LHC data and aspects of new physics

We consider the implications of current LHC data on new physics with strongly interacting sector(s). We parametrize the relevant interaction Lagrangian and study the best fit values in light of current data. These are then considered within a simple framework of bosonic technicolor. We consider first the effective Lagrangian containing only spin-0 composites of the underlying theory, which corresponds to a two Higgs doublet model. With respect to this baseline, the effects of the vector bosons, a staple in strong interacting theories, are illustrated by considering two cases: first, the case where the effects of the vector bosons arise only through their mixing with the electroweak SU(2)L gauge fields and, second, the case where also a direct interaction term with neutral scalars exists. We find that the case with a direct coupling of the composite vector fields to the Higgs allows the tested model to fit the experimental results with goodness comparable to that of the SM.


Introduction
The recent discovery of a light scalar with properties compatible with those of the Standard Model (SM) Higgs boson, h 0 , imposes new experimental tests on previously viable beyond the Standard Model (BSM) theory frameworks. Fervent activity in this direction has focused mostly on the possibility that a new charged particle could enhance the Higgs decay rate to two photons [1][2][3][4][5][6][7][8][9][10][11][12][13]. This is measured at LHC and Tevatron, with the full dataset, to be slightly enhanced compared to the SM prediction [14][15][16][17], with the diphoton signal strength equal to 1.55 ± 0.31 at ATLAS and 0.78 ± 0.28 at CMS. While most of the efforts were focused on the Higgs physics associated with a new charged scalar or a vector fermion, both of which naturally arise in supersymmetry [18][19][20][21][22][23][24] or composite Higgs frameworks [25][26][27][28], less extensive research has been conducted recently on the possibility that a heavy charged vector boson be responsible for the observed deviations of the Higgs couplings from the corresponding SM predictions [9,[29][30][31].
A heavy charged vector boson is naturally predicted by phenomenological theories featuring additional gauge groups, like Technicolor, Little Higgs, and Kaluza-Klein models [32][33][34][35][36][37]. In this paper we want to explore the effect of couplings of a heavy W boson to the Higgs on LHC and Tevatron observables. To approach this task we first, in section 2, perform a fit with the parameters of a simple effective Lagrangian featuring rescaled Higgs couplings to SM particles as well as to a heavy charged scalar and a heavy charged vector boson. To have a concrete model to test against the results of the general fit, in section 3 we introduce a low energy effective Lagrangian for a simple bosonic technicolor model, the bosonic Next to Minimal Walking Technicolor (bNMWT) [38][39][40][41]. The low energy effective Lagrangian for the scalar sector of bNMWT corresponds to a Type-I Two Higgs Doublet Model (2HDM) [42]. We scan the allowed parameter space of this model for data points viable under direct search constraints and electroweak (EW) precision tests, compare the data points to the measured Higgs physics observables, and find the optimal fit of the model. In section 4 we introduce two composite vector boson triplets in the low energy Lagrangian, while conserving gauge invariance at the microscopic level, which both mix with the SM W ± and directly couple to h 0 , and repeat the goodness of fit analysis above to determine the optimal values of the W and W couplings to h 0 . We illustrate separately the features which originate from the mixing and from the direct coupling. Our essential conclusion is that mixing alone produces a negligible change of the fit to the current data, while a direct interaction gives a more relevant improvement of the fit, at a level of goodness comparable to that of the SM.

