Physics etters B 77 202) 409 49 Contents lists availale at SciVerse ScienceDirect Physics etters B www.elsevier.com/locate/physlet Reproducing the Higgs oson data with vector-like uarks N. Bonne, G. Moreau aoratoire de Physiue Théoriue, Bât. 20, CNRS, Université Paris-sud, F-9405 Orsay Cedex, France article info astract Article history: Received 22 June 202 Received in revised form 2 August 202 Accepted 26 Septemer 202 Availale online 2 Octoer 202 Editor: G.F. Giudice Vector-ike V) uarks arise in the main alternatives to the supersymmetric extensions of the Standard Model SM). Given the experimental possiility of a 25 GeV Higgs oson with rates significantly different from the SM expectations, it is motivating to study the effects of V uarks on the Higgs oson cross sections and ranching ratios. We perform a systematic search for the minimal field contents and gauge group representations of V uarks ale to significantly improve the fit of the measured Higgs rates, and simultaneously, to satisfy the direct constraints on V uark masses as well as the electro-weak precision tests. In particular, large enhancements can e achieved in certain diphoton channels as pointed out y oth the ATAS and CMS Collaorations optimizing then the Higgs rate fit. This is a conseuence of the introduction of V uarks, with high electric charges of or, which are exchanged in the Higgsto-diphoton loop. Interestingly, the field contents and formal Higgs couplings otained here are similar to those of scenarios in warped/composite frameworks arising from different motivations. The various exotic-charge uarks predicted, possily elow the TeV scale, might lead to a rich phenomenology soon at the HC. 202 Elsevier B.V. All rights reserved.. Introduction The main drawack of the Standard Model SM) is proaly the gauge hierarchy prolem induced y the divergent uantum corrections to the mass of the Higgs oson [ 4]. Various alternatives to the supersymmetry, from the AdS/CFT correspondence [5] paradigm, address this prolem: the so-called little Higgs models [6 8], the composite Higgs [9 3] and composite top [4] scenarios, the Gauge Higgs unification mechanism see e.g. Refs. [5,6]) or the warped extra-dimension setup proposed y. Randall and R. Sundrum RS) [7,8] and its well-motivated version with SM fields in the ulk [9] allowing to generate the fermion mass hierarchy [20 36]. All these frameworks predict the existence of additional color-triplet states with vector-like gauge couplings; these Vector-ike V) uarks arise as Kaluza Klein KK) excitations in the higher-dimensional scenarios, as excited resonances of the ounded states constituting the SM particles in composite models and essentially as partners of the top uark eing promoted to a larger multiplet in the little Higgs context. The V uarks are also prevalent as KK excitations of ulk fields in other higher-dimensional frameworks as e.g. in Ref. [37]) or as new components emedded into the simplest SU5) representations in gauge coupling unification theories [38]. Hence V uarks are predicted in most of the alternatives to supersymmetry and their masses can reach values elow the TeV scale as it could occur e.g. for the so-called custodians, KK states arising in the custodially protected warped extra-dimension models [39 44]. 2 Now from the experimental side, all the recent data on Higgs oson searches performed at the Tevatron and arge Hadron Collider HC) constitute an important insight in the exploration of the Electro-Weak Symmetry Breaking EWSB) sector. Hints in the data collected in 20 y the ATAS and CMS experiments, which were oserved in various final states, could correspond to slight excesses of events induced y a Higgs oson with a mass of m h 25 GeV as announced in Ref. [45]. New and updated HC results have appeared at the Moriond 202 conference; then oth HC experiments reported local 3σ excesses [46,47] ut more analyzed event statistics is still needed to confirm that these excesses with respect to the ackground estimation are not statistical fluctuations. The CDF and D0 Collaorations have also detected an excess around 25 GeV in the ottom uark search channel, h, corresponding to a local significance of 2.7σ [48]. * Corresponding author. E-mail address: moreau@th.u-psud.fr G. Moreau). V leptons can also appear; it must e noted however that those are typically heavier than the V uarks within the warped/composite models. There is also the possiility of extra chiral fermions, like a fourth generation which is now uite constrained y the data on Higgs physics. 2 Custodians might even appear in warped extra-dimensional frameworks of supersymmetric models [94]. 0370-2693/$ see front matter 202 Elsevier B.V. All rights reserved. http://dx.doi.org/0.06/j.physlet.202.09.063
40 N. Bonne, G. Moreau / Physics etters B 77 202) 409 49 Under this hypothesis of the existence of a 25 GeV Higgs oson, deviations with respect to the SM are oserved: oth ATAS and CMS report an increase of all the Higgs production rates in the diphoton channel h γγ) compared to the SM Higgs rate, eing close to the 2σ level in some cases [see the precise data in the following detailed discussion]. The comined CDF and D0 analyses point towards a est-fit cross section, for p p hv V [V Z 0, W ± osons], centered at 2 times the SM cross section [48] also for m h = 25 GeV. 3 Finally, the Higgs production rate in the channel h W + W is elow the SM rate y more than σ still at 25 GeV) in the CDF + D0, ATAS and CMS results. The other measurements are in a reasonale agreement with the SM expectations. The investigation of the Higgs sector, in addition to shed light on the cornerstone of the SM, represents a window on physics eyond the SM. The Higgs properties may e.g. help to discriminate etween various new theories that could manifest themselves indirectly at the TeV scale. In this spirit, it is interesting to try to explain the aove deviations of the Higgs rates from their SM predictions on the asis of corrections to the Higgs