Phenomenology of 2HDM with VLQs

In this paper, we examine the consistency of the Large Hadron Collider (LHC) data collected during Run 1 and 2 by the ATLAS and CMS experiments with the predictions of a 2-Higgs Doublet Model (2HDM) embedding Vector-Like Quarks (VLQs) for $pp \to H,A$ production and $H,A\to\gamma\gamma$ decay mechanisms, respectively, of (nearly) degenerate CP-even ($H$) and CP-odd ($A$) Higgs bosons. We show that a scenario containing one single VLQ with Electro-Magnetic (EM) charge $2/3$ can explain the above ATLAS and CMS data for masses in the region 350 GeV $\leq m_{\rm VLQ}\leq 1.5$ TeV or so, depending on $\tan\beta$, and for several values of the mixing angle between the top quark ($t$) and its VLQ counterpart ($T$).We then perform a global fit onto the model by including all relevant experimental as well as theoretical constraints. The surviving samples of our analysis are discussed within 2$\sigma$ of the LHC measurements. Additionally, we also comment on the recent anomalous result reported by CMS using Run 2 data on the associated Standard Model (SM) Higgs boson production with top quark pairs $pp\to t\bar th$ with an observed significance of 3.3$\sigma$. Other than these specific examples, we also present a phenomenological analysis of the main features of the model, including the most promising $T$ decay channels.


I. INTRODUCTION
After the Higgs boson discovery in Run 1 of the Large Hadron Collider (LHC) at CERN [1,2], the ATLAS and CMS collaborations have carried out a broad programme looking for new physics Beyond the Standard Model (BSM) at the TeV scale. In particular, they have developed a powerful detection machinery of spin-0 resonances. However, new physics phenomena might take different forms from those established so far and, once discovered, they will require a complementary effort in order to understand their underlying nature.
In fact, there are already several potential anomalies in the Run 1 Higgs data indicating possible deviations from the SM expectations in the Higgs sector. In particular, the signal strength of the tth associated production mode is the most prominent one, while milder effects are seen in the fits to those extracted from the other production modes active at the LHC, i.e., gluon-gluon scattering (ggh), Higgs-strahlung (hV) and Vector Boson Fusion (VBF).
A possibility to capture at once all such anomalies is offered by the presence of Vector-Like Quark (VLQs) as they can, on the one hand, affect the SM-like Higgs (henceforth denoted by h) production and decay phenomenology (as they would enter the loops mediating the processes gg → h as well as h → γγ and Zγ) and, on the other hand, mediate a tth final state (tth). Intriguingly, the same VLQs affecting h processes would also do so for heavier Higgs states, which may pertain to a BSM scenario. To be specific in defining our framework, we investigate the effects of VLQs in the production and decay of Higgs bosons within a 2-Higgs Doublet Model type-II (2HDM-II). In practice, we concentrate here on new states of matter that are heavy spin 1/2 particles that transform as triplets under color but, unlike SM quarks, their left-and right-handed couplings have the same Electro-Weak (EW) quantum numbers. Furthermore, their couplings to Higgs bosons do not participate in the standard EW Symmetry Breaking (EWSB) dynamics onset by the Higgs mechanism, hence they are not of Yukawa type (i.e., proportional to the mass), rather they are additional parameters, which can then be set as needed in order to achieve both compliance with present data and predict testable signals for the future.
The ATLAS and CMS collaborations, while collecting data at 7, 8 and 13 TeV, performed searches for VLQs with different quantum numbers, probing single and pair production mechanisms, as well as decay modes into all three generations of SM quarks (for the most updated experimental results of ATLAS and CMS we refer to the respective web pages [3][4][5]). However, new extra quarks can be charged under new symmetries, like T -parity in Little Higgs [6][7][8][9][10][11][12] and Kaluza-Klein parity in Extra Dimension [13][14][15][16][17]

models. Such
VLQs have been searched for at both the Tevatron [18,19] and LHC [20,21], though no evidence for the existence of other quarks, beside those of the SM, has been obtained. Direct bounds on heavy chiral quarks can be interpreted as bound on VLQs, but it must be stressed that decay channels of VLQs are different from decay channels of heavy chiral quarks [22].