LHC and Tevatron data fit
In this section we perform a fit to LHC and Tevatron data to determine the values of the Higgs couplings favored by the experiment. We follow the methods of previous similar analyses [1][2][3][4][5][6][7][8][9][10][11][12][13] while updating their results with the latest experimental data, featuring up to 8 fb −1 of additional integrated luminosity relatively to the previous datasets. The following model-independent analysis serves as a comparison with the model-specific goodness of fit study we perform in sections 3, 4.
The experimental results are expressed in terms of the signal strengths, defined aŝ where Ω is the efficiency associated with the given final state Ω in an exclusive search, while for inclusive searches one simply has σ tot = σ pp→h(X) , the h production total cross section. The signal strengths from ATLAS, CMS, and Tevatron are given in table 1. All results above for Higgs decays at ATLAS [43,44] and CMS [15,45], as well as those at the Tevatron [16,17], use the full respective dataset, with the only exception being the coupling strength for the decay to ττ at ATLAS [46] which uses 13 fb −1 of integrated luminosity at 8 TeV and 5 fb −1 at 7 TeV. The bb quark pair is produced in association with a vector boson, with an efficiency assumed equal to one, while the other searches are inclusive. We also include in our analysis the dijet associated γγ production based on the full dataset [14,15], with signal strengths and efficiencies 1 listed in table 2.
Within the class of models we will study, the part of the Lagrangian relevant for the recent LHC data is of the form where the fourth and fifth terms involve, respectively, charged (but color singlet) vector and scalar bosons. We fix the mass parameters to the physical mass of the corresponding particle and v w to the EW vacuum expectation value (vev), v w = 246 GeV. Application of the Lagrangian in eq. (2.2) in our study requires on one hand that the dimensionless couplings, i.e. the Yukawas, are sufficiently small. Practically one needs only worry about the coupling of the top quark, and in our numerical analysis we demonstrate explicitly that on the average over the viable part of the parameter space we have On the other hand, we must require that the masses of the composite vectors and charged scalars are smaller than the cutoff scale below which the effective description is expected to be valid. In our analysis we choose the cutoff scale to be Λ T C ∼ 4πv w ∼ 3 TeV. The effects of composite vectors and charged scalars in our results are parametrized only in terms of the dimensionless coefficients a V and a S provided that the states W and S ± are sufficiently heavy; see the discussion around eqs. (2.5)-(2.8). In the model considered in section III and IV this requirement is satisfied since the composite states originating from a new strongly interacting sector naturally have their masses in the TeV range.
Consequently to eq. (2.2), the cross sections and branching rates relevant for Higgs physics are related to the corresponding quantities of the SM in a simple way. We definê and then, in terms of the coupling coefficients in eq. (2.2), we havê

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where the gg and h final states are produced through a loop triangle diagram with only quarks as virtual particles. The calculation of the Higgs decay rate to two photons is more involved. By using the formulas given in [47], we can write where the index i is summed over the SM charged particles as well as S ± and W ± , N i is the number of colors, e i the electric charge in units of the electron charge, and the factors F i are defined by (2.7) In the limit of heavy W ± and S ± , one finds Given the experimental lower bounds on m W and m S [48,49], the error on F W is irrelevant while |F S | gets enhanced by about 10% for m S = 150 GeV: since the experimental error on µ γγ is large and constructive interference of the S ± and W ± is favored by the experiment, we also assume the error involved by the above approximation for F S to be negligible. We notice also that in the limit of heavy masses for the charged scalar and vector bosons the light Higgs decay to such (virtual) states is highly suppressed by kinematics, and therefore no additional decay channels have to be taken into account besides those of the SM.
To evaluate the theoretical predictions for the measured observables, we need the SM production cross sections for the Higgs boson and the SM branching ratios for its decay. The production cross sections of a Higgs boson with a 125 GeV mass at the LHC and Tevatron for the final state Ω are given [50]  To determine the experimentally favored values of the free parameters a f , a V , a V , a S , we minimize the quantity (2.12) where the measured values and errors of the observables are given in tables 1, 2, while the numerical predictions of the theory are easily determined from eqs. (2.3)-(2.8), with the SM input values given in table 3. In defining χ 2 above, we assumed the correlation matrix to be simply the identity matrix. We note that it is not possible to constrain both a S and a V since they both contribute only to the diphoton decay. The optimal values given below then refer to either of the two taken equal to zero: (2.14) The results above are derived in the limit of heavy S ± and W ± . For masses of the same order of m h the optimal a S and a V can be straightforwardly derived by dividing the corresponding values in eqs. (2.13) by the ratio of the decay amplitudes F W and F S , eqs.(2.6), divided each by their respective heavy particle limits given in eqs. (2.8). We stress that because of the limited number of observables used in the analysis and the fact that possible systematic errors are unaccounted for, the P -value quoted above (and also the ones evaluated in the subsequent section) should be used exclusively to compare the models studied in this work with the SM. The SM produces for only the Higgs physics data, which indeed is a rather ideal result. The inclusion of the EW parameters S and T (S = T = 0 for SM) [52][53][54] in the fit improves further the quality of the fit: which shows that the SM is still perfectly viable in light of current collider data.
In the next section we use the Higgs physics constraints derived here to test the viability of a simple bosonic walking technicolor model [41] whose low energy effective Lagrangian belongs to the class specified by the generic Lagrangian of eq. (2.2).