couplings. This approach is particularly relevant in the contexts of the well-motivated V uarks, discussed aove, which are ale to modify the Higgs interactions through fermion mixing and new loop contriutions. In this etter, we adopt the generic approach of considering V uarks as possile manifestations of several classes of theories eyond the SM, without specifying those theories. We elaorate the three types of minimal V uark models and optimize their parameters) allowing to correct the 25 GeV Higgs couplings so that i) most of the Higgs rates are significantly closer to their central measured values than the SM expectations and in particular for the channels h γγ,, W + W, ii) all the Higgs rates elong to the σ experimental regions and in turn improve the gloal fit of the SM, iii) the direct limits on the masses of involved V uarks are respected and their contriutions to the EW precision oservales are acceptale. If the presently oserved deviations from the SM Higgs rates are indeed to e explained y some V uarks then our results predict the existence of at least two states = V uarks with the same electric charge Q e.m. as the ) plus at least either a pair of V uark with Q e.m. =+) accompanied y a or a pair of with a. t components the same Q e.m. as the top) may arise too. Some realistic mass intervals otained are 4 : m 650 00 GeV, m 800 000 GeV, m 650 000 GeV, m 800 900 GeV, m 2 840 GeV and m t2 900 00 GeV. 5 We do not claim those values to e the only allowed ranges as such a conclusion would rely on exhaustive and thus long explorations of the parameter spaces which are uite large in the considered scenarios. et us mention that for certain gauge group representations, the or uark can e stale. Interestingly, one should also remark that the essential field content and couplings addressing the Higgs rate anomalies, in all the models constructed here, also hold in specific set-ups of the custodially protected RS scenario or composite model). In that sense, the present Higgs data could e seen as an indication for the RS scenario and these specific custodial set-ups. Note that this kind of custodial set-up [containing principally two and two or custodians] has not een considered so far in the literature on RS composite) model phenomenology [39,40] including the implications for Higgs searches at colliders [49,44,50 53] with HC inputs [54] except in Ref. [43] [55] for a dual composite analysis) disconnected from Higgs searches where it arises from some considerations on the EW Precision Tests EWPT). The V field configurations that we point out could e realized in the context of any theory where the effects on the Higgs sector with a different origin from the V uarks are negligile, like e.g. in RS scenarios with custodians around the TeV scale and decoupling KK excitations of the gauge osons much aove 3 TeV which is generally the order of the ound from EWPT [39,56,57]); then the minimal realistic V uark configurations and the optimized Higgs rates would e mainly identical as those otained in the present simplified framework. The other possiility is to have complete theories underlying the SM where V uarks appear, together with e.g. light extra gauge osons or an extended Higgs sector, so that several types of effects could affect the SM Higgs rates, in which case our results could e useful for theorists as a guide on V uark influences. At this stage, one should mention related works. In Ref. [58] see also references therein), it is shown that specific scenarios addressing the naturalness prolem via the presence of top-partners such as t like the little Higgs, multi-higgs and pseudo-goldstone Higgs oson possile pattern of composite Higgs models) scenarios, are constrained in a non-trivial way y recent Higgs rate estimations [even efore the Tevatron data]. Constraints from the recent Higgs data have also een imposed explicitly on the Minimal Composite Higgs Models with fermions emedded in spinorial or fundamental representations of SO5) [59 6]. Effective approaches constraining generic Higgs operators, including possile deviations to the EW gauge oson couplings, can e found in Ref. [62] see Ref. [63] for effective interactions involving oth the top uark and Higgs field). Another study at the effective coupling level shows that ad-hoc massive fermions in color SU3) c representations up to the 27 and with Q e.m. 2 can explain the simultaneously oserved ineualities in the author notations): gv <, V γ > 2, gγ > [64] data from Tevatron not included). 6 Some of the recent HC investigations on the Higgs scalar have also een considered in completely different theoretical contexts such as the Universal Extra Dimensions, where the constraints from the γγ and W + W channels leave only an allowed narrow window near m h = 25 GeV [65]. Within the minimal supersymmetric extensions of the SM, the corrections to the hw + W vertex due to the extended Higgs sector constitute also the main source of corrections to the loop-induced hγγ coupling, a prolematic correlation preventing to otain opposite corrections to the W + W and γγ ratesaswanted today [66] and references therein). Finally, the fourth generation [67], the radion[68] or the dilaton [64] have difficulties to interpret the rate enhancement oserved recently at HC, for m h = 25 GeV, in the Vector Boson Fusion VBF) channel: VV h γγ, while 3 The uncertainty on the m h resolution is aout 0 GeV and the est-fit cross section decreases increases) elow aove) 25 GeV. 4 For comparison, the most severe lower limit on an extra-uark is at 6 GeV assuming the ranching ratio for the relevant decay channel at unity) [80]. 5 In our notations, e.g. denotes the lightest mass eigenstate and 2 the second lightest eigenstate the lightest one eing the oserved ottom uark: rigorously ut sometimes noted just as usual). 6 These authors demonstrate the No-Go theorem that no color-triplet fermion with Q e.m. can realize V γ > 2 and gγ >. We escape it y introducing several fermions with Q e.m. 2.