Thus, if the VLQs have a strong mass degeneracy, the visible decay products of the VLQ are too soft to be detected and, as a consequence, the bounds on the VLQ mass can be very weak, analogous to the case of strong degeneracy between squarks and neutralinos in supersymmetry. Intriguingly, as we shall detail below, even in our simple scenario, VLQ mass values down to 400 GeV are still possible, so that they could strongly affect, e.g., the gg → h → V γ (with V = γ, Z) rates. Now, let us also assume that additional (pseudo)scalar objects possibly behind the LHC experimental data do originate from the same EWSB mechanism governing the generation of the ≈ 125 GeV Higgs state. This is indeed a possibility not excluded by current theoretical and experimental constraints. Under these circumstances, it is then of phenomenological importance to consider the case of a second Higgs doublet participating in EWSB alongside the one responsible for the discovered Higgs state. This mass generation dynamics is well known in the form of 2HDMs [23]. We are therefore left with a new physics construct that would include a 2HDM supplemented by one or more VLQs as a potential scenario that could accommodate the LHC data on the ≈ 125 GeV Higgs boson and additionally explain results above the SM yield.
In this paper, we wish to build on the results of [24][25][26][27], where a similar possibility was discussed (by some of us), in which the role of a 2HDM was played by a SM-like Higgs doublet supplemented by an additional Higgs singlet. We intend to review here a 2HDM plus single VLQ scenario, where the VLQ has the same Electro-Magnetic (EM) charge of the top quark (with which it then mixes), as a candidate to study the implications of the heavy Higgs searches by the ATLAS and CMS collaborations both with 8 TeV and the latest 13 TeV data. Furthermore, we will relate such data samples to those involving γγ and Zγ final states. In addition, we will show an enhancement of the pp → tth cross-section at the LHC induced by small mixing of the top quark with the additional state T . Finally, we will discuss the possibility of VLQs produced as real objects in the detector decaying into Higgs boson states, both neutral and charged.
Our paper is formatted as follows. In the next section, we describe in some detail the model concerned. In the three subsequent sections, we present our results, followed by our conclusions.

II. A 2HDM EXTENDED BY AN UP-TYPE VECTOR-LIKE QUARK
A simple extension of the SM is the well-known 2HDM that expands the Higgs sector of the SM by an additional Higgs doublet. The spectrum of the model contains additional Higgses and possesses an alignment limit [28], in which one of the Higgses completely mimics the SM one.
To describe our model, we start with the well known CP-conserving 2HDM scalar potential for (Φ 1 , Φ 2 ) with a discrete symmetry Φ 1 → −Φ 1 that is only violated softly by dimension two terms [23,29]: where all parameters are real. The two complex scalar doublets Φ 1,2 may be rotated into a basis, H 1,2 , where only one obtains a Vacuum Expectation Value (VEV), where G 0 and G ± are the would-be Goldstone bosons and H ± are a pair of charged Higgses.
Herein, A is a CP-odd pseudoscalar which does not mix with the other neutral states in the CP-conserving case. The physical CP-even scalars h and H are mixtures of ϕ 0 1,2 and the scalar mixing is parameterized as 1 1 Hereafter, s X ≡ sin X and c X = cos X.
where tan β = v 2 /v 1 is the angle used to rotate Φ 1,2 into H 1,2 and α is the additional mixing needed to diagonalize the CP-even mass matrix. As mentioned in the introduction, in order to alter the gluon-gluon-Higgs, photon-photon-Higgs and/or Z-photon-Higgs couplings, one can advocate the inclusion of new heavy fermions such as a VLQ partner of the top quark with the same EM charge. In fact, there are many SM extensions that require vector-like fermions in their spectrum (for an overview see [25,30]). Such a new VLQ will mix with the top quark through the Yukawa interactions and can contribute, therefore, to some SM observables. To derive these new interactions, we first study the Yukawa sector within a 2HDM extended by a VLQ pair (T L , T R ) in the 1 2/3 representation of the SM EW group. In the 2HDM-II, our concern here, one doublet couples to up quarks and the other one couples to down quarks and charged leptons. The most general renormalizable model for the quark Yukawa interactions and mass terms can be described, limited to third generation quarks and new VLQs, by the following Lagrangian, whereH i ≡ iτ 2 H * i (i = 1, 2), Q 0 L are the SM quark doublets and the u i R 's are the SM up-type quark singlets. Note that additional kinetic mixing terms of the form T L t i R can always be rotated away and reabsorbed into the definition of y t,T . Furthermore, one can, without loss of generality, choose a weak interaction basis where y t is diagonal and real. In the weak eigenstate basis (t 0 L , T 0 L ), the top quark and VLQ mass matrix is where y t and ξ T are the Yukawa couplings for the top quark and VLQ, respectively, v = 246 GeV is the VEV of the SM Higgs doublet while M T is a bare mass term of the VLQ, which, as intimated, is unrelated to the Higgs mechanism of EWSB. It is clear from the above mass matrix that the physical mass of the heavy top, m T , is different from M T due to the t − T mixing. Furthermore, such a mass matrix can be diagonalized by a bi-unitary transformation such that with M the matrix given in Eq. (5) and M d the diagonalized one. The unitary matrices In fact, the mixing angles θ L and θ R are not independent parameters. From the bi-unitary transformations applied to Eq. (6), we can derive the following relations: The above equations in turn give the following relationships between θ L and θ R , see [25]: After rotating the weak eigenstates (t 0 L , T 0 L ) into the mass eigenstates, the Yukawa Lagrangian takes the following form: The neutral Higgs couplings to top (t) and heavy top (T ) quark pairs normalized to the h SM tt one are given in Appendix A.
