JJuly 9, 2018 14:21 ws-rv961x669 Book Title GV-Singapore-talk page 1
Chapter 1Colour Octet Extension of 2HDM
German Valencia ∗† School of Physics and AstronomyMonash University, Melbourne, Australia.
In this talk we consider some aspects of the Manohar-Wise extension of the SMwith a colour-octet electroweak-doublet scalar applied to 2HDM. We present the-oretical constraints on the parameters of this extension to both the SM and the2HDM and discuss related phenomenology at LHC.
1. Introduction
Now that the Higgs boson has been found everyone is asking whether it is reallyTHE Higgs. Alternatively, the question is whether there any more scalars, and wegot a hint last December that there may be one at 750 GeV.
Many extensionsof the scalar sector of the SM have been studied: two higgs doublet models, extrasinglets, triplets ... but mostly colour singlets. There are known phenomenologicalconstraints on these extensions: triplets tend to run into trouble with the ρ parame-ter; multiple doublets introduce FCNC, and so on. FCNC can be avoided in severalways: one can require each doublet to couple to same charge quarks (known astype II 2HDM); or one can impose minimal flavour violation, where all flavourbreaking is due to Yukawa matrices.Assuming that the new scalars are singlets under the flavour group, MFV allowsonly SU(2) doublets that are colour singlets or colour octets, and the addition of acolour octet to the SM was introduced by Manohar and Wise (MW). Colour singletsare the usual case of the 2HDM whereas colour octets are another possibility thathas received less attention. Other possibilities exist if the scalars transform underthe flavour group. There are also many complete models that have colour octetscalars, such as unification with SU (5); with SO (10), models where the Higgsboson is not elementary such as topcolour, technicolour models and many more.New colour octet scalars can have a large effect on loop level Higgs decay, whichis also the dominant production mode. One of first examples of NP ruled out by theHiggs observation was the fourth generation, in which gluon fusion production of the ∗ [email protected] † On leave from Department of Physics, Iowa State University, Ames, IA 50011.1 a r X i v : . [ h e p - ph ] J un uly 9, 2018 14:21 ws-rv961x669 Book Title GV-Singapore-talk page 2 Higgs would be about 10 times larger than in the SM, due to the extra contributionsfrom t (cid:48) , b (cid:48) in the loop. Similar large effects can appear in Higgs physics in thepresence of colour octet scalars but in this case the couplings that appear in Higgsproduction can have either sign and their magnitude is a free parameter so thatthey could, for example, cancel the new contributions from a fourth generation. Other examples of their exotic phenomenology are that they can produce the Higgswith completely different Yukawa coupling for top, or induce large CP violationin Higgs production. Even though there are many studies of this type, thesecolour-scalars are very hard to see directly at LHC.
2. The model
The most general renormalizable scalar potential for the SM plus MW is a V = λ (cid:18) H † i H i − v (cid:19) + 2 m s Tr S † i S i + ˜ λ H † i H i Tr S † j S j + ˜ λ H † i H j Tr S † j S i + (cid:16) ˜ λ H † i H † j Tr S i S j + ˜ λ e iφ H † i Tr S † j S j S i + ˜ λ e iφ H † i Tr S † j S i S j + H . c . (cid:17) + ˜ λ Tr S † i S i S † j S j + ˜ λ Tr S † i S j S † j S i + ˜ λ Tr S † i S i Tr S † j S j + ˜ λ Tr S † i S j Tr S † j S i + ˜ λ Tr S i S j Tr S † i S † j + ˜ λ Tr S i S j S † j S † i . (1)where v ∼