N. Bonne, G. Moreau / Physics etters B 77 202) 409 49 4 Fig.. eft: Domain leading to 25 GeV Higgs oson rates inside the experimental σ intervals for the Model II, with the, ) doulet cf. E. 7)), in the plan m versus m in GeV). The values of the other parameters are fixed at Y =.0, Y =, Y = 2.5, Y = 0.5, Y = 0.053, Y =, Y =, Y /3 =, m = 200 GeV, m = 900 GeV, m = 000 GeV. Contour-level curves for the physical masses m and m,2 are also shown. The other mass eigenvalues are almost constant over the shown plan like, m 4GeV,m 2 840 GeV, m 3 290 GeV, m t 73 GeV, m 900 GeV, or mainly depending on m like, m t2 900 00 GeV in the domain shown, or around 2 TeV in this domain: m t3 250 3000 GeV, m 3 500 3000 GeV, m 2 600 3000 GeV. Right: Central values and σ error ars for the strength modifiers μ hγ, μ hv, μ hτ, μ V, μ W, μ γ and μ Xγ defined in Section 2.) measured y the experiments indicated in front, for m h = 25 GeV. The various strength modifiers are indicated y the associated cross sections and ranching ratios. The plus symols mean that the experimental results are comined. In each case the SM prediction corresponds to μ = leading to the gloalχ 2 SM value written in the figure. The small lack circles correspond to the theoretical predictions of the strength modifiers for the point of parameter space also indicated as a circle on the left-side plot. This parameter set leads to the oliue S, T and Higgs fit χ 2 values indicated near the circle on the top-left part of the figure. The little lack suares are associated to a second parameter set where only one of the parameter values is changed: Y = 2.2. a fermiophoic Higgs oson could explain it [69]. Increasing consideraly this channel rate is also doale y introducing new states with large electric charges that can e exchanged in the hγγ-loop, in the spirit of the highly-charged uarks introduced here; this idea was realized in the different context of the type II see-saw mechanism where douly-charged Higgs scalars arise [70]. 7 In Section 2, we discuss the effects of different models of V uarks on the Higgs oson oservales. Then these models and their parameter space are confronted to the collider data in Section 3. We conclude in Section 4. 2. Model uilding 2.. The Higgs oson data We first define all the Higgs rate oservales which have een measured at the Tevatron and HC assuming a 25 GeV Higgs oson. Those are the following signal strength modifiers given with the last references for their experimental value): μ hγ = σ h B h γγ /σ SM B SM h h γγ [48,7,72], μ hv = σ h B h V V /σ SM B SM [48,7,73], μ h h V V hτ = σ h B h ττ /σ SM B SM h h ττ [7,73], μ V = σ hv B h / σ SM hv BSM h [48,74,7,73], μ W = σ h B h WW /σ SM h BSM h WW [73] and μ γ = σ h B h γγ /σ SM h BSM h γγ [72,75], where B stands for the ranching ratios, σ h for the total cross section of the Higgs production dominated y the gluon gluon fusion mechanism gg h), σ hv for the cross section of the Higgs production in association with a V -oson and σ h for the VBF rate. One needs to introduce also the uantity [76,66], μ Xγ = σ hx B h γγ = 0.3 σ gg h + σ h + σ hz + σ hw B h γγ σ SM B SM hx h γγ 0.3 σ SM gg h + σ SM h + σ SM hz + σ, SM B SM hw h γγ where the factor 0.3 has een estimated recently from simulating additional QCD jets [66] to account for the efficiency of events issued from the gluon gluon fusion to pass the cuts for the selection of the hv and h productions asically on the Higgs oson transverse momentum). Similarly, to e rigorous there is a factor of aout 0.033 for the suppression of the gluon gluon fusion events containing jets at NO) y the dijet-class tagging in the μ γ measurement; the uncertainty on this factor is of 70% [77] ut it does not alter significantly anyway the theoretical estimation of μ γ in our framework given the σ gg h corrections and the asence of σ h modifications). The experimental values for all these μ s oservales are synthesized in the right-part of Fig. or euivalently of Fig. 2). In order to summarize the various results on these figures, we have comined the ATAS and CMS data with the asic uadrature method for every search channel where oth experiments provide results except for the h channel where we find it more instructive to discuss the data separately see the next paragraph). The comination has een done without including the correlation; this is correct for the statistical error and the uncorrelated systematic errors while the correlated systematic ones, like the theoretical uncertainty, are expected to e su-leading compared to all the others [58] so the way those are comined should not e crucial). More precisely, the comined error, for example on μ hw for the given channel pp h WW, has een otained from the suare root of the ATAS and CMS 7 One could also mention related studies aout another type of V uark effects on Higgs searches: new channels of Higgs production through V uark decays [95].
42 N. Bonne, G. Moreau / Physics etters B 77 202) 409 49 Fig. 2. eft: Same as in Fig. ut for the Model I with the, ) doulet [see E. 2)] in the plan m versus m in GeV). The fixed parameters read as, Y =, Y = 3, Y = 0.053, Y =, Y /3 =, m = 200 GeV, m = 900 GeV. Three contour-level curves for m are shown. Other masses are almost constant over the plan, m 4GeV,m 2 840 GeV, m 3 290 GeV, m t 73 GeV, and the remaining ones are, m 2 750 2750 GeV [in the presented domain], m = minm, m ), m 2 = maxm, m ) [as there is no mixing term]. Right: Same as in Fig. for the experimental data ut with theoretical predictions from the Model I [with, )]. The lack suares are associated to the same input parameter values as for the lack circles except that Y = 2.2. uncertainties added in uadrature; in fact, this procedure has een applied separately for the errors aove and elow the experimental central values to otain the final comined errors, respectively, δμ + hw and δμ which appear on the right-part of Fig.. hw What comes out at a first glance on the experimental results of Fig. is, in particular, the enhancement of the estimated rates for the three diphoton channels compared to their respective SM predictions. One notices also the significant reduction of σ h B h WW relatively to its SM expectation, oserved simultaneously y the Tevatron and HC. Concerning the h channel, if one does not consider the ATAS est-fit value which is negative, an enhancement appears with respect to the SM especially at Tevatron where the otained accuracy is etter. The other channels fall into the σ regions. In Section 3.2, we will discuss the χ 2 function we assume gaussian distriuted measurements) defined y χ 2 = i μ i μ exp i ) 2 δμ i ) 2 where the sum