Vector resonances at LHC Run II in composite 2HDM

We consider a model where the electroweak symmetry breaking is driven by strong dynamics, resulting in an electroweak doublet scalar condensate, and transmitted to the standard model matter fields via another electroweak doublet scalar. At low energies the effective theory therefore shares features with a type-I two Higgs doublet model. However, important differences arise due to the rich composite spectrum expected to contain new vector resonances accessible at the LHC. We carry out a systematic analysis of the vector resonance signals at LHC and find that the model remains viable, but will be tightly constrained by direct searches as the projected integrated luminosity, around 200 fb$^{-1}$, of the current run becomes available.


I. INTRODUCTION
Recently both the ATLAS and CMS collaborations updated the direct search limits on heavy vector resonances by using 13 TeV data with integrated luminosity ranging from 12 In TC the Higgs couplings, which are constrained by LHC measurements within a few percent uncertainty, depend on the particular ultraviolet (UV) completion used to transmit EW symmetry breaking to the Standard Model (SM) fermion sector. To simplify the phenomenological analysis and its comparison with LHC data we choose a simple TC model as a template for more general extended TC theories. In the TC model at hand the interactions between the technifermions and SM fermions are mediated by an EW doublet scalar field [8][9][10][11][12][13] (which we treat as elementary but can in principle be composite as well).
The scalar sector of such UV complete model corresponds to that of a composite two Higgs doublet model 1 (2HDM) [15][16][17][18][19][20][21]. Due to the strong interacting dynamics the model features a spectrum of higher-spin composite states, which distinguish this model from the ordinary type-I 2HDM. The main goal of this paper is to test the viability of this model given the LHC measurements of the light Higgs couplings to SM particles and LHC direct search con-1 Such name has been used originally in the context of composite pseudo-Goldstone boson Higgs models [14]. straints on heavy scalar and vector resonances, and to determine the expected reach of LHC Run II for the vector heavy states appearing in this model. The paper is organized as follows: In section II we will first briefly introduce the model.
In section III we update the fit of the model parameters to concur with the LHC data on the Higgs couplings, and in section IV we confront the signals of the vector resonances of the model with the current direct search constraints and present projections for the near future reach of the LHC experiments. Then in section V we offer our conclusions and a brief outlook for future research.

II. COMPOSITE VECTOR BOSON INTERACTIONS
The model we study, a composite 2HDM [16,17], extends the particle content of the Next to Minimal Walking Technicolor (NMWT) [22][23][24] by a scalar field, H (to be considered as a remnant of a UV complete theory, not necessarily strongly interacting), which features the same couplings as the SM Higgs field, and moreover couples to the technifermion fields via a renormalizable Yukawa interaction with coupling y TC . At an energy below the scale of the TC strong interaction, Λ TC ∼ 4πv w 3 TeV, the strongly interacting technifermions form a tower of composite states, analogously to QCD, whose interactions are encoded in an effective Lagrangian featuring the same global symmetries as the fundamental theory. The scalar sector of the 2HDM effective Lagrangian is expressed in terms of H and a composite matrix scalar field M as follows and At lower order in y TC , considered to be perturbatively small, the composite vectors A µ L and A µ R couple only to the field M [17], with whereW andB are the SU(2) L and U(1) Y gauge fields, respectively. In Eq. (5) we neglected derivative couplings of the composite vectors given that these are anyway constrained to be small by the measured small values of the oblique parameters [25,26]. The fermion sector is the same as that of the SM. The full Lagrangian, as defined in Eqs.
In the next section we perform a basic analysis of the phenomenological viability of composite 2HDM at LHC.

