which combined with the other parameters implies 725 MS0 R 1200 GeV. 6.1 Two Higgs doublet model parameters We reproduce the known shape of the region allowed by unitarity in the tan cos( plane [14]:4 it is very narrow for tan larger than about 10 as can be seen in gure 3 and it gets smaller as MH increases, so that the red region shown is mostly determined by the value mH = 600 GeV, the lowest in our range. The same gure shows that there is a small overlap between the regions allowed by unitarity (red) and those allowed by the e ective loop decays of the Higgs (blue) in both type-I and type-II 2HDM but this overlap region is enlarged with the addition of the colour octet (green). However, the colour octet tends to populate regions that are not allowed by the tree-level unitarity constraints. Next, we illustrate in gure 4 the two dimensional projections of the multidimensional region allowed by the tree-level unitarity constraints in the parameters of the 2HDM. The more signi cant correlation found is that between 3 and 4 . The darker regions in the plots re ect the concentration of points in the narrow region allowed in the tan cos( plane. We considered the question of overlap between the allowed regions in gure 4 and additional constraints arising from the one-loop Higgs decays, and found that tree-level unitarity is more restrictive in all cases. We show in gure 5 the region most constrained ) ) by h ! gg and h ! . 6.2 Parameters that mix the 2HDM sector with the colour-octet sector The two dimensional projections of the region allowed by tree-level unitarity for this sector are shown in gure 6. The gures show approximate correlations of the form j2 1 + 2j < 14, j2!1 + !2j < 15 and j2 1 + 2j < 11. In the same manner we study the twodimensional projections of the region allowed at 1 by the loop induced Higgs decays. The only projections indicating a possible correlation are shown in gure 7. 4We use the condition a00 12 instead of ja00j 1. 4 λ -4 -8 4 λ -4 -8 4 λ 1 5 λ 3 0 1 2 3 0 1 2 3 0 10 15 Now we present the points allowed by tree-level unitarity in a h ! gg-h ! gure 8. The black contours are taken from ref. [80]5 and are respectively the 1 plot in and 2 allowed regions, with the cross being the best t point. The SM point is, of course, (1,1). On these contours we have overlaid the blue regions which consist of the points allowed by unitarity for the 2HDM parameter space, and the red regions corresponding to those allowed by unitarity for the 2HDM augmented by the colour-octet. The colour-octet extends the region which can be explained with a 2HDM mostly in the direction of a larger BR(h ! gg). This gure does not give any insight into the values of di erent parameters in various regions of the plot. We have studied this issue by looking at all the possible correlations between pairs of parameters and the value of the (h ! gg, h ! ) point in gure 8, but found no notable correlations beyond those already shown in gure 7. Given the complexity of eq. (5.10) this is not too surprising. One could also constrain the points illustrated in this gure by requiring them to lie within the 95% con dence level region of gure 1. Since this is only an approximation to the global t, it is easier to require instead 5We thank Kristjan Kannike who provided us with these ts. -10 -5 5 10 2HDM scalars and the colour-octet scalars. 5 2 0 ω -5 -10 10 5 0 -5 -10 0 ω1 0 ν 1 2 κ 5 0 -5 -10 10 5 0 -5 -10 0 κ 1 0 ω1 2 ν 1 0 ω -5 -10 0 ν 1 0 ν 1 and h ! for 2HDM-I (blue) and 2HDM-II (red). that they satisfy 0:04 cos( ) 0:08 and 0:1 tan 5, roughly mapping the region shown in gure 1 of ref. [70] for 2HDM-II. The result is indistinguishable from the red region already in gure 8. These results illustrate how the loop induced Higgs decays are at present the best channels to constrain a Manohar-Wise type colour-octet. We can consider the e ect of the additional parameters from the colour-octet sector as follows. For each of the points in parameter space that satis es the tree-level unitarity constraints we can compute two di erent points (h ! gg, h ! ). The rst one would use the results of the 2HDM ignoring the additional contributions from the colour octet. These points are shown in blue in gure 9. The second point (in red) is the one corresponding to the calculation in the full model, already shown in gure 8. h ! extended 2HDM. plot. The blue points correspond to 2HDM whereas the red points correspond to the 2.0 1.8 1.6 M1.4 S / ) (→h1.2 1.0 0.8 0.6 are shown in a h ! gg-h ! plot. The red points correspond to the h ! gg; calculated in the full, colour octet augmented, model. The blue points correspond to the h ! gg; rates being rates being calculated without the contributions from the colour octet. The region allowed by both tree-level unitarity and Higgs decays at one-loop can be used to predict the loop-induced decays of the heavier neutral scalars. As an example we show in gure 10 the decay rates for the heavy neutral scalar of the 2HDM, H0, into two photons and two gluons. constraints as well as the h ! gg and h ! 1 constraints shown in a H ! gg-H ! The blue points correspond to 2HDM whereas the red points correspond to the extended 2HDM. plot. 7 Summary and conclusions We have constructed an extension of 2HDM in which a colour-octet electroweak-doublet (MW) is added. Starting from the most general renormalizable scalar potential we have reduced the number of allowed terms with the usual theoretical requirements of minimal avour violation and custodial symmetry. We have scanned the remaining parameter space to nd the region which satis es perturbative unitarity and have presented two dimensional projections of this region. The high energy two-to-two scattering matrix elements imply that correlations exist between certain pairs of the new couplings which are observed in these projections. We have then confronted the model with available LHC results in the form of tted couplings of the Higgs boson which we identify with the lightest scalar in the 2HDM. After collecting constraints on the parameters of the 2HDM from tree-level Higgs couplings we constrain the new sector couplings to the colour-octet using a current t on the one loop h ! and h ! gg couplings. Addition of the colour-octet a ects most the one loop h ! and h ! gg modes where it enlarges the allowed region of parameter space in the tan cos( ) plane, but not notably in the overlap zone with tree-level unitarity constraints as seen in gure 3. Of course, introducing a new colour-octet scalar doesn't populate more points in the unitarity allowed region when projected to the 2HDM parameter space. The colour-octet also enlarges the region of overlap with the 1 bounds h ! h ! gg, but the branching ratio of h ! gg tends to increase more signi cantly than that of h ! as can be seen in gure 8. Finally we predict the one loop couplings of the heavier neutral scalar H ! H ! gg using the points in parameter space that satisfy all our constraints. and and Acknowledgments This research was supported in part by the DOE under contract number DE-SC0009974. Li Cheng thanks Margarida Rebelo for useful correspondence on 2HDM and we thank Kristjan Kannike who provided us with the ts from ref. [80]. Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. so far, arXiv:1304.5225 [INSPIRE]. arXiv:1305.4587 [INSPIRE]. [1] ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE]. 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Li Cheng, German Valencia. Two Higgs doublet models augmented by a scalar colour octet, Journal of High Energy Physics, 2016, 79, DOI: 10.1007/JHEP09(2016)079