is taken over the different channel oservales defined in the eginning of this susection, namely i = hγ, hz, hw, hτ, V, W, γ, Xγ, and μ exp are the measured central values for the corresponding signal strengths. The errors used here are derived y i symmetrizing the errors shown in the right-part of Fig. : δμ i ) 2 =[δμ + ) 2 + δμ ) 2 ]/2. i i 2.2. The V uark effects In order to improve the fit to the Higgs data, one would first need to increase the channel in Fig. [right-part] with respect to the SM. For that purpose, one needs to enhance the h ranching fraction since the presence of V uarks does not induce large tree-level corrections to the hv V vertex nor to the initial V coupling involved in the hv production. To increase the Γ h width at m h = 25 GeV, at least two V -like states say and ), mixing together and with the SM state, need to e introduced so that the asolute value of the ottom Yukawa coupling can e increased significantly thanks to additional elements in the Yukawa coupling matrix arising in the,, ) asis. 8 At least a Yukawa coupling mixing and and another one inducing the mixing are necessary; since the Higgs field is in an SU2) doulet, gauge invariance imposes that and must e emedded in different SU2) representations, as well as for the left-handed state or the R ) and. Restricting to two -like states and to multiplets smaller than a triplet to have the minimal field content set-up extended set-ups do not ring different kinds of effects), one must thus emed in a singlet and in a doulet. More concretely, the theoretical prediction for μ V relies on the ratio Γ h /Γ SM h = Y /Y SM 2 where Y SM is the ottom Yukawa coupling in the mass asis within the SM and Y is the same coupling ut including the mixing effects [ lightest mass eigenstate]. Y is the diagonal element of the coupling matrix C m, in the mass asis, 2, 3 ), corresponding to the h R coupling; one has C m = U C U R where the unitary asis-transformation matrices U /R are otained y i-diagonalizing the model-dependent ottom mass matrix as, U M U R = diagm,m 2,m 3 ) [see Section 2.3 for an explicit example]. Similarly, to increase theoretically the diphoton channels in the h and hx productions as suggested y Fig. wehavetoen- hance B h γγ. One cannot increase σ gg h,tofavorσ hx,sinceσ h B h γγ is already significantly increased from the B h γγ enhancement reuired y the σ h B h γγ data) so that in view of the data σ gg h must decrease for compensating this large σ h B h γγ variation as it 8 Even if ovious, it is interesting to notice that V leptons would not allow to increase Γ h y tree-level effects.
N. Bonne, G. Moreau / Physics etters B 77 202) 409 49 43 will occur in this etter. Because of this aspect, the large experimental values of σ h B h γγ as well as σ hx B h γγ and the aove Γ h ehavior, the needed theoretical enhancement of B h γγ via Γ h γγ has to e important. The possile increase of the loop-induced hγγ coupling [78] from the top uark loop-contriution, through a t t mixing increasing largely the top Yukawa coupling, is not possile as this SM top coupling is already close to its perturativity ound and moreover the dominant and opposite-sign) triangular loop-contriution to hγγ remains to e from the W ± -oson exchange. Now decreasing the top Yukawa coupling leads indeed to an increase of the effective hγγ coupling through a smaller destructive interference etween the top and W ± loop contriutions. Nevertheless, even for a strong suppression of /0 /00) of the physical top Yukawa coupling for which it is already difficult to reproduce the measured top uark mass 9 thehγγ coupling increase gives rise to a B h γγ enhancement y a factor of only.5.6) [with respect to SM]. Such a factor is not large enough to e completely satisfactory e.g. in view of the data on σ h B h γγ in the right side of Fig. [there is no significant correction to σ h in the present context]. Including the Γ h increase effect descried in the previous paragraph even tends to suppress B h γγ. The last promising way to increase the hγγ coupling is to introduce V uarks with high electric charges leading to new loop- multiplets of contriutions favored y the two photon couplings. The two first possile exotic charges otainale y extending SU2), t are Q e.m. = and Q e.m. =, as induced y the relation Y = Q e.m. I 3 Y hypercharge, I 3 SU2) isospin), and have in turn asolute values higher than the top uark one. However, given the present direct ounds around 600 GeV [see elow] for the masses of such V uarks, asically decaying like t,, respectively: W, tw), we have found that their loopcontriutions to the hγγ coupling do not reach large enough amounts in regard to Higgs fit improvements. Then one has to introduce the next-higher asolute charges, held y and, to increase again the electromagnetic couplings of the hγγ loop. The Yukawa couplings and masses of these, must e such that their loop-amplitude interferes constructively with the W ± -oson exchange to generate enhancements. The condition for, say, the to e exchanged in the hγγ loop is clearly that it must couple directly to the Higgs oson; this means that there should e at least two components, noted and, elonging to different gauge representations. To e minimal in terms of field content and without loss of generality, we restrict ourselves to two or two ) components emedded in SU2) representations up to triplets including those reveals another type of model with respect to the / decay. Besides, we do not consider charges, Q e.m. >, as those do not ring effects of different nature and are less usual charges even if Q e.m. = 0/3 and /3 are considered e.g. in Ref. [55]). Therefore, the only possiilities are to emed either in a singlet and inadouletor in a doulet and in a triplet or similarly for ). et us illustrate generically the effect of such V uarks, noted here k laeled y k =, 2,...), with high charges, Q e.m. k > 2/3, y descriing the expression for the diphoton decay width ratio we consider the dominant W ±, top and ottom loop contriutions in the presence also of an aritrary numer of, t V states): Γ h γγ = Γh γγ SM A [τ m W )] + 4v i 2 A[τ 3 )2 m ti )] Y ti m ti + j A[τ m 3 )2 Y j )] j + m k Q e.m. k )2 Y k j A [τ m W )] 4v + 2 3 )2 Yt SM A[τ m t )] m t + 3 )2 Y SM A[τ m )] m 2 A[τ m k )] 2 where A[τ m)] and A [τ m)] are respectively the form factors for spin /2 and spin particles [78] normalized such that A[τ m) ] and A [τ m) ] 7 withτ m) = m 2 h /4m2, v is the Higgs oson vacuum expectation value and m W the W ± - oson mass. The diagonal Yukawa couplings Y k and mass eigenvalues m k of the mass asis are derived like in the ottom uark case see