JHEP01(2014)041 3 Model and constraints
In Technicolor (TC) an additional, confining gauge interaction causes techniquarks, charged under TC and the EW interaction, to condense and break spontaneously the EW symmetry [32,33]. This mechanism allows the W and Z bosons, and the composite states of the strongly coupled TC sector to acquire mass, while the SM fermions remain massless.
The TC sector we consider has SU(2) L ×SU(2) R chiral symmetry and is described in terms of the complex composite meson field M T = (φ + , φ 0 ) by an effective Lagrangian To provide mass for ordinary matter fermions, an additional interaction linking them to the TC condensate has to be provided. In bosonic TC models, this link is provided by one (or more) elementary scalar(s) [55][56][57][58][59]. While in this paper we consider nonsupersymmetric theories, bosonic technicolor effective Lagrangians also arise as low energy realizations of supersymmetric technicolor theories [60][61][62]. In the context of bosonic TC, it is therefore the techniquark condensate that breaks EW symmetry, while the scalar plays the role of "spectator". The Higgs Lagrangian is written in terms of the usual complex doublet H as The link between the technicolor and the SM matter fields obtained at the effective Lagrangian level is due to the Yukawa couplings of the Higgs field H. In addition to the usual couplings to the SM matter fields, these include also the couplings to techniquarks, y T CΨL HΨ R . When constructing the effective Lagrangian for the composite sector of the theory, this coupling generates further terms in the effective TC Lagrangian so that the technicolor sector is described by [41] where c i are unknown parameters and f is the vev of M . Since eq. (3.4) is an effective Lagrangian description, its parameters are supposed to encode higher order and nonperturbative corrections from the underlying theory. This justifies the application of the model at tree level in our study. The model that we consider is therefore specified by the effective Lagrangian