246 GeV is the Higgs vev.After symmetry breaking, the non-zero vev of the Higgs gives the physical Higgsscalar h a mass m H = 2 λv and it also splits the octet scalar masses as, m S ± = m S + ˜ λ v , m S R,I = m S + (cid:16) ˜ λ + ˜ λ ± λ (cid:17) v , (2)The parameters m S , and ˜ λ , , should be chosen such that the above squared massesremain positive.Our next step is to extend the type I and type II two Higgs doublet models witha colour octet electroweak doublet as in MW. The scalar potential is required tosatisfy desirable properties: minimal flavour violation and custodial symmetry andis constructed in steps as follows. We start with the well known 2HDM potentialfor (Φ , Φ ) assuming CP conservation and a discrete symmetry Φ → − Φ that isonly violated softly by dimension two terms. V (Φ , Φ ) = m Φ † Φ + m Φ † Φ − m (cid:16) Φ † Φ + Φ † Φ (cid:17) + λ (cid:16) Φ † Φ (cid:17) + λ (cid:16) Φ † Φ (cid:17) + λ (cid:16) Φ † Φ (cid:17) (cid:16) Φ † Φ (cid:17) + λ (cid:16) Φ † Φ (cid:17) (cid:16) Φ † Φ (cid:17) + λ (cid:20)(cid:16) Φ † Φ (cid:17) + (cid:16) Φ † Φ (cid:17) (cid:21) . (3) a We use a normalization of λ with the conventional relation λ = G F m H / √
2. We use ˜ λ i todistinguish from λ i of the 2HDM. b A condition that is more restrictive than MFV. uly 9, 2018 14:21 ws-rv961x669 Book Title GV-Singapore-talk page 3
Colour Octet Extension of 2HDM Next we can add the most general, renormalizable potential that describes thecouplings of the colour octet S to the two colour singlets (Φ , Φ ) as well as the selfinteractions of the colour octet. This potential can be easily constructed by analogywith Eq. 1. The octet self interactions do not change, V ( S ) = 2 m S Tr S † i S i + µ Tr S † i S i S † j S j + µ Tr S † i S j S † j S i + µ Tr S † i S i Tr S † j S j + µ Tr S † i S j Tr S † j S i + µ Tr S i S j Tr S † i S † j + µ Tr S i S j S † j S † i . (4)Interactions between one of the two colour singlets and the colour octet mimic Eq. 1, V (Φ , S ) = ν Φ † i Φ i Tr S † j S j + ν Φ † i Φ j Tr S † j S i + (cid:16) ν Φ † i Φ † j Tr S i S j + ν Φ † i Tr S † j S j S i + ν Φ † i Tr S † j S i S j + h . c . (cid:17) V (Φ , S ) = ω Φ † i Φ i Tr S † j S j + ω Φ † i Φ j Tr S † j S i + (cid:16) ω Φ † i Φ † j Tr S i S j + ω Φ † i Tr S † j S j S i + ω Φ † i Tr S † j S i S j + h . c . (cid:17) (5)Lastly, we look at terms that include both Φ and Φ as well as S , c V N (Φ , Φ , S ) = κ Φ † i Φ i Tr S † j S j + κ Φ † i Φ j Tr S † j S i + κ Φ † i Φ † j Tr S j S i + h . c . (6)In our notation the SU (2) indices i, j are shown explicitly, S i = T A S Ai , and thetrace is over colour indices. The complete potential is thus, V (Φ , Φ , S ) = V (Φ , Φ ) + V ( S ) + V (Φ , S ) + V (Φ , S ) + V N (Φ , Φ , S ) . (7)After symmetry breaking, this potential yields the following scalar masses m H ± = 2 m sin 2 β − λ + λ v , m A = 2 m sin 2 β − λ v ,m h = 2 m sin 2 β cos ( β − α ) + v (cid:18) λ sin α cos β + λ cos α sin β − λ α sin 2 β (cid:19) ,m H = 2 m sin 2 β sin ( β − α ) + v (cid:18) λ cos α cos β + λ sin α sin β + λ α sin 2 β (cid:19) ,m = v (cid:2)(cid:0) λ cos β − λ sin β (cid:1) tan 2 α − λ sin 2 β (cid:3) α cot 2 β − . (8)where λ = λ + λ + λ , and v = v + v with v , the vevs of Φ , respectively.Similarly, for the colour octet sector m S ± = m S + v (cid:0) ν cos β + ω sin β + κ sin 2 β (cid:1) ,m S R = m S + v (cid:2) ( ν + ν + 2 ν ) cos β + ( ω + ω + 2 ω ) sin β + ( κ + κ + κ ) sin 2 β ] ,m S I = m S + v (cid:2) ( ν + ν − ν ) cos β + ( ω + ω − ω ) sin β + ( κ + κ − κ ) sin 2 β ] . (9) c Note that these terms are allowed by MFV but not by the discrete symmetry commonly used torestrict the 2HDM potental. uly 9, 2018 14:21 ws-rv961x669 Book Title GV-Singapore-talk page 4 The Yukawa couplings, L Y = L Y (Φ , Φ ) + L Y ( S ), in the flavour eigenstatebasis are L Y (Φ , Φ ) = − (cid:0) g D (cid:1) αβ ¯ D R,α Φ † Q βL − (cid:0) g U (cid:1) αβ ¯ U R,α ˜Φ † Q βL − (cid:0) g D (cid:1) αβ ¯ D R,α Φ † Q βL − (cid:0) g U (cid:1) αβ ¯ U R,α ˜Φ † Q βL + h . c .,L Y ( S ) = − (cid:0) g D (cid:1) αβ ¯ D R,α S † Q βL − (cid:0) g U (cid:1) αβ ¯ U R,α ˜ S † Q βL + h . c . (10)where ˜ H i = ε ij H ∗ j as usual for all three scalar doublets H = Φ , , S , and α, β areflavour indices. Minimal flavour Violation