the eginning of this susection) ut using now oviously the coupling, mass and unitary matrices for the k states in a given scenario. The Y k signs can e such that certain k exchanges interfere constructively with the W ± loop amplitude A [τ m W )] 8.3 whereas A[τ m k > 600 GeV)].0). Then it is clear that increasing the associated asolute charges Q e.m. k tends to enhance Γ h γγ relatively to the SM width). A nice feature aout the presence of highly-charged uarks is to greatly increase Γ h γγ and only this width, since the diphoton channels suffer from some of the largest experimental discrepancies with the SM. As another good conseuence of the field configurations selected aove, σ h B h WW will e significantly reduced as it seems indeed to e indicated y the data see Fig. ): B h WW is reduced due to the Γ h increase and σ h due to the destructive interference etween the or ) loop and the top uark loop contriuting to σ gg h [78]. Of course, this latter feature of destructive interference with the top contriution 0 must e preserved in the presence of additional V t or for instance. 2.3. The minimal models The comined theoretical conditions discussed in Section 2.2) for improving the fit of the Higgs data presented in Section 2.) leadto the following exhaustive list of minimal models for the V uarks. A first class of models, denoted as Models of type I, is defined y the following four possiilities for the field content:, ) t 3/6, ), ), /3 t, ) t or /6 ) t,, 5/6 ), ) t /6, ), ), /3 t, ) t or /6, ) t, 5/6 2),, t ) t,, ) t, 3/6 ), /3 t, ) t or ) t,, 5/6 3) /6 m k 9 Any variation of the physical top Yukawa coupling is induced y the Yukawa couplings in the interaction asis and the unitary transformation matrices which are oth constrained to reproduce as well the fixed top uark mass. 0 This feature is rendered possile, in contrast with fourth generation uark models, y the vectorial nature of the / whose mass origin does not reside exclusively in the EWSB.
44 N. Bonne, G. Moreau / Physics etters B 77 202) 409 49,, ) t,, ) t /6, ) /3, t, ) t /6, 4) where we have written the field components in their transposed SU2) group representations together with the hypercharge as a gloal suscript. The Models I2) i.e. defined y the field content of E. 2)) and I4) are characterized y a stale in the case where is the lightest field of all its multiplet partners namely and 2). Indeed, the only potential decay channel in I2), W, would then e kinematically closed. In I4), the decay channel through a virtual intermediate state, W W W, would e foridden y the asence of mixing recall that SM ottom uark). In I2) and I4), open decay channels for the partners could e, W + and 2 ) W + W + W +, where would then appear as missing energy at colliders. The comparale case where or 2 is the lightest field among all its multiplet partners leading to a stale or 2)doesnot occur in the parameter space we will consider. A similar discussion hold for and its partners within the Models I) and I3). A second class of models, Models II, is defined y these two possile field contents:,, t ) t,, ) t, 3/6, t) t, 7/6 ), /3 t, ) t /6 or, ) t 5/6. 5) These models are characterized y the dominant decay channel of the highest-charge component: ) W + t W + W + kinematically open in realistic frameworks), as allowed y the t t mixing for which, t ) has een added. The other possile decay into the t 2 instead of the t eigenstate is su-leading due to the phase space suppression induced y the t 2 mass or the three-ody nature of the ) decay if t 2 is virtual. The last type of models, Models III, is defined y ) t,,,, ) t, /6, ) t, 5/6 ) /3 and/or t, ) t /6. 6) Here the dominant decay of the highest-charge component is ) W W W kinematically open), as induced y the mixing allowed y the presence of, ). The similar decay otained y replacing with 2 has a much smaller rate. At this stage, it is interesting to realize a certain theoretical consistence: all the minimal models otained here are similar to concrete warped extra-dimension [43] and their dual composite Higgs [55] scenarios constructed to satisfy EWPT), in the sense that these concrete scenarios also possess the aove crucial features allowing to improve the Higgs rate fit. Indeed, the representations I, II, III in Ref. [43] with the extension of E. 6) therein) or B2 in Ref. [55] contain two custodians coupled via a Yukawa term as well as two custodians mixed together and with the uark through Higgs interactions, reflecting thus perfectly the V uark configuration of the present Models I2), I4), III. Furthermore, the emeddings IV of Ref. [43] or T3 of Ref. [55] have two custodians with a Yukawa coupling as well as two custodians with the reuired mixings, exactly as for the uark set-ups here in Models I), I3), II. The additional fields and mixings arising in these concrete realizations like, states or heavy KK towers) are not expected to pertur drastically the potential Higgs rate ameliorations, and on the contrary, could even add more freedom. Besides, considering here all in all a uniue set of V fields not a replica per generation corresponds to the assumption in Refs. [43,55] where typically the custodians for the first two uark and three lepton) SM generations decouple. We end up this susection y writing explicitly the agrangian for one of these models. With the field content in E. 5) for the Model II with say the, ) t 5/6 doulet, all the possile mass terms and Yukawa couplings appearing in the generic agrangian, invariant under the SU3) c SU2) U) Y gauge symmetry, are ) t II = Y H t c R + Y ) ) t Ht c R + Y H ) + Y /R t t H /R t R/ R/ ) ) ) ) t + Y H c R + Y t H R + Y H c R + Y /3 H R/ + m c R + m R /R ) ) ) + m + m ) t t + m ) ) R R R + m + H.c. 7) t t R where H represents the SM Higgs doulet, /R the fermion chiralities, the Y s dimensionless Yukawa coupling constants and the m s various V uark masses. et us remark that the Y, Y and Y /3 terms could each e split into two terms with different chirality configurations and coupling constants. A field redefinition rotating c R and R allows to eliminate the m term without loss of generality. The Yukawa couplings for the first two up-uark generations are not written in the agrangian 7) as their mixings with the top-partners t, t should e much smaller than the t t, t mixing. Indeed, new heavy t -like states are closer in mass to the top uark and the top is in general more intimately connected to the ultraviolet physics, like in warped/composite frameworks. Since the CKM mixing angles [79] Note that this multiplet contains a that can play the rôle of the usual singlet for the ottom Yukawa enhancement.