In our 2HDM+VLQ scenario, neutral and charged current interactions receive contributions from the new VLQ, with f, f = t, T . The new couplings are modified as follows: Finally, the interaction with the charged salar boson and the new quark T can be written

III. RESULTS AND DISCUSSIONS
In our numerical calculation, we consider the scenario with a light Higgs boson h as the SM-like state, with m h = 125 GeV. We take into account theoretical constraints from vacuum stability, unitarity and perturbativity. We then enforce bounds from precision EW data (such as the oblique parameters S, T and U ) and adopt constraints on the charged Higgs boson mass from the 2HDM-II using b → sγ rates, which set a limit m H ± > 580 GeV [61].
In addition, we perform a global χ 2 analysis for the signal strengths of the observed Higgs boson h from the combined production modes i = 1 (ggh+tth) as well as i = 2 (VBF+Vh) and decay modes into f = γγ, ZZ, W + W − , τ − τ + and bb [31]: where the signal strength variable µ f i is defined as in terms of a production cross-section, σ, and a decay Branching Ratio (BR  as explained, h now plays the role of the SM-like Higgs state. Under these assumptions, the ATLAS search in Ref. [42] is the most constraining one and excludes a heavy T quark with mass lower than ≈ 640 GeV at the 95% Confidence Level (CL). This lower limit can, however, be weakened down to ≈ 350 GeV if T couples to first and second generation quarks as well [43]. This is certainly a possible model construction, however, in our case, we do not pursue this in any detail, as such additional interactions would not enter the Higgs boson observables which we intend to study. We are nonetheless entitled to scan on m T starting from such low m VLQ values. In our 2HDM+VLQ construct, if we assume

B. Constraints on the t-T mixing
In this section, we will show that t-T mixing can be constrained both from EW Precision Observables (EWPOs) and from recent LHC data on the ≈ 125 GeV Higgs boson. In general, when the new physics scale is much larger than the EW scale, virtual effects of the new particles in loops are expected to contribute to the EWPOs that have been precisely measured at LEP1, LEP2, SLC and Tevatron. These EWPOs are known as the oblique parameters S, T and U [44] and can be used to put constraints on new physics. In our case, the mixing between t-T will generate couplings between the SM gauge bosons and the new VLQ, T , which will induce contributions to S and T [45].
We have computed the extra contributions of the VLQ to ∆T = T − T SM and ∆S = S −S SM by implementing the model into the FeynArts [46], FormCalc [47,48] and LoopTools [49,50] where the A 0 and B 0 functions are the standard Passarino-Veltman ones used in the convention of LoopTools [50]. Note that our results agree numerically with Ref. [51]. Taking the above analytical expressions into account, our model will remain viable as long as ∆T VLQ and ∆S VLQ are compatible with the latest extracted values [52] which are given by where a correlation coefficient ρ = +0.91 and ∆U = 0 have been used. We thus perform a random scan on the s L and m T parameters imposing compatibility with ∆T and ∆S at 95% CL, which yields a constraint on s L as a function of the VLQ mass, m T , as shown in In addition to the EWPOs constraints studied above, the penguin induced b → sγ decay is also sensitive to new physics. The current experimental value is BR(B → X s γ) exp = (3.32 ± 0.15) × 10 −4 , for E γ > 1.6 GeV [53], and the SM prediction with Next-to-Next-to-Leading Order (NNLO) QCD corrections is BR(B → X s γ) SM = (3.36 ± 0.23) × 10 −4 [54,55].