III. VIABLE PHENOMENOLOGY AND THE LHC FIT
We (1), and g TC , m A , r 1 , and r 2 , from the vector sector in Eq. (5). To assess the viability of the model, we scan the parameter space for data points that produce the observed SM mass spectrum, and satisfy the lower bounds on the scalar and pseudoscalar masses as well as the experimental bounds on the EW oblique parameters [25,26] S = 0.00 ± 0.08 , T = 0.05 ± 0.07 , ρ(S, T ) = 90% .
The region of parameter space that we scan, as described in [17], is limited by potential stability and perturbativity in λ H , λ M , and y TC , while the order of the coefficients c i is fixed by dimensional analysis [28]. For the remaining vector sector parameters we choose values in the region, natural for TC, 500 GeV < m A < 2500 GeV , 2 < g TC < 6.5 , where we impose the relation r 1 = −r 2 , which cancels the SM Higgs field coupling to the axial combination A µ L +A µ R , to simplify the phenomenological analysis without compromising the viability of the model. Finally, we select the data points that satisfy the LHC constraints on the Higgs couplings to W , Z, γ, b, and τ , as done in [17]: for this purpose we calculate χ 2 at each viable data point for the five Higgs coupling strengths, defined bŷ where X is a possible state produced in association with the light Higgs, and jj a particle pair. The coupling strength values measured by both ATLAS and CMS [29] in inclusive processes are summarized in Table I. The Higgs couplings relevant for this analysis are those of SM particles and new resonances, contributing to leading order loop couplings, whose coupling coefficients are defined where all the fields in the equation above are physical eigenstates. The coefficients of the SM Higgs linear couplings to matter fields in Eq. (12) can be expressed in terms of the Lagrangian parameters by where s α , c α , t α are shorthands for sin α, cos α, tan α, respectively, with α, β defined by the rotation matrices The coupling coefficients of the charged vector resonances in Eq. (12) can be written in compact form by expanding at leading order correction in and x as where As one can see from the last of Eqs. (16), the light Higgs coupling to W is negligible at leading order: this is a consequence of setting r 1 = −r 2 , Eqs. (10), which makes the mixing term between the axial composite vector field and the SM gauge field, Eq. (A2), small in the limit of small . Given that the heavier vector resonances couple to SM fermions only through the mixing with the SM gauge fields, also the W couplings to SM fermions are small. Finally, the same statements are true also for Z , given that setting r 1 = −r 2 in Eq. (A1) makes the mixing term between axial and gauge vector fields small.
The charged non-SM particles in Eq. (12) contribute only to the diphoton decay, while the decay rates of SM particles get rescaled by the square of the corresponding coupling coefficient. 2 We then select the data points satisfying the 90% confidence level (CL) constraint P χ 2 > χ 2 min > 10% (18) with 7 d.o.f., given that the number of observables is twelve while the effective free parameters is five. To see that the effective free parameters are just five one can notice that it is possible to fit simultaneously only five (three coupling strengths plus S and T) of the observables. 3 Of the 10000 scanned data points satisfying perturbativity, potential stability, direct search constraints in Eqs. (8), and producing the observed SM mass spectrum, a total of 1381 points satisfy also the constraint in Eq. (18): in Fig. 1 these points are shown in green (68% CL) and blue (90% CL), while those in orange are viable with 95% CL, in the plane of the fermion and sum of the charged heavy vector resonances' coupling coefficients. 4 As 2 All the relevant expressions, including those of the coupling coefficients in terms of the independent parameters of the model, are given in [17]. 3 The effective free parameters for the Higgs linear couplings are just three: one for the fermions, one for the EW vector bosons, and one for the new physics contribution to the loop mediating the Higgs decay to diphoton. 4 Notice that the contribution of the charged heavy vector resonances to the diphoton decay rate is proportional to the squared sum of their coupling coefficients, given that their masses are much heavier than the light Higgs mass. neglecting higher order effects such as parton showering, intial and final state radiation, and detector resolution. The most constraining final state turns out to be dimuon production for the neutral vector resonance, and charged lepton and neutrino for the charged vector resonance. These are electroweak processes and therefore are not too sensitive to QCD effects or NLO corrections. Furthermore, the uncertainty associated with our neglect of the detector resolution effects is mitigated by the fact that the experimental resolution for lepton momentum is very high. Thus we find it justifiable to perform the initial analysis at parton level. The relevant production channels we present here are the Drell-Yan production of a Z subsequently decaying to a dilepton or a diboson, expressed by the Feynman diagrams in Fig. 2, and the production of a W decaying to a charged lepton and a neutrino. We find that 90% of the scanned data points are already ruled out by the W search, 98% can be ruled out with the data set of 45 fb −1 and nearly all (99.8%) of the scanned parameter space points are within reach with 200 fb −1 .
The limit on the diboson channel is less tight, as can be seen from Fig. 5, and most of the scanned data points are below the current limit [4], shown by the red solid line. The feature seems more pronounced in the diboson channel, but is present also in the dilepton and lepton plus neutrino channels. We performed the goodness of fit analysis by scanning the model's parameter space for data points producing a viable SM particle mass spectrum, and selecting those points that satisfy at 90% CL the experimental constraints on those couplings as well as the lower bound on the mass of a heavy Higgs scalar. The selected data set consists of 1381 viable data points. We then implemented the model in the event generator Madgraph [30] and calculated, for each viable data point, the cross section at the parton level for the dilepton and diboson channels of Drell-Yan production of heavy neutral vector bosons, and lepton plus neutrino channel for the production of a charged vector boson at the LHC. By comparing these results with the latest LHC constraints we showed that a major portion of the otherwise viable data points is already excluded by the direct searches of heavy vector resonances in the dilepton and lepton plus neutrino channels, while almost the entire parameter space we have considered will be tested by the end of LHC Run II in 2022. On the other hand the experimental constraints on the diboson channel are less tight as they are able to rule out only a smaller portion of the selected data set. These results show that the LHC experiments have the potential to discover signatures of TC in direct resonant production channels. Alternatively, if no new heavy vector boson resonances are discovered, very stringent constraints will be imposed on the TC framework of the type we have considered here, as a significant portion of parameter space naturally selected by naive dimensional analysis would be ruled out.

V. CONCLUSIONS AND OUTLOOK
Heavy vector boson direct searches at the ATLAS and CMS experiments can in principle complement flavor experiments carried out at LHCb, whose 2015 data show large deviations from the SM predictions in flavor violating observables which might well be explained by a new heavy neutral vector particle [34][35][36][37]. Flavor violating interaction terms in extended TC models are a natural by-product of fermion mass terms, and therefore would be a well motivated extension of the present template TC model.