N. Bonne, G. Moreau / Physics etters B 77 202) 409 49 45 are typically small, the first two up-uark flavors should essentially decouple from the sector t, t, t. A similar discussion hold including the down-uark sector and the, components. 2 For example, the ottom Yukawa couplings and mass terms generated after EWSB y the agrangian 7) can e synthesized respectively in h ψ C ψ R and ψ M ψ R, within the interaction asis ψ =,, ) t, where the coupling and mass matrices read as vy / 2 vy / 2 0 C = Y Y 0 0 0 Y /3 2 Y Y /3 0 3. Fitting the Higgs oson rates, M = m m vy /3 / 2 vy / 2 vy /3 / 2 m. 3.. The theoretical parameter space We first consider the Model II which is uite attractive. In the left-part of Fig., we present a domain of the parameter space where all the theoretical values of the Higgs rates elong to the experimental σ regions [in the sense of Section 2.] which are shown on the right-part of Fig.. The Model II considered in this figure contains the, ) doulet of E. 5) and its fundamental parameters appear in E. 7). For this parameter space exploration, we have typically let the relative μ Xγ rate lying within a still acceptale.4σ region, to take into account an uncertainty in the QCD simulation of the efficiency for the gluon gluon fusion contriution cf. Section 2.). As the theoretical μ s uantities are normalized to the SM prediction, the QCD corrections arising in the V uark contriution should essentially compensate the QCD corrections of the SM rate. Within the domain of parameter space presented in the left-part of Fig., we oserve that all the V uark masses are well aove their strongest direct experimental constraints which are at most, m 2 > 6 GeV with the conservative assumption B 2 t W = ) [80], m t2 > 560 GeV again with B t2 W = ) [8], m > 6 GeV assuming B t W, like a 2 state, which is a good approximation as the channel t ) 2 W is su-leading) [80] and m > 560 GeV assuming similarly B W, as a t 2 state, in a good approximation) [8]. There are no existing searches so far for a particle with the uncommon main decay, t W + W + see discussion after E. 5)); anyway its mass values are uite high as illustrates Fig. we have taken 650 GeV as the lower limit and even higher for 2.The2 mass eigenstate decays either like the or as 2 Z, h leading to a final state which has not een searched so far. Identical considerations hold for the 3, 3 and t 3 eigenstates. Concerning the couplings, all the asolute values of the fundamental Yukawa parameters entering E. 7) have een taken larger than 0.5 not to introduce new unexplained hierarchies with respect to the top Yukawa coupling, Y, whose amount is close to unity as in the SM. The fundamental input parameter that is the ottom Yukawa coupling, Y, has also the same order of magnitude 3 as in the SM even if the asolute physical coupling is slightly enhanced typically y mixings to increase the decay channel). The asolute Yukawa couplings in the mass asis do not exceed 2.5 and are thus elow the usual perturativity upper ound at 4π. The acceptale domain in the left-part of Fig. is typically ounded from elow y the σ constraint on μ hz and from aove y the condition on μ Xγ. This ehavior of the Higgs oson rates is essentially due to the decoupling limit where m and m tend to high values in which the rates tend to their SM predictions. Similarly, on the figure, the independence of the smallest mass eigenvalue m from m, at high values of the latter relatively to m, is explained y the decoupling effect of m in the mass matrix [and reciprocally for m ]. It is also the case for m ut not exactly for m 2 as this mass matrix also involves m. It is remarkale that the domain in Fig., leading to Higgs rates in a good agreement with the present data, is relatively large. Similar domains arise for different values of the parameters which have een fixed for drawing this figure. et us finish this susection y discussing the indirect constraints on the V uarks. For the third generation uark sector, the tree-level corrections induced y the t t ) mixings on the t ) vertex are expected to dominate over the loop-level oliue corrections to the gauge oson propagators. Because of the relative heaviness of t states, the predicted value for the V t CKM matrix element, including the t t mixings, agrees with the experimental measurement otained without assuming 3 3 unitarity) through the single top production study [79]. In relation with the Z vertex, one could also try to address the EP anomaly on the forward ackward asymmetry for the ottom uark as done in the specific RS context [4,42,82,83], assuming a discrepancy not due to under-estimated experimental errors, ut this is eyond our scope. Concerning the interactions of leptons and first generations of uarks, one has to compute the corrections to the gauge oson vacuum polarizations induced at one loop y exchanged V uarks [84,85] in the present model. The values of the oliue parameters S, T 4 that we can reach elong to the σ regions induced y the long list of EW precision oservales 5 measured mainly at EP [79]. Thisistrue in particular for the parameters inside the domain of Fig. typically down to m 900 GeV. Moving down to m 000 GeV along this domain leads to T values up to 0.5 withs 0. 0.2) which would need to e compensated y other new physics effects than the V uark ones. Such effects might e induced y new fields heavier than the V uarks so that the former would correct T which is extremely sensitive to new physics effects via EW oservales measured typically at the per mille level) ut would leave the uality of the improved fit to Higgs rates mainly unaffected given its present large error ars typically of several ten s of percents). Such a scenario 2 The t or states could contriute to Flavor Changing Neutral Current FCNC) reactions which are experimentally well constrained; theoretically these FCNC contriutions rely precisely on the whole SM set of Yukawa coupling constants for uarks. The treatment of such a high degree of freedom in the parameter space is eyond thescopeof our study. 3 A precise reproduction of the ottom and top uark masses would reuire to include mixings with the first two generations. 4 S, T encode the new physics effects only so that those vanish for the pure SM case. 5 Remind that three crucial types of EW oservales restricting the plan S versus T are m W, Γ Z ll and the asymmetries sin 2 θ W ).
46 N. Bonne, G. Moreau / Physics etters B 77 202) 409 49 could e realized e.g. in a warped framework with relatively light custodians, heavy KK fermionic towers, heavy KK gauge osons and possily a gauge custodial symmetry protecting the T parameter) in the ulk. 3.2. The fits versus oliue parameters In the right-part of Fig., we show the theoretical predictions of the Higgs oson rates still within the Model II for a point of parameter space first optimizing the fit for a same fit uality then choosing the smallest S, T lack circles) and for another point favoring the oliue parameters S, T lack suares). Both points are compatile with the direct constraints on V uark masses. The circle-points in this figure show that it is possile to otain Higgs rates eing all within the σ regions. In this case, the fit is optimized in the following sense: starting from this situation where the four predictions for μ hγ, μ hz, μ V and μ Xγ are at the extreme σ distances, one cannot improve one of these four uantities without moving another one of those out of its σ region. One way of seeing this is as follows; the only possiility to increase μ Xγ while keeping μ hγ at σ is to increase B h γγ and decrease σ h.nowthis σ h decrease would worsen the fit on μ hz as the only possile compensation y a B h ZZ increase via a Γ h decrease is foridden if μ V is to stay at the σ level. The conclusion of this feature is that other parameters reaching the same uality of Higgs rate fit as aove can e found ut there exist no parameters improving the fit y comparison with the optimized situation descried in the previous paragraph. Furthermore, neither different/additional SU2) multiplets nor higher electric charges of V uarks relatively to the present minimal model could improve the fit in that sense. 6 These conclusions are the conseuences of a certain tension among the Higgs rate data which restricts a little it the potential fit ameliorations rought y V uarks whatever are the model and parameters). et us also mention here that improving the Higgs fit through an enhancement of B h γγ with a simultaneous suppression of σ h as induced here y V uark effects seems to e favored y the generic analysis at the level of cross sections and ranching fractions [66]. From a theoretical point of view, improving the fit on μ γ y increasing the hv V coupling from other origins of effects than the V uarks is at the price of extending the Higgs sector [86]. However, modifying this vertex, possily through a custodial symmetry reaking [75], is proaly the only way to reproduce the low μ hw experimental value without affecting too much the perfect agreement on μ hz of the SM [cf. Fig. ]. The suare-points in Fig. correspond to S, T values clearly inside the ellipse associated to the σ domain for comined EWPT [79]. These points improve the fits of all the Higgs rates compared to the SM, especially μ V, μ Xγ, μ γ, μ hw and with the exception of μ hγ the same typical deviation from data as in the SM), μ hz larger ut still acceptale deviation). This configuration leads to a clear improvement of the gloal χ 2 function compared to the SM, as written in the figure [for μ hγ, μ hw only the most precise value, i.e. from ATAS + CMS, is included in χ 2 whereas for μ V only CDF + D0]. 7 In addition to improvements similar to those, the circle-points all elong to the σ regions of the Higgs rates with a remarkale increase for μ γ ; nevertheless, the associated S, T values are slightly outside the σ ellipse [79]. There might however e other kinds of effects from the physics underlying the SM responsile for such necessary small T compensations S value eing not prolematic here) which could even let essentially unchanged the Higgs fit induced y the V uark effects as descried at the end of Section 3.. Therefore, a noticeale ut acceptale tension appears etween optimizing the Higgs rate fit y introducing highly-charged V uarks and still respecting the EWPT. 3.3. The other models An example of parameter domain leading to Higgs rates within the σ regions is also shown for the Model I with the, ) doulet [defined y E. 2)] in the left-part of Fig. 2. The fundamental parameters are noted similarly to the Model II discussed in previous susection. In this case, the constraints on m deserve some more attention. Indeed, the particle is stale for the reasons exposed in Section 2.3 that apply here due to the kinematical feature, m < m m eing the mass of the non-mixed and thus eigenstate ), visile in Fig. 2. Now such a stale particle has never een searched at colliders so far, ut one can try to extrapolate constraints on it from investigations on other Heavy Stale Charged Particles HSCP) even if this is a non-trivial task; constraints have een imposed on long-lived supersymmetric partners namely a gluino g, atau-slepton τ,atop-suark t and the most stringent ones have een derived recently at the HC [87] see Ref. [88] for analog studies at the Tevatron). After the hadronization stage, a long-lived gluino should form an R-gluonall gg with a proaility of typically 30% ased on simulations) and a color-singlet meson g u, d, s uarks) with Q e.m. =± also for a significant fraction, whereas a long-lived stop might form a meson t = d, s) with a fraction typically aout 50% [89]. To get an idea of a possile mass ound on the stale which will also form a Q e.m. =± R-hadron 8,more precisely a aryon uu, one could apply the mass-dependent limits on the g t ) production rates otained in Ref. [87] to the pair production cross section calculated at NNO for the 7 TeV HC. We find, m 850 GeV 800 GeV). Nevertheless, there are various limitations to the validity of this extrapolation: the fraction of uu should e simulated specifically e.g. with the PYTHIA or HERWIG simulators) and is certainly different from the g t ) fraction, while the spin configuration and/or color-multiplet also differ from each other. Furthermore, the nuclear interactions experienced in matter y R-hadrons, suffering from large uncertainties, may lead to charge exchange; a recent work [90] modeling the HSCP nuclear interactions favors a scenario where the majority of R-hadrons made of a gluino or a suark would emerge neutral in the muon detectors. Assuming this result extends to all the R-hadrons made of the, ) and using again the exclusion limits on the gluino stop) production rates [87] otained now under this charge suppression 6 Of course e.g. increasing the electric charge of V uarks could allow to access larger V uark masses achieving identical goodness of fits. 7 Correlations are neglected. 8 Inelastic hadronic interactions could change the charge-sign of the exotic hadron [96].