The usual approach to suppressing FCNC in 2HDM is to introduce discrete sym-metries that force for the Type I, g D,U = 0, for Type II, g U = g D = 0.The typeI can be enforced with φ → − φ , and the type II with φ → − φ , d R → − d R . We use instead MFV requiring that there be only two flavour symmetry breakingmatrices: G U which transforms as (3 U , ¯3 Q ) under the flavour group and G D whichtransforms as (3 D , ¯3 Q ). The matrices appearing in Eq. 10 become g D = η D G D , g D = η D G D , g D = η D G D g U = η U G U , g U = η U G U , g U = η U G U . (11)where η D,Ui , i = 1 , ,
3, are complex scalars. The two types of two Higgs doubletmodel can be defined by • Type I: η D = η U = 0 • Type II: η U = η D = 0MFV is less restrictive than the discrete symmetries and allows quartic termsin the scalar potential that are odd in either of the doublets. In particular it allowsthe terms with coefficients ν , , ω , and κ , , in Eqs. 5 and 6. It also allows theadditional terms in the regular 2HDM sector, V (cid:48) (Φ , Φ ) = λ (cid:16) Φ † Φ (cid:17) (cid:16) Φ † Φ (cid:17) + λ (cid:16) Φ † Φ (cid:17) (cid:16) Φ † Φ (cid:17) + h . c .. (12)We do not include these two terms in our numerical studies. Custodial symmetry
To impose custodial symmetry we follow the matrix formulation. Scalar doubletsare written as, M ab = (cid:16) ˜Φ a , Φ b (cid:17) = (cid:18) φ ∗ a φ + b − φ − a φ b (cid:19) , a, b = 1 , , (13) S A = (cid:16) ˜ S A , S A (cid:17) = (cid:18) S A ∗ S A + − S A − S A (cid:19) , (14)and the custodial symmetry is imposed by writing the scalar potential directly interms of O (4) invariants.There are two methods proposed in the literature, uly 9, 2018 14:21 ws-rv961x669 Book Title GV-Singapore-talk page 5 Colour Octet Extension of 2HDM • Using only M and M . This results is all the λ i being real and κ = κ , ν = ν , ν = ν ∗ , ω = ω , ω = ω ∗ , λ = λ . (15) • Using only M results instead in ν = ω = κ = κ (cid:63) , κ = 2 ν , ν = ω (cid:63) ,λ = λ , λ = λ = λ , m = m . (16)For the vacuum to be invariant as well one needs v (cid:63) = v which is toorestrictive so we will only use the first method.Imposing custodial symmetry results in ∆ ρ = 0 up weak corrections as can beeasily verified. It also results in m H ± = m A and in m S ± = m S I . It has beenpointed out before that it is also possible to satisfy ∆ ρ = 0 with m H ± = m H and in m S ± = m S R , and that this follows from ‘twisted’ custodial symmetry.The results in Eq. 15 can be compared with those obtained in the SM plus MWcase, 2˜ λ = ˜ λ , λ = 2˜ λ = ˜ λ , ˜ λ = ˜ λ , ˜ λ = ˜ λ (cid:63) . (17) Unitarity constraints
In this section we consider high energy two-to-two scalar scattering to constrainthe strength of the self interactions with the requirement of perturbative unitar-ity. Although the potential is renormalizable, the tree-level scattering amplitudesapproach a constant at high energy that is proportional to the quartic couplings.Perturbative unitarity then constrains their size in a manner entirely analogous tothe unitarity bound on the SM Higgs boson mass and generalizations. Wewill consider scattering of all the scalar particles that appear in the model at energiesmuch larger than their masses. The strongest limits on the couplings are obtainedby considering scattering of two particle states of definite colour and I = 0. In thiscontext, I = 0 is the singlet of the approximate O (4) symmetry.We begin by showing some of the resulting constraints for the SM plus MW caseand comparing tree level unitarity with the improvement one can get by allowingthe couplings to run. A further improvement is achieved by including the modi-fications to the running of the SM quartic coupling (or Higgs mass). This can beseen on the left panel of Figure 1.We next extend unitarity constraints to the 2HDM plus MW case, with theadditional requirement of the known conditions for having a positive definite Higgspotential with a Z symmetry, λ > , λ > , λ > − (cid:112) λ λ , λ + λ ± λ > − (cid:112) λ λ . (18)We will always identify the lightest neutral scalar h with the 125.6 GeV state foundat LHC. The heavy scalar is allowed to have a mass in the range 600 ≤ m H ≤
900 GeV and the pseudoscalar and charged scalars in the range 400 ≤ m A = uly 9, 2018 14:21 ws-rv961x669 Book Title GV-Singapore-talk page 6 m H ± ≤ ×
14 and can be diagonalized exactly. When thecolour octet is added the matrix becomes 18 ×
18 and we diagonalize it numerically.Unitarity constraints are obtained again from the J = 0 partial wave. We showone of the more interesting projections of these constraints on the right panel ofFigure 1. Fig. 1. The left panel shows the region in the ˜ λ − ˜ λ plane that satisfies the unitarity constraintin the SM plus MW at 1 TeV in red. Including unitarity constraints on the running of m h up to100 TeV in green and up to 10 GeV in blue. The right panel shows a comparison of unitarityconstraints (red points) to 1 σ constraints from h → gg and h → γγ in the 2HDM-II (blue points)and the 2HDM plus a colour octet (green). The region allowed by tree-level unitarity for the sector of the potential thatcouples the colour singlets and octets shows approximate correlations of the form | ν + ν | < ∼ | ω + ω | < ∼
15 and | κ + κ | < ∼ This is also the correlationobserved in SM + MW for ˜ λ − ˜ λ that is shown in Figure 1. Tree-level Higgs decay
The tree-level Higgs couplings to t ¯ t , b ¯ b and τ + τ − as well as to W W and ZZ already constrain the parameter space of the 2HDM requiring it to be close to theSM. We illustrate the following constraints in Figure 2 as per the ATLAS-CMS combination of data for the case where BSM physics is allowed in loops andin decays, κ b = 0 . +0 . − . , κ τ = 0 . +0 . − . , κ t = 1 . +0 . − . . (19)On the left panel we look at the type-I 2HDM and show the region allowed atthe 2 . σ level by the ATLAS-CMS combination (dashed blue) superimposed on theregion allowed by tree-level unitarity (red dots). We use 2 . σ because the 2HDM-Iis ruled out by this data at the 2 σ level due to the conflicting requirements of an uly 9, 2018 14:21 ws-rv961x669 Book Title GV-Singapore-talk page 7 Colour Octet Extension of 2HDM enhanced top-quark coupling and a reduced b -quark coupling. On the right panelwe show the type-II 2HDM at 2 σ . In this case the strongest constraint arises fromthe tau-lepton couplings. Fig. 2. Constraints on the cos( β − α ) − tan β plane arising from LHC fits to κ t , κ b and κ τ .Leftfor 2HDM-I at 2 . σ (dashed blue) and right for 2HDM-II at 2 σ . The red area is that allowed bytree-level unitarity. Direct bounds on the colour octet
One would expect that the LHC can rule out additional light colour scalars fromtheir non-observation. It turns out however that the existing bounds are not veryrestrictive.The basic constraints arise from decays into two jets or a t ¯ t pair. CMS limits on acolour-octet scalar S from dijet final state quote M S < . However, this isa for a model with production cross-section a few thousand times larger. Similarly,bounds on Z (cid:48) resonances decaying to t ¯ t pairs can be interpreted as posing nosignificant constraint for these scalars. It is known that the cross sections forproducing pairs of coloured scalars are larger than those for single scalar productionfor much of the parameter space. The relevant constraints would then be dijet pairsand four top-quarks. But again the models that have been studied have much largerproduction cross-sections than MW and effectively there are no direct constraintsfrom LHC yet. One loop constraints
The additional contribution to the Higgs boson production due to the octet-scalarloops in the limit of very heavy quarks and colour scalars in the loop can be writtenas L = ( √ G F ) / α s π G Aµν G Aµν h (cid:18) n hf + v m S
38 (2˜ λ + ˜ λ ) (cid:19) (20)where n hf is the number of heavy quark flavours, one in the case of SM3 and threein the case of SM4. This result shows the important role that additional colourscalars can play in the effective one-loop couplings of the Higgs. uly 9, 2018 14:21 ws-rv961x669 Book Title GV-Singapore-talk page 8 Next we present the points allowed by tree-level unitarity in a h → gg vs h → γγ plot in Figure 3. The black contours are taken from The universal Higgs fit . TheSM point is, of course, (1,1). On the left panel we have overlaid the region allowedby tree level unitarity of the SM plus MW model for two values of M S , 1 TeVand 1.75 TeV. On the right panel we have overlaid the blue regions which are thepoints allowed by unitarity for the 2HDM parameter space, and the red regionscorresponding to the 2HDM augmented by the colour-octet. The figure illustrates Fig. 3. Best fit to BR ( h → γγ ) vs BR ( h → gg ): the red dot (black x) is the best fit, thesolid and dashed curves show the 1 σ and 2 σ allowed regions respectively. In the left panel we havesuperimposed the range of predictions in the SM + MW for two values of M S and values of ˜ λ , spanning the parameter space allowed by tree-level unitarity. On the right panel we superimposethe parameter space that satisfies the unitarity constraints for the 2HDM (blue points) and forthe 2HDM + MW (red points). how the loop induced Higgs decays are at present the best channels to constrain aManohar-Wise type colour-octet. The colour-octet also extends the region whichcan be explained with a 2HDM mostly in the direction of a larger BR ( h → gg ).Recent interest in a possible 750 GeV di-photon resonance, compels us toexplore the possibility of it being the H in a 2HDM extended with a colour-octet.Other papers have used a colour-octet in this context recently. Figure 4 showsthis is not possible. The observed signal interpreted as a resonance requires a cross-section σ ( pp → γγX ) in the vicinity of 10fb. The largest B ( H → gg ) that canbe obtained are about three orders of magnitude too small to reach the necessarycross-section.
3. Conclusions
We discussed Higgs phenomenology of a scalar sector augmented with a new mul-tiplet of colour octet scalars as in the Manohar-Wise model which is motivated byMFV both for a one Higgs doublet model (SM) and a two Higgs doublet model(type I and II). Starting from the most general renormalizable scalar potential wehave reduced the number of allowed terms with the usual theoretical requirements d We thank Kristjan Kannike who provided us with these fits. uly 9, 2018 14:21 ws-rv961x669 Book Title GV-Singapore-talk page 9
Colour Octet Extension of 2HDM σ ( pp → γγX ) normalised to B ( H → gg ) through a 750 GeV H as afunction of B ( H → gg ) for points allowed by both unitarity and h → gg , h → γγ at 1 σ . of minimal flavor violation and custodial symmetry. We considered constraints onthe masses and parameters of the model from unitarity and vacuum stability andsaw that the additional colour scalars are very difficult to rule out or to observedirectly.The measured hgg and hγγ couplings are in agreement with the SM, but thereis still room for new physics at the 50% level. They constitute one of the bestplaces to constrain a MW extension. For SM plus MW we found that the Higgsone-loop effective couplings place constraints on the model that fall between thosefrom tree level unitarity and those from RGI unitarity. We found that the existenceof such colour scalars would effectively remove the constraints on the top Yukawacoupling arising from these couplings.We confronted the model with available LHC results in the form of fitted cou-plings 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 Higgscouplings we constrain the new sector couplings to the colour-octet using a currentfit on the one loop h → γγ and h → gg couplings.Finally we predict the one loop couplings of the heavier neutral scalar H → γγ and H → gg using the points in parameter space that satisfy all our constraints.We find that this cannot be the 750 GeV di-photon resonance that might have beenseen at LHC.This research was supported in part by the DOE under contract number de-sc0009974. We thank Harald Fritzsch for the opportunity to participate in a veryproductive meeting. References
1. G. Aad et al. [ATLAS Collaboration], Phys. Lett. B , 1 (2012) [arXiv:1207.7214[hep-ex]]. uly 9, 2018 14:21 ws-rv961x669 Book Title GV-Singapore-talk page 10
2. S. Chatrchyan et al. [CMS Collaboration], Phys. Lett. B , 30 (2012)[arXiv:1207.7235 [hep-ex]].3. CMS Collaboration [CMS Collaboration], collisions at 13TeV,” CMS-PAS-EXO-15-004.4. The ATLAS collaboration, ATLAS-CONF-2015-081.5. S. L. Glashow and S. Weinberg, Phys. Rev. D , 1958 (1977).doi:10.1103/PhysRevD.15.19586. R. S. Chivukula and H. Georgi, Phys. Lett. B (1987) 99.7. G. D’Ambrosio, G. F. Giudice, G. Isidori and A. Strumia, Nucl. Phys. B (2002)155 [hep-ph/0207036].8. A. V. Manohar and M. B. Wise, Phys. Rev. D , 035009 (2006) [hep-ph/0606172].9. See for example, J. F. Gunion, H. E. Haber, G. L. Kane and S. Dawson, Front.Phys. , 1 (2000). G. C. Branco, P. M. Ferreira, L. Lavoura, M. N. Rebelo, M. Sherand J. P. Silva, Phys. Rept. , 1 (2012) [arXiv:1106.0034 [hep-ph]]. and referencestherein.10. J. M. Arnold, M. Pospelov, M. Trott and M. B. Wise, JHEP , 073 (2010)doi:10.1007/JHEP01(2010)073 [arXiv:0911.2225 [hep-ph]]. HEP :: Search :: Help ::Terms of use :: Privacy policy Powered by Invenio v1.1.2+ Problems/Questions [email protected]. P. Fileviez Perez and C. Murgui, arXiv:1604.03377 [hep-ph].12. S. Bertolini, L. Di Luzio and M. Malinsky, Phys. Rev. D , no. 8, 085020 (2013)doi:10.1103/PhysRevD.87.085020 [arXiv:1302.3401 [hep-ph]].13. C. T. Hill, Phys. Lett. B , 419 (1991). doi:10.1016/0370-2693(91)91061-Y14. E. Farhi and L. Susskind, Phys. Rept. , 277 (1981). doi:10.1016/0370-1573(81)90173-315. X. -G. He and G. Valencia, Phys. Lett. B , 381 (2012) [arXiv:1108.0222 [hep-ph]].16. X. G. He, Y. Tang and G. Valencia, Phys. Rev. D , 033005 (2013)doi:10.1103/PhysRevD.88.033005 [arXiv:1305.5420 [hep-ph]].17. X. -G. He, G. Valencia and H. Yokoya, JHEP , 030 (2011) [arXiv:1110.2588[hep-ph]].18. C. P. Burgess, M. Trott and S. Zuberi, JHEP , 082 (2009) [arXiv:0907.2696[hep-ph]].19. L. M. Carpenter and S. Mantry, Phys. Lett. B , 479 (2011) [arXiv:1104.5528[hep-ph]].20. T. Enkhbat, X. -G. He, Y. Mimura and H. Yokoya, JHEP , 058 (2012)[arXiv:1105.2699 [hep-ph]].21. B. A. Dobrescu, G. D. Kribs and A. Martin, Phys. Rev. D , 074031 (2012)[arXiv:1112.2208 [hep-ph]].22. Y. Bai, J. Fan and J. L. Hewett, JHEP , 014 (2012) [arXiv:1112.1964 [hep-ph]].23. J. M. Arnold and B. Fornal, Phys. Rev. D , 055020 (2012) [arXiv:1112.0003 [hep-ph]].24. G. Cacciapaglia, A. Deandrea, G. D. La Rochelle and J. -B. Flament, arXiv:1210.8120[hep-ph].25. I. Dorsner, S. Fajfer, A. Greljo and J. F. Kamenik, arXiv:1208.1266 [hep-ph].26. G. D. Kribs and A. Martin, arXiv:1207.4496 [hep-ph].27. M. Reece, arXiv:1208.1765 [hep-ph].28. J. Cao, P. Wan, J. M. Yang and J. Zhu, arXiv:1303.2426 [hep-ph].29. X. G. He, H. Phoon, Y. Tang and G. Valencia, JHEP , 026 (2013)doi:10.1007/JHEP05(2013)026 [arXiv:1303.4848 [hep-ph]].30. X. D. Cheng, X. Q. Li, Y. D. Yang and X. Zhang, J. Phys. G , no. 12, 125005 uly 9, 2018 14:21 ws-rv961x669 Book Title GV-Singapore-talk page 11 Colour Octet Extension of 2HDM (2015) doi:10.1088/0954-3899/42/12/125005 [arXiv:1504.00839 [hep-ph]].31. D. Buttazzo, arXiv:1403.6535 [hep-ph].32. X. G. He, G. N. Li and Y. J. Zheng, Int. J. Mod. Phys. A , no. 25, 1550156 (2015)doi:10.1142/S0217751X15501560 [arXiv:1501.00012 [hep-ph]].33. J. Yue, Phys. Lett. B , 131 (2015) doi:10.1016/j.physletb.2015.03.044[arXiv:1410.2701 [hep-ph]].34. A. Pomarol and R. Vega, Nucl. Phys. B , 3 (1994) doi:10.1016/0550-3213(94)90611-4 [hep-ph/9305272].35. B. W. Lee, C. Quigg and H. B. Thacker, Phys. Rev. D , 1519 (1977).36. S. Kanemura, T. Kubota and E. Takasugi, Phys. Lett. B , 155 (1993) [hep-ph/9303263].37. J. Horejsi and M. Kladiva Eur. Phys. J. C , 81 (2006) doi:10.1140/epjc/s2006-02472-3 [hep-ph/0510154].38. I. F. Ginzburg and I. P. Ivanov, Phys. Rev. D , 115010 (2005)doi:10.1103/PhysRevD.72.115010 [hep-ph/0508020].39. W. J. Marciano, G. Valencia and S. Willenbrock, Phys. Rev. D , 1725 (1989).doi:10.1103/PhysRevD.40.172540. J.-M. Gerard and M. Herquet, Phys. Rev. Lett. , 251802 (2007)doi:10.1103/PhysRevLett.98.251802 [hep-ph/0703051 [HEP-PH]].41. E. Cerver and J. M. Grard, Phys.Lett. B , 255 (2012) doi:10.1016/j.physletb.2012.05.010 [arXiv:1202.1973 [hep-ph]].42. N. G. Deshpande and E. Ma, Phys. Rev. D , 2574 (1978).doi:10.1103/PhysRevD.18.257443. L. Cheng and G. Valencia, arXiv:1606.01298 [hep-ph].44. A. Barroso, P. M. Ferreira, R. Santos, M. Sher and J. P. Silva, arXiv:1304.5225[hep-ph].45. P. M. Ferreira, R. Santos, M. Sher and J. P. Silva, arXiv:1305.4587 [hep-ph].46. H. E. Haber and O. Stal, Eur. Phys. J. C , no. 10, 491 (2015)doi:10.1140/epjc/s10052-015-3697-x [arXiv:1507.04281 [hep-ph]].47. The ATLAS and CMS Collaborations, ATLAS-CONF-2015-044.48. V. Khachatryan et al. [CMS Collaboration], Phys. Rev. Lett. , no. 7, 071801(2016) doi:10.1103/PhysRevLett.116.071801 [arXiv:1512.01224 [hep-ex]].49. S. Chatrchyan et al. [CMS Collaboration], Phys. Rev. D , no. 7, 072002 (2013)doi:10.1103/PhysRevD.87.072002 [arXiv:1211.3338 [hep-ex]].50. M. I. Gresham and M. B. Wise, Phys. Rev. D , 075003 (2007) [arXiv:0706.0909[hep-ph]].51. P. P. Giardino, K. Kannike, I. Masina, M. Raidal and A. Strumia, JHEP , 046(2014) doi:10.1007/JHEP05(2014)046 [arXiv:1303.3570 [hep-ph]].52. R. Ding, Z. L. Han, Y. Liao and X. D. Ma, Eur. Phys. J. C , no. 4, 204 (2016)doi:10.1140/epjc/s10052-016-4052-6 [arXiv:1601.02714 [hep-ph]].53. J. Cao, C. Han, L. Shang, W. Su, J. M. Yang and Y. Zhang, Phys. Lett. B , 456(2016) doi:10.1016/j.physletb.2016.02.045 [arXiv:1512.06728 [hep-ph]].54. W. Altmannshofer, J. Galloway, S. Gori, A. L. Kagan, A. Martin and J. Zupan, Phys.Rev. D93