Since the SM result is close to the experimental data,B → X s γ will give a strict bound on new physics effects. The effective Hamiltonian arising from the W ± and H ± bosons for b → sγ at the µ b = 4.8 GeV scale can be written as: where the EM and gluonic dipole operators are given as: Here QCD corrections to C 7γ (µ b ) and C 8G (µ b ) in the 2HDM-II have been calculated. Based on the C SM 7γ (µ b ) value extracted in [60], we get C SM 7γ (µ b ) ≈ −0.310 when BR(B → X s γ) SM = 3.36 × 10 −4 is applied. In order to study the influence of the b → sγ process on the 2HDM+VLQ model, we follow the approach in [55] and split the BR(B → X s γ) as follows: where C i 7γ,8G are the Wilson coefficients at the µ H = m H ± scale (the matching scale is µ 0 ∼ m t at which the heavy particles are decoupled [55]) , wherein the quadratic C i 7γ,8G terms are ignored due to the requirement of C i 7γ,8G < 1. Using the current experimental value, the bound on C i 7γ,8G is: According to the charged Higgs interactions, the H ± contributions coming together with t and T to C i 7γ,8G are expressed as [57]: with x i = m 2 i /m 2 H ± and i = t, T . The form factors are given in Appendix B.

D. Constraints from LHC data
The couplings of the SM-like Higgs are sensitive to the parameters cos(β − α) and tan β.
Therefore, the LHC data on the 125 GeV Higgs boson can give strong constraints on these.
In Fig. 3, we show the constraints on the ordinary 2HDM (left) and 2HDM+VLQ (right) using Higgs data from Run 1 (gray) and Run 2 (yellow) at 95% CL. The bounds on cos(β −α) are much more stringent for the ordinary 2HDM-II, where the SM-like coupling region of the 125 GeV Higgs forces | cos(β − α)| < 0.14, and increasingly more stringent for larger widths are given by 2 The analytical expressions for φ → gg decays are easily obtainable from those for φ → γγ. Similarly, for gg → φ production.
Clearly, the charged Higgs boson contributions are smaller compared to the fermionic ones.
Even for large g φH ± H ∓ , the charged Higgs effects are still negligible, henceforth, we neglect these.
The relevant modifications to the signal strength µ h γγ (a function of the production crosssections and decay BRs) are defined in our scenario as These come from the presence of an additional VLQ in the loops as well as from the modification of the htt coupling for both Higgs production (gg → φ) and Higgs decay (φ → V γ).
The theoretical value for µ h γγ will depend on m T , s L as well as the new Yukawa y T . However, in the decoupling limit cos(β − α) = 0, the dependence of htt and hTT on y T cancels due to a factor cos(β − α) = 0. What then remains is solely an m T and s L dependence, at least in the V = γ case. The formula in Eq. (30) holds for the Zγ case as well, wherein, however, the role of the T loops can be altered significantly relative to that of the others by the additional degree of freedom carried by the ZTT vertex (unlike the case of the γTT one, which is fixed by the Ward identity). Further, unlike the case of γγ, Zγ also benefits from non-diagonal loop transitions wherein the vertices H, AtT and ZtT (and c.c.) are involved.
These differences between the two decay channels will play a key role in the remainder of our analysis.
The effects of a new heavy quark, T , have direct consequences for the signal strengths of the SM-like Higgs boson. In Fig. 4, we illustrate a contour plot for µ h γγ over the (s L , y T ) plane. The dashed black, solid black and solid red contours capture µ h Zγ = 1, 1.5 and 2, respectively. The three contours fall within 1σ of the ATLAS and CMS measured value of µ h γγ = 1.10 ± 0.23 (stat) ± 0.22 (syst). One can therefore conclude that this LHC constraint is less stringent than the oblique parameters previously discussed. However, once the µ h γγ measurement improves with Run 2 data from the LHC and reaches the level of 10% or less deviation from the SM value, then the ≈ 125 GeV di-photon event constraints will be more stringent. The pattern of µ h Zγ is also given. It is remarkable that, for µ h γγ compatible with LHC data at the ±2σ level, µ h Zγ can see an enhancement up to a factor of nearly 2.