N. Bonne, G. Moreau / Physics etters B 77 202) 409 49 47 hypothesis, we find, m 750 GeV 800 GeV). As for the limit on the τ production rate, it ends up at a 500 GeV mass [87]. Hence, taking the mean of the aove four estimated limits, we otain an indicative ound, m 800 GeV, that is represented over the domain drawnintheleft-partoffig. 2; one sees that a large part of the domain is passing this indicative test. There also exist studies on long-lived charged massive particles outside colliders see e.g. the reviews in Ref. [89] and Ref. [9]) leading in particular to limits on their aundance in ordinary matter; these particles can ind to a nucleus forming anomalously super)heavy isotopes which have een searched, or even fall onto/through oceans and lakes to form heavy water molecules. For example, constraints on astrophysical fluxes of those particles have also een looked at. 9 However, no dedicated analysis outside colliders) has really een performed to constrain significantly the mass of stale color-triplet fermions with high fractional electric charges. The eigenstate decays as, W + or 2 ) W + hw +, Z 0 W + open in most of the considered domain). In this case the stale could also e searched at colliders as missing energy associated with oson production, ut there were no investigation so far on these kinds of decays within the present framework [the mass, m, has typically high values anyway as shown in Fig. 2]. Similarly, the 2 decays, 2 h, Z 0 and 2 ) W W + W,leadto specific signatures not yet analyzed. The constraint for the unmixed eigenstate mass, m > 560 GeV since B W, as possily for a t 2 ) [8], is also clearly respected. Finally, the -sector is exactly as in the Model II of previous susection so that the positive conclusions for the 2,3 mass ounds are similar. The suare-points in the right-part of Fig. 2 for the considered Model I correspond to reasonale S, T values at the order of the σ ellipse of EWPT [79]. Those theoretical predictions improve the fits of most of the Higgs rates compared to the SM, leading to a net improvement of the χ 2 value. The circle-points even all elong to the σ regions with again a remarkale increase for μ γ ;however,the associated S, T values are now clearly outside the σ ellipse [79]. OthertypesofnewphysicseffectscouldreducetheT parameter down to acceptale values the S parameter eing already in a realistic range as discussed in the end of Section 3.. The Models of type III [see E. 6)] lead to similar allowed domains of parameter space as aove, as well as comparale ualities of the Higgs rate fits. The main difference with previous models concerns once more the type of ound applying to the mass of the V uark with the highest asolute electric charge, namely here. As explained in Section 2.3, it decays predominantly as, ) W W W, whose final state mimics that of, 2 t W W + W. In otained acceptale parameter ranges, the m values stand inside the interval 700 000 GeV eing clearly aove the experimental ound, m > 6 GeV B WW ) [80]. In the Models III, there are no stale V uarks. Of course, we are not going to present detailed numerical results for the various minimal models of types I, II and III presented in Section 2.3, ut similar ualitative and uantitative results to the ones presented throughout this etter hold. We finish this part with a discussion on the composite Higgs models. In this context, the strong dynamics can induce sizale corrections to the Higgs couplings with gauge osons which are ale to reak unitarity in the EW gauge oson scattering efore one reaches the cutoff scale Λ typically Λ 3 TeV). Nevertheless, the contriutions from composite spin resonances, appearing generally well elow the compositeness scale Λ in such a case, are expected to restore the unitarity of the theory up to Λ [92]. Within this context or its dual description with a warped extra dimension), oth the Higgs couplings to gauge osons and fermions can receive corrections, and, oth the composite fermionic and non-fermionic ound states can e exchanged in the loops inducing the hγγ coupling possily increasing the relevant ranching B h γγ. Hence, the Higgs couplings would have additional sources of deviations compared to the context of the present etter where the deviations originate only from the fermion sector. In this composite Higgs framework, our effective study would thus constitute a guide specifically on the Higgs coupling corrections from the fermion sector. A possiility is that the composite spin states are all at the cutoff scale Λ and in turn that the corrections to the Higgs couplings with gauge osons are sufficiently small so that the unitarity of the theory is preserved up to Λ. In this situation, the deviations to the Higgs couplings from the fermion sector could e the main ones. This situation is thus an example of realization of the framework studied throughout the present etter. 4. Conclusions We have shown that the presence of V uarks is sufficient to modify the SM Higgs oson rates such that all those elong to the present experimental σ regions. The minimal field contents and gauge group representations of V uarks allowing to achieve such improvements have een otained. The key idea is to introduce V uarks with high-enough electric charges to increase sufficiently the diphoton channel rates. Simultaneously, all the in)direct constraints can e satisfied, even if we have pointed out a little tension etween optimizing the Higgs rate fit and respecting the EWPT. The models otained predict a rich phenomenology at HC with several exoticcharge uarks possily around the TeV. For example, the pair production of,decayingas t W + W +, could lead to a spectacular final state with six W gauge osons two more W s than in the pair production [93]). One must mention that oviously the present measurements of the Higgs oson rates have large uncertainties. If the next data, in particular from the 8 TeV HC, confirm the existence of a 25 GeV Higgs field, two typical situations might arise. First, the main features of the present rate measurements, like diphoton channels significantly larger than in the SM, might e confirmed pointing towards manifestations of a theory eyond the SM. In this case, a simple adjustment of the present fundamental parameters should suffice to optimize the Higgs rate fit. Even the conclusion on the est-fit configuration underlined here would remain unchanged with respect to the central values; it is moreover true for any pure V uark model independently of its field content and gauge multiplets). A second possiility is that significant changes appear among the Higgs rate measurements so that the new diphoton rates get closer to 9 et us just mention the following; it has even een proposed some time ago that certain charged massive particles could also constitute candidates for the dark matter oftheuniverseseeforinstancerefs.[97 00]).