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where L SM is the usual SM Lagrangian containing the sectors L Higgs and L Yuk . The coefficients c i in eq. (3.4) are estimated by naive dimensional analysis [63,64] to be Finally, the requirement for the potential to be bounded from below imposes The mass eigenstates are obtained by diagonalizing first the kinetic terms and then applying a rotation to diagonalize the mass terms in the scalar and pseudoscalar sectors. First, the Higgs fields M and H are expressed as After this transformation, the fields M 1,2 are written in terms of the charge eigenstates as (3.10) The rotation angles α and β determine the physical states in the scalar and pseudoscalar sectors so that the Goldstone bosons, G ± and G 0 , provide the respective longitudinal components of the W ± and Z bosons, while h 0 , H 0 , A 0 , and H ± are the neutral scalars, pseudoscalar, and charged scalar mass eigenstates, respectively: (3.11) The mixing angle β is defined so that tan β = f 2 /f 1 . The masses of the lightest composite states, including neutral scalars, are naturally expected to be of O(Λ T C ) ∼ 1 TeV. For bosonic TC the strong dynamics effect on the Higgs mass can be somewhat tamed by the mixing of the composite and elementary neutral scalar states, since the latter state can have a squared mass term much smaller than the former. This mechanism is analogous to the TeV-scale seesaw recently put forward in [65]. Moreover, it has been shown [66] that the top-quark loop contribution can greatly reduce the tree level TC prediction on the Higgs mass. A further suppression of the light Higgs mass is expected in NMWT because of walking dynamics [39]. From here on we assume that one or a combination of JHEP01(2014)041 the mechanisms above is at work and use m h 0 = 125 ± 1 GeV as an input to fix the value of one of the free parameters of the low energy effective theory.
To compare the model predictions with the LHC and Tevatron measurements, we need the coefficients of the SM Higgs linear couplings introduced in eq. (2.2) to be expressed in terms of the bNMWT parameters: 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 in eq. (3.11) and ρ by We are now ready to test the particle spectrum and its couplings against the latest experimental data. First, we scan the parameter space looking for data points that produce the right SM mass spectrum and satisfy the direct searches for charged particles at LEP [49] and a heavy neutral scalar at LHC [67] as well as the EW precision constraints from the S and T parameters [52][53][54]. More specifically, we impose the constraints (3.14) The quantity r(S, T ) is the correlation coefficient for the S and T parameters [54]. The constraint on the trigonometric functions is to ensure that the heavy Higgs does not couple to SM fermions more strongly than a SM Higgs with the same mass does; this allows us to use straightforwardly the LHC constraint on m H 0 . The upper bounds on m A 0 , m H 0 are enforced by the cutoff of O(Λ T C ≈ 4πv w ) of the effective Lagrangian. We also require the free parameters to produce the remaining SM mass spectrum and satisfy the bounds in eq. (3.8). Then, we scan for such viable points in the domain 2HDM by using the formulas in appendix A. The disclaimer is that we are testing only a portion of the parameter space available to such a model, and more precisely the range of values typical for underlying strong dynamics. Note that the value of y t is fixed by the Higgs sector, and in the scan we only monitor that its value remains below 4π. Actually, over the scanned 5000 viable points, we find that on the average y t = 0.92 ± 0.17 with the maximum (minimum) value being 1.48 (0.27). Hence, the leading order perturbative treatment of the top Yukawa coupling which we have applied in our analysis is justified.
We also check that the perturbative calculation of the diphoton decay rate holds for each of the 5000 scanned data points. In doing so we perform a rough estimate of the loop amplitudes by assuming the virtual particles to have momenta much smaller then their masses and then by integrating the phase space volume up to the typical energy of the process, which is equal to the light Higgs mass. While such an estimate misses the enhancement of the amplitude given by on-shell virtual particles and the contribution of high momenta, it still allows us to compare the relative order of magnitude of the two loop contributions to the one loop order amplitude. The leading order contribution to the Higgs decay amplitude to two photons is given by a virtual W at one loop, which we simply label A 1L W . At next to leading order virtual scalars at two loops give the largest contribution, since the cubic couplings can be of O(v w 4π) 2 , while the other relevant couplings are SM-like in size. Scalar cubic and quartic couplings, both large, might indeed give non-perturbative contributions at even higher order. For this reason, besides the ratio between the two loop leading contribution in figure 1 (A 2L s ) and A 1L W , we also calculate the ratio between A 2L s and the virtual H ± contribution at one loop (A 1L H ± ), both of which are given below: To ensure consistency of the perturbative calculation of the light Higgs decay rate to diphoton, we require with the ratios estimated by eqs. (3.17). We find that all of the 5000 scanned data points satisfy the first relation above, while 609 do not satisfy the second relation. In all the following results we retain only the scanned data points that satisfy eqs. (3.19). The distribution of viable data points of the bNMWT allowed parameter space in the (S, T ) plane is shown in figure 2. The 90% Confidence Level (CL) allowed region is shaded in green while the viable data points featuring m 2 H > 0 (m 2 H < 0) are plotted in black (grey). We make this distinction because for positive m 2 H the SM Higgs sector alone would not break EW symmetry, and therefore EW symmetry breaking is generated through bosonic TC interactions. The black dots are, thus, relevant for bNMWT while the grey ones refer more generically to the Type-I 2HDM. It is clear that the viable region in S and T accessible by bNMWT is very limited.  In figure 3 we plot the viable data points in the (a S , a f ) and (a S , a V ) planes, respectively, together with the 68% (green), 90% (blue), and 95% (yellow) CL regions obtained in the previous section: these plots represent a slice of the a f , a V , and a S parameter space passing through the optimal point (blue star) given in eq. (2.13). There is a perfectly specular viable region, which we do not show here, intersecting another χ 2 global minimum point, obtained by flipping the signs of a V , a f , and a S in eq. (2.13). In figure 3, left panel, the upper viable region, containing the best fit point, obtains the observed slight enhancement of the Higgs diphoton decay rate exclusively by the charged scalar contribution which interferes constructively with the W boson contribution. This results from a rather large linear coupling of h 0 to S ± . In the lower viable region, the slight enhancement of the Higgs diphoton decay rate is entirely due to the SM fermions which couple to h 0 with the same sign as W ± and, therefore, give constructive interference, while the scalar interferes destructively to balance an otherwise excessive enhancement of the decay rate to two photons. The same comments apply to the viable regions presented in figure 3, right panel.

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The bNMWT data points are closely clustered around the SM values. This was somewhat expected, because of the small mixing of the two neutral Higgs fields for a heavy JHEP01(2014)041 Finally, in figure 4 we show the bNMWT data points in the (a V , a f ) plane that passes through the SM point (a S = a f = a V = 0) to which they approximately belong. In bNMWT the Higgs-vector boson coupling is always reduced compared to its SM value, as shown in figure 4, while the experiment favors an enhancement of the same coupling. While bNMWT looks generally disfavored compared to the SM, most of the scanned data points lie within the 90% CL region.
We note that figure 2 also includes bNMWT points with flipped sign of a f , a V , and a S . These points belong to the plane passing through the specular optimal point, and therefore we do not include them in figures 3 and 4.
Among the scanned viable bNMWT data points featuring m 2 H > 0, the one minimizing χ 2 is a V = 1.00 , a f = 0.98 , a S = 0.0 , S = T = 0 . (3.20) The result above is derived in the limit of heavy H ± for the diphoton decay amplitude, eqs. (2.8). The average mass of H ± and A for the viable data points is about 800 GeV: even for the lightest charged scalar mass, equal to 170 GeV, the change in the light Higgs decay rate to diphoton is smaller than 1%, and therefore negligible compared to the experimental uncertainty. This justifies the heavy H ± approximation we used for for the diphoton decay amplitude, eqs.  2), defined in terms of the TC Lagrangian variables by eq. (3.12), one can expect the Higgs physics data presented in section 2 to allow at most for three d.o.f., plus two since we also include the EW parameters S and T in the fit. In practice, the range of values found with the scan for a S , S, T , is very small compared to the uncertainty affecting each of those parameters. We assume, therefore, to have only two free parameter, a f and a V , which produce the following statistical results: The charged scalar for the viable data points has a mass on average equal to 2.6 TeV, with a minimum around 400 GeV. This justifies the heavy mass limit we used in determining the optimal point above.
The results obtained so far for bNMWT do not take into account the contributions to Higgs physics coming from heavy charged vector bosons, which are a staple of strong dynamics. In the next section we study this subject by introducing the relevant interaction terms in the Lagrangian and by working out the corresponding Higgs physics phenomenology.

JHEP01(2014)041 4 Extra charged vector bosons and experimental data fit
Extra vector bosons arise naturally in TC as composite resonances with a mass of the order of the strong interaction scale Λ T C . Of particular interest to us here is the possibility that an extra charged vector boson, W , be responsible for the observed slight enhancement to the diphoton decay rate of the Higgs even if m W m h 0 . Given the LHC constraints on the mass m W , equal to 2.55 TeV [48], it is safe to take the heavy W limit, eq. (2.8), for the Higgs decay rate to γγ in eq. (2.5).
To introduce, in the effective Lagrangian, direct Higgs couplings to an extra massive vector boson which conserves gauge symmetry at the fundamental scale, we use the hidden local symmetry principle [68,69], which has been already applied to NMWT in [40,70]: here we just outline the main steps required to introduce composite vector bosons while conserving gauge invariance in the fundamental theory.
We begin by defining the following covariant derivatives where A µ is the vector boson associated with the G ≡ SU(2) × SU(2) global symmetry of L T C , which we have gauged above, and N L (N R ) is a scalar field in the fundamental of SU(2) L (U(1) Y ) and antifundamental of G. From the equations above, we can define a new vector field and its transformation under the full gauged symmetry by where u L is a unitary transformation operator of SU (2). The definition and transformation law of P R are obtained simply by replacing L with R in eq. (4.2). The only dimension four, gauge invariant P µ non-derivative coupling terms to M are the following where M is the matrix representation of the EW doublet M . We do not consider derivative couplings of the composite vectors to minimize the contributions to the oblique corrections, in particular to the S-parameter. Assigning non-zero vevs for N L and N R , their kinetic terms generate a squared mass term for two vector boson combinations: The resulting massless eigenstates give the ordinary W µ and B µ vector bosons, which instead acquire mass through EW symmetry breaking. In addition, there are two vector boson triplets, one vectorial (V µ ) and the other axial (A µ ). Since their interaction terms, given by eq. (4.3) evaluated at the vev defined in eq. (4.4), respect custodial symmetry and give the same contribution to the axial-axial and vector-vector EW vector boson polarization functions [71], the total contribution of the vector bosons to the EW precision parameters is identical to the SM one, and S and T are, therefore, zero [40,70]. Moreover

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the vector boson contributions to FCNC have been tested against the experimental results and shown to be phenomenologically viable [72]. To simplify our analysis we fix so that onlyW µ and the vector resonance, V µ , couple to the neutral Higgs fields. The restrictions we have made on the couplings of the composite vector mesons can be released at the expense of introducing more free parameters into the model. However, we take the restricted interactions as sufficient for exhibiting the viability of the present model, and expect that the values of the parameters we determine through our analysis will serve as a useful benchmark example of viable portion of the parameter space also for cases where additional interactions are included. The charged vector boson mass matrix in the (W , V, A) basis can be written in a compact form as  and (4.8) We now study the implications of this setup in light of the LHC and Tevatron data fit we have at our disposal.

Mixing of vector fields
Let us begin with a rather general and simple case. We require that onlyW , the elementary gauge field, couples to h 0 , and therefore the W coupling to the light Higgs is generated only through terms mixingW with the composite vector fields V and A. The squared mass matrix in the gauge basis (W , V, A) is obtained simply by setting s = 0 in eqs. (4.6), (4.7): (4.9) We define the rotation to the mass eigenbasis in terms of x and , eqs. (4.8), by , (4.10)

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with corresponding eigenvalues The mixing matrix in eq. (4.10) shows that only W and W contribute to the gauge fieldW .
We checked that the Fermi coupling, G F , determined by evaluating the amplitude for the muon decay (µ − → ν µνe e − ), respects the usual relation The vector coupling coefficient a V is suppressed, compared to the result in eq. (3.12), because of mixing: with (4.14) The W coupling to h 0 is zero instead because we set r 2 = −r 1 in eq. (4.3). Finally, the fermion and scalar coupling coefficients in eq. (3.12) remain unchanged. The lower limit on the mass of a sequential 3 W from direct searches at ATLAS [48], equal to 2.55 TeV at 95%CL, can be readily applied to the case above by properly rescaling the lower limit: with s ϕ , m W , m W defined in terms of x, , and m A by eqs. (4.14), (4.11). By plotting the experimentally viable region defined by eqs. (4.15) on the x and plane, we find the maximum allowed value of = 0.36 (at the 95%CL), reached at x = 0 (equivalent to the limit of large m A ).
In strong dynamics the value of m A is expected to be of O(TeV), which determines x to be of O(10 −2 ). In general this needs not to be the case, as larger values of x for small are allowed by the experiment. On the other hand we are interested primarily in testing bNMWT, and therefore in the following we will limit our analysis by assuming x 1. This choice, moreover, guarantees that the W couplings do not change dramatically. Also, is expected to be small because of eqs. (4.8) and the fact that g T C g L . An expansion in both and x therefore produces (4.16) In this limit the effect of mixing on the W and W couplings is negligible. Moreover, because the sum of a V and a V is independent of , so is the Higgs decay rate to two photons.

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Therefore, the optimal values for bNMWT with m A = 1 TeV, < 0.36, and m 2 H > 0 (m 2 H < 0) correspond to the ones with no mixing ( = 0), presented in eqs. (3.20) (eqs. (3.22)). In In the next subsection we study the phenomenologically more appealing scenario in which the composite vector fields feature a direct coupling to neutral Higgs fields.

Direct Higgs coupling to W and W
Next we want to study the effects of a direct Higgs coupling to the composite vector field V , and consider s = 0. In this case, the charged vector boson mass matrix in the (W , V, A) basis is given by eq. (4.6). The mass eigenvalues are lengthy cubic roots. These can be expanded in x and , which in TC are both expected to be small: where contributions of O(x n 5−n ) are neglected, with n = 0, . . . , 5. TheW and V coupling terms to the light Higgs can be derived from the mass matrix by taking its derivative with respect to v w and introducing a factor ζ to take into account the rotation of M to the mass eigenbasis: (4.18) The vector boson coupling coefficients get an enhancement factor because of the s coupling: where at O(x n 5−n ), with n = 0, . . . , 5. We collected together the W and W contributions to the Higgs decay to diphoton by summing up their respective coupling coefficients in eq. (4.19).
It is interesting to notice that, at all orders in x: (4.21) The fermion and scalar coefficients are still determined by eqs. (3.12). We obtain the optimal value of s by performing the global fit in the limit of negligible vector mixing ( = 0) and decoupled neutral heavy Higgs: a f = a V = 1 , a S = 0 , a V = 2s 2 1 + 2s 2 , ⇒ s = 0.21 +0. 18 −0.21 .
(4.22) Figure 5. Viable data points in the (a V , a V ) and (a V , a f ) planes, together with the 68% (green), 90% (blue), and 95% (yellow) CL region: in black are the values relevant for bNMWT while those in grey refer generically to Type-I 2HDM with the addition of two charged vector bosons. The blue stars mark the optimal coupling coefficients on the respective planes intersecting the optimal point with a S = 0.
We use the same set of viable points scanned over the bNMWT parameter space with no W and W , and re-calculate the coupling coefficients a V and a V at each data point for random values of s and , with 0 ≤ s ≤ 1 and 0 ≤ ≤ 0.1, and m A = 1 TeV. We plot the resulting bNMWT data points together with the experimentally favored regions in the (a V , a V ) and (a V , a f ) planes in figure 5, and in the (a V , a f ) plane in figure 6, respectively, all passing through the optimal data point defined in eq. (2.13). The plots are again limited to the positive a V half-plane. For m 2 H < 0 the mixing factor ζ, eq. (4.18), can be negative, which makes a V flip sign, compared to a V , because of eqs. (4.20). Already by visual inspection, it is clear that the s coupling allows bNMWT to cover a large portion of the 68% CL favored region. We verified that all the three parameters a f , a V , and (to a lesser degree) a V are free (meaning that they are little correlated and with a range of values comparable to the error affecting the optimal values in eq. (2.13)), which was expected since we introduced the new parameter s. In this case the bNMWT data point minimizing χ 2 for m 2 H > 0 is The W and W masses corresponding to the optimal points above are equal to about 1 TeV. In the scanned slice of parameter space the upper limit on vector boson masses JHEP01(2014)041 , respectively, are equally favored by the experiment and both feature a probability greater than the one for the general fit, eq. (2.13), which does not include the S and T EW parameters (and therefore has two less d.o.f.) but gives a similar value of χ 2 min . The value of χ 2 min corresponding to the data points above is smaller than that obtained without composite vector bosons, eqs. (3.21), (3.22), though the additional free parameter counterbalances this gain. As a last remark, we note that a V is rather unconstrained by the chosen set of observables, and so a broader set of observables related to W physics would be necessary to further test the viability of bNMWT.

Conclusions and outlook
In this paper we have considered quantitatively how much the coefficients of Higgs couplings to electroweak gauge bosons (a V ) and fermions (a f ) as well as to possible extra scalars (a S ) can deviate from their corresponding values in the Standard Model (a V = a f = 1, a S = 0) in light of the current LHC and Tevatron data. We then considered a bosonic technicolor model, bNMWT [41], and studied its viability by performing a scan on the parameter space JHEP01(2014)041 which implements the direct constraints on the mass spectrum as well as the constraints from precision EW data (in terms of the S and T parameters). The scalar sector of the bosonic technicolor model we considered can be more generally viewed as a type-I 2HDM.
The essential consequence of underlying strong dynamics is the existence of new vector resonances in the particle spectrum. We implemented these new states in an effective Lagrangian to study their effects. We considered in detail the implications of the effective Lagrangian on the couplings of the Higgs boson to the physical W and Z bosons as well as to fermions. Then, we studied first the simple case of minimal coupling to the SM fields, which amounts to considering only the mixing of the two new triplets of vector bosons and the SU(2) L gauge fields without direct interaction between the composite vector bosons and SM fields. In this simple scenario we determined the 95%CL upper bound on the amount of mixing allowed by experimental data. We showed that this generic scenario in bNMWT cannot be resolved by the current data.
Finally we illustrated the possible effects of the direct coupling between composite vector bosons and neutral scalar fields within our effective Lagrangian scheme. We showed that the direct coupling produces a goodness of fit of the bNMWT predictions to the current experimental data comparable to that of the SM, though somewhat lower (P -value for the SM: 60% vs. 45% for bNMWT). Based on the results we have derived in this paper, one can proceed to evaluate the cross sections for the production of composite vectors, for example through Drell-Yan processes or quark-antiquark annihilation with one or three leptons plus missing energy in the final state. Searches for such particles at LHC would provide further constraints on the model or could lead to new major discoveries and help decipher the physics underlying the electroweak sector of the SM.

Acknowledgments
The support from Finnish Cultural Foundation, Central Finland Regional fund is gratefully acknowledged.
A Two Higgs doublet model potential Let us write our bosonic technicolor Lagrangian explicitly as a two-Higgs doublet model (2HDM). The starting point is given by eqs. (3.4), (3.5). The kinetic mixing term in eq. (3.4) is rotated away and the model canonically normalized by eq.(3.9). Applying one more rotation we can express the SM Yukawa couplings in the following form where the full transformation is given by As eq. (A.1) shows, only one of the two Higgses (by convention H 2 ) couples to SM fermions, which ensures that there are no tree-level contributions to Flavor Changing Neutral Currents (FCNC): such a model in literature has been referred to as Type-I 2HDM [42].