IV. CONFRONTING THE 2HDM+VLQ WITH LHC DATA
In order to explain the LHC data in the framework of our 2HDM+VLQ construct, we consider the gg → φ and φ → γγ (with φ = H and A) processes where the contribution of all the quarks including T is considered. In the SM, only the top-quark loop gives a significant fermionic contribution. Besides the top-quark, the new VLQ state T can also contribute in the 2HDM+VLQ case, for both the SM-like and the other heavy Higgs production modes in addition to their decays into di-photons.
We start by assuming that we are in the alignment limit of the light Higgs boson h,  The cross-section for this process is given by where Γ VLQ (φ → gg) is the gg width of the SM augmented by the extra VLQ loop contribution. The SM Higgs cross-section is taken from the Higgs working group study of Ref. [65].
In our 2HDM+VLQ scenario, the cross-section can be enhanced from the additional VLQ loop, which introduces the hTT coupling which can be large. Its sign is such that it can enable constructive interference with the top quark loop. Furthermore, the BR VLQ (H, A → γγ) can overall be enhanced as well through a similar dynamics, though it should be recalled here that the dominant loop is due to W ± 's which typically have an opposite sign to the t and T loops, owing to the different spin statistics. In away from the s L ≈ 0 limit (left frame), the pp → H, A process can differ by two orders of magnitude compared to the ordinary 2HDM-II.
In the left panel of Fig. 6 we present the dependence of σ(pp → φ) × BR(φ → γγ) upon the mixing angle s L for tan β = 1, 2, 3, 4 while the right panel shows the same quantity as a function of tan β with fixed mixing angles s L . Both panels are for a large Yukawa of the new top, y T = 4π. In this illustration, we limit ourselves to low tan β values which are favored by τ τ LHC data and also because of perturbative unitarity coming from the 2HDM scalar potential. We emphasize that, in the decoupling limit which we consider, the W ± loop in H → γγ vanishes since it is proportional to cos(β − α) ≈ 0 while A → γγ has no W ± loop at all because of the CP-odd nature of the A state. Furthermore, for H, A → gg, we are only left with top quarks and VLQ contributions. It is clear from Fig. 6 that, away from the s L ≈ 0 limit (left frame), the pp → H, A → γγ process can significantly contribute to the high mass di-photon event sample. Hence, the recent studies carried out by ATLAS and CMS have the potential to significantly constrain our model. For example, for H, A masses around 500 GeV, tan β values of 2-3 are not possible, as no particular feature has emerged from the LHC data in the relevant m γγ invariant mass range (hence they are compatible with the SM rates, driven by qq, gg → γγ events). In fact, the strongest constraints would emerge (right frame) for any m A = m H value whenever a loop threshold opens up, whether this is the tt one at 350 GeV or the TT one at higher energies (possibly excluding tan β ≈ 4 values), which may happen through both Higgs [66] and Z [67,68] boson mediation.
for low tan β and negative y T . It is clear that substantial differences (up to a factor of two) can exist between the two scenarios, so long that s L is sizably different from zero. (Local maxima in the plot correspond to relative sign changes between the VLQ loop contributions and the 2HDM ones). In fact, over most of the possible s L interval, both γγ and Zγ in the 2HDM+VLQ depart simultaneously from the ordinary 2HDM-II case. As pointed out in the introduction, ATLAS and CMS have reported a possible increase in the signal strength of the tth associated production mode in the LHC data. The most recent preliminary results from Run 2 relayed by CMS still show an enhancement of µ pp tth = 1.5 ± 0.5 times the SM prediction with an observed significance of 3.3σ compared to the expected one of 2.5σ (obtained from combining results of Run 1). Many different final states contribute to this enhancement, but the most significant excesses are observed in multi-lepton final states which probe closely tth production. One possibility to explain the excess is that it could be due to the modified Higgs coupling to the SM top quark, resulting in an enhanced tth production. Mixing within the top sector, i.e., between the t and T states, also allows for a sufficiently large enhancement of the pp → tth rates. Hence, a possibility offered by our scenario could be the potential to explain a tth enhancement. In this case, rates for the loop-induced processes of the h should remain SM-like, despite the VLQ contributions in our scenario. In Fig. 8 we show contour plots of µ pp tth in the (sin θ L , tan β) plane (right) and (m T , y T ) plane (left) in the 2HDM+VLQ given SM-like Higgs couplings. As can be seen from the figure, there is a strong dependence upon both the parameters sin θ L and tan β. Clearly, the 2HDM+VLQ can reproduce a higher value of the tth signal strength than in the SM, typically µ pp tth ≈ 1.5, for small tan β and sin θ L = 0.22, i.e., a parameter space configuration ideally testable within the experimental range of LHC Run 2 through direct T production.
In fact, in the light of a possible explanation of potentially anomalous tth data afforded by a heavy top with m T ≈ 600 GeV, we end this section with a few comments on the possible production and decay patterns for such a VLQ state, as the ensuing signatures would be a distinctive feature between a standard 2HDM-II and its VLQ version. Unlike the case of the SM+VLQ framework where the BR of T → bW + , T → tZ and T → th are, respectively, 50%, 25% and 25% for heavy m T , in models with more than one Higgs doublet, several decay patterns can appear from the interaction of the new heavy quark with the extended Higgs sector, e.g., T → bW + , tZ, th, tH, tA, bH + , where the last three cases are unique to a 2HDM sector. (The partial widths for all these modes are given in Appendix C). In Fig. 9 we illustrate the BRs of the T quark as a function of sin θ L (right panel) and as a function of tan β (left panel). We assume a heavy scalar scenario where m H = m A = 500 GeV, H ± = 600 GeV and m T = 1 TeV. As seen from the right plot for tan β = 0.7, T → bW + and T → bH + are comparable and could reach 25% at small mixing sin θ L = 0 instead of 50% in the SM for T → bW + . However, T → th and tZ are slightly smaller compared to SM+VLQ case (less than 12%). a function of tan β and with small mixing sin θ L = 10 −2 . We see that in the limit sin θ L → 0, when the non-standard T decay modes T → tH, tA are suppressed due to their coupling, which is proportional to sin θ L , T → bH + is comparable to T → bW + for tan β ≈ 0.5 − 0.7 and may offer an alternative discovery mode. We stress here that b → sγ constraint is fulfilled for such small tan β ≈ 0.5 − 0.7 if m H ± = 600 GeV.

V. CONCLUSIONS
In this paper, we have extended the ordinary 2HDM-II by a singlet heavy VLQ with the same EM charge as the top quark. In the (near) decoupling limit of the 2HDM-II, one neutral CP-even Higgs state, h, can mimic the SM-like Higgs boson seen at the LHC Run 1 at ≈ 125 GeV while the other two neutral Higgs states, H and A, can be constrained as the model has to accommodate the data observed by ATLAS and CMS at the LHC Run 2 in both the low and high mass region, which are to date consistent with SM expectations. We have then proceeded to a phenomenological comparison between the 2HDM+VLQ scenario and the ordinary 2HDM case, limitedly to the LHC environment.
We have illustrated that a different decay pattern emerges in the 2HDM+VLQ with respect to the standard 2HDM when γγ and Zγ samples are compared to each other. Then, we have shown that, at the same time, an enhancement of σ(pp → tth) by a factor up to 2 can occur, which would explain an increased value of such a cross-section at the LHC, i.e., in the direction of a possible enhancement seen in Run 2 data. All this can occur for VLQ masses of order 600-800 GeV, so that we have finally highlighted that non-SM-like decays of this VLQ state, particularly via H ± channels, would be evidence of a 2HDM sector.
In fact, by combining these instances, a peculiar 'smoking-gun' situation may emerge in the 2HDM+VLQ scenario discussed here, where one has γγ rates at large invariant masses essentially compatible with the SM background, yet a depletion (with respect to the 2HDM yield) can be seen in the Zγ sample, with or without an enhancement of the tth cross-section.
One could indeed disentangle this as being due to this particular BSM structure by finally revealing a variety of T → bH + decays emerging from QCD induced TT production.
Remarkably, all such phenomenology can be obtained for parameter space configurations compliant with current theoretical and experimental constraints, as we have scrupulously assessed using up-to-date tools, yet ameanable to prompt phenomenological investigation in the upcoming years at the LHC, during Run 2 and 3.
Appendix A: Yukawa couplings in the 2HDM+VLQ These are as follows: