In full generality, the Higgs doublet may have a non-zero Yukawa interaction with any pair of chiral fermions that transform under SU(3)$_c \times$SU(2)$_w \times$U(1)$_Y$ as $\psi_L \sim (R_c, R_w, Y)$ and $\psi_R^{u,d} \sim (R_c, R_w - 1, Y \pm \frac{1}{2})$:

$$ - \mathcal{L}_Y = \sum_{\psi_L} \left[ \sum_{\psi_R^u} y_{\psi_L \psi_R^u} (\overline{\psi_L} \psi_R^u \tilde{H}) + \sum_{\psi_R^d} y_{\psi_L \psi_R^d} (\overline{\psi_L} \psi_R^d H) \right] + \text{h.c.} . \quad (B.2) $$

Here the parentheses stand for the appropriate contraction of the SU(2)$_w$ indexes. Let us denote the components of $\psi_L$ by the index $m = j, j-1, \dots, -j+1, -j$, where $j = (N_w - 1)/2$. Then, the multiplet $\overline{\psi_L}$ with components $(\overline{\psi_L})_m \equiv (\overline{\psi_L})_m$ transforms in the conjugate representation $R_w^*$. It is possible to define a multiplet $\overline{\psi_L'}$ that properly transforms in the representation $R_w$, by using the SU(2)$_w$ conjugation matrix $R$, $(\overline{\psi_L'})_m = R_{mn}(\overline{\psi_L})_n \equiv (-1)^{j-m}(\overline{\psi_L})_{-m}$. The $2j$ components of $\psi_R^u$ pair with the upper (lower) $2j$ components of $\overline{\psi_L'}$ to form the upper (lower) component of a weak doublet $D$. The corresponding Clebsch-Gordan coefficients are given by

$$ \langle j, j - \frac{1}{2}; m, -m \pm \frac{1}{2} | \frac{1}{2}, \pm \frac{1}{2} \rangle = \pm(-1)^{j-m} \sqrt{\frac{j \pm m}{j(2j+1)}} . \quad (B.3) $$

Contracting $D$ with $\tilde{H}$ into a weak singlet, $D_a(i\sigma_2)_{ab}\tilde{H}_b$, one finds

$$ (\overline{\psi_L} \psi_R^u \tilde{H}) \equiv \sum_{m=-j+1}^{j} \sqrt{\frac{j+m}{j(2j+1)}} \left[ (\overline{\psi_L})_m (\psi_R^u)_{m-\frac{1}{2}} \tilde{H}_{\frac{1}{2}} + (\overline{\psi_L})_{-m} (\psi_R^u)_{-m+\frac{1}{2}} \tilde{H}_{-\frac{1}{2}} \right] . \quad (B.4) $$

The same expression holds for $\psi_R^u \leftrightarrow \psi_R^d$ and $\tilde{H} \leftrightarrow H$ as well. Of course, all the results above also apply when one makes everywhere the replacement $L \leftrightarrow R$.

The relative size of the Clebsch-Gordan coefficients has important phenomenological consequences, e.g. the different components of the fermion multiplets acquire a different mass after EWSB. The overall normalisation of the SU(2)$_w$ contraction is also important, to establish the perturbative range for a Yukawa coupling $y$: for instance, the contribution of $y$ to the Higgs wavefunction renormalisation at one-loop goes as $y^2/(16\pi^2)$ times the sum of the Clebsch-Gordan coefficients squared, taken over all possible isospin components in the loop. Adopting the above conventions, such a sum is normalised to one, and we can easily define the region where perturbation theory can be trusted, by requiring $y/(4\pi) \ll 1$. However, we keep the conventional normalisation for the doublet-doublet contraction into a singlet, with no overall factor $1/\sqrt{2}$, that strictly-speaking should be included: the issue of SU(2)$_w$ normalisation is more relevant for large weak multiplets.

We note that the perturbative upper bound on a Yukawa coupling $y$ depends on the process under consideration. Schematically, the next-to-leading order amplitude is given by the leading order one times a factor $y^n g^m F_c/(16\pi^2)$, where $g$ stands for other couplings such as gauge couplings, and $F_c$ is the colour factor, with typical values $F_c = 1, N_c, C(R_c)$. In the example of the Higgs wavefunction normalisation adopted above, one has $n = 2, m = 0$ and $F_c = N_c$, therefore we could have taken into account the SU(3)$_c$ contraction by adding
a factor $1/\sqrt{N_c}$ on the right-hand side of eq. (B.4), or alternatively requiring $y\sqrt{N_c}/(4\pi) \ll 1$. However, the one-loop amplitudes relevant in our analysis (EW precision tests, Higgs couplings to fermions and gauge bosons, etc.) behave differently from each other, and the perturbativity criterion varies correspondingly. In some cases the colour enhancement is absent, or compensated by small gauge couplings, or by a small mixing between new and SM fermions. Therefore, we find more conservative to stick to the bound $y \ll 4\pi$.

At EWSB, $H^0$ can be replaced by $(v+h)/\sqrt{2}$, to obtain the couplings of the physical Higgs boson $h$ to the fermions in the interaction basis. All fermions with equal charge and in the same colour representation may mix, and their mass matrix $\mathcal{M} = U_L \text{diag}(m_1, \dots, m_n) U_R^\dagger$ may include both $v$-independent vector-like mass terms, and the EWSB contributions $\sim yv$. Thus, one can derive the $h$-couplings to the fermion mass eigenstates as follows:

$$ 
\begin{aligned}
-\mathcal{L} & \supset \overline{f_{L\alpha}}[\mathcal{M}(v)]_{\alpha\beta}f_{R\beta} + \overline{f_{L\alpha}}\frac{\partial}{\partial v}[\mathcal{M}(v)]_{\alpha\beta}f_{R\beta}h + h.c. \\
& = \sum_i m_i \overline{f_{Li}}f_{Ri} + \overline{f_{Lj}}\left[U_L^\dagger\frac{\partial \mathcal{M}(v)}{\partial v}U_R\right]_{jk}f_{Rk}h + h.c. \\
& = \sum_i m_i \overline{f_i}f_i + \overline{f_j}(y_{jk} + i\gamma_5 \tilde{y}_{jk})f_k h.
\end{aligned} 
\quad (B.5) $$

where $y$ and $\tilde{y}$ are hermitian matrices defined by

$$ y = \frac{\lambda + \lambda^\dagger}{2}, \qquad \tilde{y} = \frac{\lambda - \lambda^\dagger}{2i}, \qquad \lambda = U_L^\dagger \frac{\partial \mathcal{M}(v)}{\partial v} U_R. \quad (B.6) $$

In the CP-conserving case $\lambda$ is real, therefore $y = y^T$ is real and $\tilde{y} = -\tilde{y}^T$ is imaginary. In the case of purely chiral masses (e.g. in the SM), one has $\mathcal{M}(v) \propto v$, therefore $\partial\mathcal{M}(v)/\partial v = \mathcal{M}/v$, $y = \lambda = \text{diag}(m_1, \dots, m_n)/v$ and $\tilde{y} = 0$. On the other hand, in presence of both chiral and vector-like masses, the Higgs boson can have both scalar and pseudo-scalar, CP-even and CP-odd, diagonal and off-diagonal couplings to the fermions mass eigenstates, and its couplings are not proportional to the fermion masses. A simplification occurs in those SM extensions such that $(\partial\mathcal{M}/\partial v)_{\alpha\beta} = \mathcal{M}_{\alpha\beta}c_\beta$, that is, each row of the mass matrix has the same dependence on $v$. In this case $U_L^\dagger$ and $U_L$ cancel out in $\lambda$ and one finds $\lambda_{jk} = m_j \sum_\beta c_\beta (U_R^*)_{\beta j} (U_R)_{\beta k}$. Similarly, when $(\partial\mathcal{M}/\partial v)_{\alpha\beta} = c_\alpha \mathcal{M}_{\alpha\beta}$, one finds $\lambda_{jk} = m_k \sum_\alpha c_\alpha (U_L^*)_{\alpha j} (U_L)_{\alpha k}$.

The mixing with new fermions modifies the Higgs boson decay width into SM fermions at the tree-level. In addition, there may be new Higgs decay channels, with one or more new fermions in the final state, as long as they are lighter than $h$. In full generality, the Higgs decay width into two fermions at leading order is given by

$$ \Gamma_{\text{tree}}(h \rightarrow \overline{f_j} f_k) = \frac{N_c \Delta_{jk}}{8\pi} m_h \left[ |y_{jk}|^2 (\beta_{jk}^+)^3 \beta_{jk}^- + |\tilde{y}_{jk}|^2 \beta_{jk}^+ (\beta_{jk}^-)^3 \right] \theta(m_h - m_j - m_k), \quad (B.7) $$

where $\beta_{jk}^\pm \equiv [1 - (m_j \pm m_k)^2/m_h^2]^{1/2}$, $\Delta_{jk} = 2$ if the final state particles are identical Majorana fermions ($j = k$ and $f_j = f_j^c$), and $\Delta_{jk} = 1$ otherwise.

Besides the Yukawa couplings to fermions, the Higgs boson has tree-level couplings to WW, ZZ and to itself. In the presence of new fermions, all the tree-level couplings
may receive corrections at the one-loop level. Even though these corrections may become relevant in view of precision measurements of the Higgs couplings, they represent in general a sub-leading effect and we will not discuss them further. In the following subsection we will focus instead on a more sensitive probe of new physics: those Higgs couplings that are absent at tree-level in the SM.

## B.2 Loop-induced Higgs couplings

At one-loop new couplings are induced between the Higgs boson and the SM particles, that are absent at tree-level. In particular, $U(1)_{em}$ and $SU(3)_c$ gauge invariance prevents renormalizable couplings to photons and gluons, therefore the tree-level amplitudes for $h \to gg$, $h \to \gamma\gamma$ and $h \to Z\gamma$ are zero, and in addition the one-loop amplitudes for these processes are free from divergences. The effective Higgs boson couplings generated at one-loop can be described in full generality by two dimension-five operators,

$$ \mathcal{L}_{hVV'} = \left( c_{hVV'} V_{\mu\nu} V'^{\mu\nu} + \frac{1}{2} \tilde{c}_{hVV'} V_{\mu\nu} V'_{\rho\sigma} \epsilon^{\mu\nu\rho\sigma} \right) h, \quad (B.8) $$

where $VV' = gg, \gamma\gamma, \gamma Z$ and $V_{\mu\nu} = G_{\mu\nu}^a, F_{\mu\nu}, Z_{\mu\nu}$ are the field strength tensors for the gluon, the photon and the $Z$, respectively. The CP-even (odd) coefficients $c_{hVV'}$ ($\tilde{c}_{hVV'}$) have mass dimension minus one, and may receive contributions from loops of both SM and new particles. One should be careful to avoid double-counting: if one considers $\mathcal{L}_{hVV'}$ as part of the effective Lagrangian valid below the EWSB scale $v$, $c_{hVV'}$ and $\tilde{c}_{hVV'}$ should include only the contributions of particles heavier than $v$.

In momentum space, the $hVV'$ couplings are given by

$$ \mathcal{L}_{hVV'}(p, p') = 2 [c_{hVV'}(p'^{\mu}p^{\nu} - p \cdot p'g^{\mu\nu}) + \tilde{c}_{hVV'}\epsilon^{\mu\nu\rho\sigma}p_{\rho}p'_{\sigma}] h(p + p')V_{\mu}(p)V'_{\nu}(p'). \quad (B.9) $$

The decay width of the Higgs boson into two vector bosons is then given by

$$ \Gamma(h \to VV') = \frac{N_c \Delta_{VV'}}{8\pi} m_h^3 \beta_{VV'}^+ \beta_{VV'}^- \left[ c_{hVV'}^2 \left( \beta_{VV'}^{+2} \beta_{VV'}^{-2} + \frac{6m_V^2 m_{V'}^2}{m_h^4} \right) + \tilde{c}_{hVV'}^2 \beta_{VV'}^{+2} \beta_{VV'}^{-2} \right], \quad (B.10) $$

where $N_c = 8$ (1) for gluons (for $\gamma$ and $Z$), $\Delta_{VV'} = 2$ for $V = V'$ and $\Delta_{VV'} = 1$ for $V \neq V'$, and finally $\beta_{VV'}^{\pm} \equiv [1 - (m_V \pm m_{V'})^2/m_h^2]^{1/2}$. In the following, we will match the explicit loop computation with the effective coefficients $c_{hVV'}$ and $\tilde{c}_{hVV'}$.

### B.2.1 Higgs coupling to two gluons

The Higgs-gluon-gluon coupling $c_{hgg}$ ($\tilde{c}_{hgg}$) receives a one-loop contribution from each coloured fermion with a non-zero CP-conserving (CP-violating) Yukawa coupling to the Higgs boson, see figure 13. The gluon coupling to fermions is determined by $SU(3)_c$ gauge invariance,

$$ \mathcal{L}_{g\bar{f}f} = g_s \sum_i \bar{f}_{ib} \gamma^\mu A_\mu^a (T_i^a)_{bc} f_{ic}, \quad (B.11) $$

where $T_i^a$ are the $SU(3)_c$ generators in the representation $R_{ci}$ of the fermion $f_i$. As the $SU(3)_c$ symmetry is unbroken, there are no ‘off-diagonal’ gluon couplings to two different
<figure><img src="image_14.png" /><figcaption>**Figure 13.** Fermionic triangle loop contributing to the coupling of the Higgs boson to two gauge bosons. A crossed diagram with the two gauge boson insertions interchanged has to be added too, and one must sum over all possible sets ($f_i, f_j, f_k$) of fermion mass eigenstates. For the gluons one has $G_{ik}^a = g_s \delta_{ik} T_i^a$, for the photon $G_{ik}^\gamma = e\delta_{ik} Q_i$, and for the Z boson $G_{ik}^Z = g(g_{ik}^V - \gamma_5 g_{ik}^A)/c_w$.</figcaption></figure>

mass eigenstates. Recall that the Higgs is mostly produced via gluon fusion, with a partonic cross-section that can be expressed as a function of the partial decay width,

$$ \sigma(gg \to h; \hat{s}) = \frac{\pi^2}{8m_h} \delta(\hat{s} - m_h^2) \Gamma(h \to gg). \qquad (B.12) $$

In the SM, the contribution of the quarks triangle loop to $h \to gg$ reads

$$ \Gamma_{\text{SM}}(h \to gg) = \frac{\alpha_s^2 m_h^3}{72 \pi^3 v^2} \left| \frac{3}{4} \sum_q A_{1/2}(\tau_q) \right|^2, \qquad (B.13) $$

where $\tau_q \equiv m_h^2/(4m_q^2)$ and the form factor is given by

$$ A_{1/2}(\tau) = \frac{2[\tau + (\tau - 1)f(\tau)]}{\tau^2}, \quad f(\tau) = \begin{cases} \arcsin^2 \sqrt{\tau} & \text{for } \tau \le 1, \\ -\frac{1}{4} \left( \log \frac{1 + \sqrt{1 - \tau^{-1}}}{1 - \sqrt{1 - \tau^{-1}}} - i\pi \right)^2 & \text{for } \tau > 1. \end{cases} \qquad (B.14) $$

As illustrated in figure 14, the top quark gives the dominant contribution, because $\tau_t \ll 1$ and $\tau_{b,c,...} \gg 1$. In a generic extension of the SM, the fermions will couple to the Higgs as in eq. (B.5), but only the diagonal, real couplings $y_i \equiv y_{ii}$ and $\tilde{y}_i \equiv \tilde{y}_{ii}$ are relevant for $h \to gg$. One obtains

$$ \Gamma(h \to gg) = \frac{\alpha_s^2 m_h^3}{72 \pi^3 v^2} (|\mathcal{A}_f^{gg}|^2 + |\tilde{\mathcal{A}}_f^{gg}|^2), \qquad (B.15) $$

where the CP-even and CP-odd amplitudes are

$$ \mathcal{A}_f^{gg} = \frac{3}{2} \sum_i C(R_{ci}) \frac{y_i v}{m_i} A_{1/2}(\tau_i), \quad \tilde{\mathcal{A}}_f^{gg} = \frac{3}{2} \sum_i C(R_{ci}) \frac{\tilde{y}_i v}{m_i} \tilde{A}_{1/2}(\tau_i), \quad \tilde{A}_{1/2}(\tau) = 2 \frac{f(\tau)}{\tau}, \qquad (B.16) $$

with the Dynkin index $C(R_{ci})$ defined below eq. (2.1).
<figure><img src="image_15.png" /><figcaption>Figure 14. Real (blue lines) and imaginary (red lines) parts of the form factors $A_{1/2}(\tau)$ (solid lines) and $\tilde{A}_{1/2}(\tau)$ (dashed lines). The horizontal lines correspond to the asymptotic values 2, 4/3 and 0. The vertical lines correspond to the reference values $\tau_t \simeq 0.13$, $\tau = 1$, $\tau_b \simeq 230$ and $\tau_\tau \simeq 1300$.</figcaption></figure>

By matching with eq. (B.10), one finds that the contribution of a fermion loop to the effective $hgg$-couplings is

$$c_{hgg}^i = \frac{\alpha_s}{8\pi v} C(R_{ci}) \frac{y_i v}{m_i} A_{1/2}(\tau_i), \quad \tilde{c}_{hgg}^i = \frac{\alpha_s}{8\pi v} C(R_{ci}) \frac{\tilde{y}_i v}{m_i} \tilde{A}_{1/2}(\tau_i), \quad (B.17)$$

where $c_{hgg} \equiv |\sum_i c_{hgg}^i|$ and $\tilde{c}_{hgg} \equiv |\sum_i \tilde{c}_{hgg}^i|$. In the heavy fermion limit, $2m_i \gg m_h$, one can use $A_{1/2}(0) = 4/3$ and $\tilde{A}_{1/2}(0) = 2$. We note that, in the literature, a factor 1/2 is sometimes missing in the expression for $\tilde{c}_{hgg}^t$.

One can use the Low Energy Theorem (LET) [113, 114] (see also [115–117]) to evaluate the effective $hVV'$ couplings induced by states much heavier than the EW scale. For a given sector of mixing states in the representation $(R_c, Q)$ of SU(3)$_c \times$ U(1)$_{em}$, the low energy result is a function of their mass matrix $M$ only. For the CP-conserving and CP-violating [118] gluon-gluon case one finds, respectively,

$$c_{hgg}^{LET} = \frac{\alpha_s}{12\pi} C(R_c) \frac{\partial}{\partial v} \ln \left[ \det (MM^\dagger) \right], \quad \tilde{c}_{hgg}^{LET} = \frac{\alpha_s}{4\pi} C(R_c) \frac{\partial}{\partial v} \arg \left[ \det (M) \right]. \quad (B.18)$$

This is very useful in the case of a large, complicated mass matrix $M$, because this expression is much easier to evaluate, with respect to an explicit computation of the mass eigenvalues $m_i$ and of the mass eigenstate couplings $y_i$ and $\tilde{y}_i$. Note, however, that this approximation requires all the mass eigenstates in a given sector to be heavy, $2m_i \gg m_h$. It is easy to check the consistency of eq. (B.17) and eq. (B.18) for one heavy chiral fermion (e.g. the SM top quark), as $M_i = m_i = y_i v$ and $A_{1/2}(\tau_i) \simeq 4/3$.

## B.2.2 Higgs coupling to two photons

The fermions charged under U(1)$_{em}$ contribute to the Higgs-photon-photon couplings $c_{h\gamma\gamma}$ and $\tilde{c}_{h\gamma\gamma}$ at one loop. In the SM, there is also the contribution from W-boson loops, that
we include using the SM tree-level couplings of the W to the Higgs and to the photon. The SM decay width is given by [113, 114, 119]

$$ \Gamma_{\text{SM}}(h \to \gamma\gamma) = \frac{\alpha^2 m_h^3}{256 \pi^3 v^2} \left| A_1(\tau_W) + \sum_{f_i \in \text{SM}} N_{ci} Q_i^2 A_{1/2}(\tau_i) \right|^2, \qquad (\text{B.19}) $$

where $\tau_W \equiv m_h^2/(4m_W^2)$, $\tau_i \equiv m_h^2/(4m_i^2)$, and the form factor for the W-loops reads

$$ A_1(\tau) = - \frac{2\tau^2 + 3\tau + 3(2\tau - 1)f(\tau)}{\tau^2}. \qquad (\text{B.20}) $$

The W contribution is dominant, $A_1(\tau_W) \simeq -8.36$, and it interferes destructively with the top-quark loop, $N_{ct}Q_t^2A_{1/2}(\tau_t) \simeq 1.83$.

In presence of extra fermions, there are new contributions to $h \to \gamma\gamma$ that depend, as in the case of $h \to gg$, on the Yukawa couplings $y_i$ and $\tilde{y}_i$,

$$ \Gamma(h \to \gamma\gamma) = \frac{\alpha^2 m_h^3}{256 \pi^3 v^2} \left[ |A_1(\tau_W) + A_f^{\gamma\gamma}|^2 + |\tilde{A}_f^{\gamma\gamma}|^2 \right], \qquad (\text{B.21}) $$

where

$$ A_f^{\gamma\gamma} = \sum_i \frac{y_i v}{m_i} N_{ci} Q_i^2 A_{1/2}(\tau_i), \qquad \tilde{A}_f^{\gamma\gamma} = \sum_i \frac{\tilde{y}_i v}{m_i} N_{ci} Q_i^2 \tilde{A}_{1/2}(\tau_i). \qquad (\text{B.22}) $$

In terms of the coefficients of the effective Lagrangian eq. (B.8), the contribution of each fermion is given by

$$ c_{h\gamma\gamma}^i = \frac{\alpha y_i v}{8\pi v m_i} N_{ci} Q_i^2 A_{1/2}(\tau_i), \qquad \tilde{c}_{h\gamma\gamma}^i = \frac{\alpha \tilde{y}_i v}{8\pi v m_i} N_{ci} Q_i^2 \tilde{A}_{1/2}(\tau_i). \qquad (\text{B.23}) $$

The LET approximation, for a set of heavy fermions in the representation $(R_c, Q)$ with a mass matrix $M$, is given by

$$ c_{h\gamma\gamma}^{LET} = \frac{\alpha}{12\pi} Q^2 N_c \frac{\partial}{\partial v} \ln \left[ \det (MM^\dagger) \right], \qquad \tilde{c}_{h\gamma\gamma}^{LET} = \frac{\alpha}{4\pi} Q^2 N_c \frac{\partial}{\partial v} \arg \left[ \det (M) \right], \qquad (\text{B.24}) $$

in analogy with eq. (B.18).

### B.2.3 Higgs coupling to a Z boson and a photon

The last loop-induced coupling to be considered is $hZ\gamma$. It is generated by W-boson loops, that we take to be SM-like, as well as by fermionic triangle loops. The Z-boson couplings to fermion mass eigenstates are defined in eq. (A.6).

The Higgs decay width into a photon and a Z in the SM is given by [120, 121]

$$ \Gamma_{\text{SM}}(h \to \gamma Z) = \frac{\alpha g^2 c_w^2 m_h^3}{512 \pi^4 v^2} \left(1 - \frac{m_Z^2}{m_h^2}\right)^3 \left| A_1(\tau_W, \lambda_W) + \sum_{f_i \in \text{SM}} \frac{N_{ci} Q_i g_i^V}{c_w^2} A_{1/2}(\tau_i, \lambda_i) \right|^2, \qquad (\text{B.25}) $$

where $\lambda_W \equiv m_Z^2/(4m_W^2) = (m_Z/m_h)^2\tau_W \simeq 0.52\tau_W$, and analogously $\lambda_i \equiv m_Z^2/(4m_i^2) \simeq 0.52\tau_i$. Note that only the $Zf_i\bar{f}_i$ vector coupling contributes, $g_i^V = T_3(f_{Li})/2 - Q_i s_w^2$. The form factors are given by

$$ A_1(\tau, \lambda) = 2[3 + 2\tau - 2\lambda(1 + 2\tau)] I_1(\tau, \lambda) - 16(1 - \lambda)I_2(\tau, \lambda), \qquad (\text{B.26}) $$

$$ A_{1/2}(\tau, \lambda) = 4[I_2(\tau, \lambda) - I_1(\tau, \lambda)], \qquad (\text{B.27}) $$
<figure><img src="image_16.png" /><figcaption>**Figure 15.** Real (blue lines) and imaginary (red lines) parts of the form factors $A_{1/2}(\tau, \lambda)$ (solid lines) and $\tilde{A}_{1/2}(\tau, \lambda)$ (dashed lines), for $\lambda = (m_Z/m_h)^2\tau \simeq 0.52\tau$. The horizontal lines correspond to the asymptotic values 2, 4/3 and 0. The vertical lines correspond to $\tau_t \simeq 0.13$, $\tau = 1$, $\tau \simeq 1.9$ ($\lambda = 1$), $\tau_b \simeq 230$ and $\tau_\tau \simeq 1300$.</figcaption></figure>

where

$$I_1(\tau, \lambda) = -\frac{1}{2(\tau - \lambda)} + \frac{f(\tau) - f(\lambda)}{2(\tau - \lambda)^2} + \frac{\lambda[g(\tau) - g(\lambda)]}{(\tau - \lambda)^2}, \quad I_2(\tau, \lambda) = \frac{f(\tau) - f(\lambda)}{2(\tau - \lambda)}, \quad (B.28)$$

$$g(\tau) = \begin{cases} \frac{\sqrt{\tau^{-1}-1} \arcsin \sqrt{\tau}}{2} & \text{for } \tau \le 1, \\ \frac{\log \left( \frac{1+\sqrt{1-\tau^{-1}}}{1-\sqrt{1-\tau^{-1}}} - i\pi \right)}{2} & \text{for } \tau > 1. \end{cases} \quad (B.29)$$

The normalisation is chosen to match with the $\gamma\gamma$ form factors: $A_1(\tau, 0) = A_1(\tau)$ and $A_{1/2}(\tau, 0) = A_{1/2}(\tau)$. The behaviour of $A_{1/2}(\tau, \lambda)$ is displayed in figure 15, for the relevant case $\lambda = (m_Z/m_h)^2\tau$. The W-boson and t-quark summands in eq. (B.25) take the value $A_1(\tau_W, \lambda_W) \simeq -6.64$ and $N_{ct}Q_tg_t^A A_{1/2}(\tau_t, \lambda_t)/c_w^2 \simeq 0.37$, with the lighter SM fermions adding a very small contribution.

In a generic fermionic extension of the SM, we find a decay width

$$\Gamma(h \to \gamma Z) = \frac{\alpha g^2 c_w^2 m_h^3}{512 \pi^4 v^2} \left(1 - \frac{m_Z^2}{m_h^2}\right)^3 \left[ |A_1(\tau_W, \lambda_W) + \mathcal{A}_f^{Z\gamma}|^2 + |\tilde{\mathcal{A}}_f^{Z\gamma}|^2 \right], \quad (B.30)$$

with the CP-even and odd fermionic amplitudes given by

$$\mathcal{A}_f^{Z\gamma} = \sum_{j,k} \frac{N_{ck} Q_k v}{c_w^2 \sqrt{m_j m_k}} [\mathrm{Re}(g_{kj}^V y_{jk}) a_{1/2}(m_j, m_k, m_k) + i \mathrm{Im}(g_{kj}^A \tilde{y}_{jk}) b_{1/2}(m_j, m_k, m_k)], \quad (B.31)$$

$$\tilde{\mathcal{A}}_f^{Z\gamma} = \sum_{j,k} \frac{N_{ck} Q_k v}{c_w^2 \sqrt{m_j m_k}} [\mathrm{Re}(g_{kj}^V \tilde{y}_{jk}) \tilde{a}_{1/2}(m_j, m_k, m_k) + i \mathrm{Im}(g_{kj}^A \tilde{y}_{jk}) \tilde{b}_{1/2}(m_j, m_k, m_k)]. \quad (B.32)$$

The explicit expression of the four independent form factors will be given below. As far as we know, this expression for $\Gamma(h \to \gamma Z)$, corresponding to a generic set of fermions, was not
available in the literature. Here the sum runs over all pairs of fermion mass eigenstates: the triangular fermion loop is formed by one $f_j$ propagator from the $h$ vertex to the $Z$ vertex, and two $f_k$ propagators from $Z$ to $\gamma$, and from $\gamma$ to $h$. As both $h$ and $Z$ can have off-diagonal couplings, $j$ and $k$ can be different. Note that only those combination of couplings that are even under the charge conjugation C contribute, because the transition $h \to Z\gamma$ is even: under C, one has $Q \to -Q$, $g_{ij}^V \to -g_{ij}^{V*}$ and $x_{ij} \to x_{ji} = x_{ij}^*$, for $x = g^A, y, \tilde{y}$. The P and CP-even (odd) amplitude corresponds to an even (odd) number of axial-vector and pseudo-scalar couplings $g^A$ and $\tilde{y}$.

Let us discuss first the loops involving one fermion mass eigenstate only ($j = k$). The diagonal couplings $g_i^{V,A}$, $y_i$ and $\tilde{y}_i$ are all real, therefore the form factors $b_{1/2}$ and $\tilde{b}_{1/2}$ are irrelevant, while the others reduce to

$$a_{1/2}(m, m, m) = A_{1/2}(\tau, \lambda), \quad \tilde{a}_{1/2}(m, m, m) = \tilde{A}_{1/2}(\tau, \lambda) \equiv 4I_2(\tau, \lambda). \qquad (B.33)$$

These two form factors are displayed in figure 15 as a function of $\tau$. As usual the normalisation matches with the $\gamma\gamma$ form factors, in particular $\tilde{A}_{1/2}(\tau, 0) = \tilde{A}_{1/2}(\tau)$. Comparing with eq. (B.10), one finds that the contributions of such fermion 'diagonal' loop to the effective $h\gamma Z$ couplings are

$$c_{h\gamma Z}^i = \frac{\alpha}{4\pi s_w c_w v} \frac{y_i v}{m_i} N_{c_i} Q_i g_i^V A_{1/2}(\tau_i, \lambda_i), \quad \tilde{c}_{h\gamma Z}^i = \frac{\alpha}{4\pi s_w c_w v} \frac{\tilde{y}_i v}{m_i} N_{cf} Q_i g_i^V \tilde{A}_{1/2}(\tau_i, \lambda_i). \qquad (B.34)$$

Let us now discuss the loops involving two fermion mass eigenstates ($j \neq k$). The form factors are given by

$$\frac{a_{1/2}(m_j, m_k, m_k)}{\sqrt{m_j m_k}} = -\frac{4}{m_Z^2 - m_h^2} \left\{ \left[ \frac{A_0(m_j) - A_0(m_k)}{m_h^2} + 1 \right] (m_j + m_k) \right. \\ + \frac{B_0(m_h^2; m_j, m_k)}{m_Z^2 - m_h^2} \left[ (m_j + m_k) \left( 2m_j^2 - 2m_k^2 - m_h^2 + \frac{m_Z^2}{m_h^2} (m_k^2 - m_j^2) \right) + 2m_k(m_h^2 - m_Z^2) \right] \\ + \frac{B_0(m_Z^2; m_j, m_k)}{m_Z^2 - m_h^2} \left[ (m_j + m_k)(m_k^2 - m_j^2) + m_k(2m_Z^2 - m_h^2) + m_j m_h^2 \right] \\ \left. + C_0(m_Z^2, 0, m_h^2; m_j, m_k, m_k) \left[ 2m_k^2(m_j + m_k) + m_k(m_Z^2 - m_h^2) \right] \right\}, \qquad (B.35)$$

$$\frac{\tilde{a}_{1/2}(m_j, m_k, m_k)}{\sqrt{m_j m_k}} = -4 \left[ \frac{B_0(m_h^2; m_j, m_k) - B_0(m_Z^2; m_j, m_k)}{m_Z^2 - m_h^2} (m_j - m_k) \right. \\ \left. + C_0(m_Z^2, 0, m_h^2; m_j, m_k, m_k) m_k \right], \qquad (B.36)$$

$$\frac{b_{1/2}(m_j, m_k, m_k)}{\sqrt{m_j m_k}} = \frac{a_{1/2}(-m_j, m_k, m_k)}{\sqrt{m_j m_k}}, \quad \frac{\tilde{b}_{1/2}(m_j, m_k, m_k)}{\sqrt{m_j m_k}} = \frac{\tilde{a}_{1/2}(-m_j, m_k, m_k)}{\sqrt{m_j m_k}}, \qquad (B.37)$$

where $A_0$, $B_0$ and $C_0$ are the standard Passarino-Veltman scalar functions [122, 123], in the convention of ref. [124]. In the literature, these 'off-diagonal' loops are often neglected but, in models with significant $h$ and $Z$ off-diagonal couplings, they may provide a contribution
to the decay width of the same order as the 'diagonal' loops. For example, the form factors in eqs. (B.35)-(B.37) have been already employed in supersymmetric models to compute the charginos loops [125-127].

It is useful to combine all the loops involving two given fermions $f_j$ and $f_k$. As $\mathrm{Re}(g_{kj}^V y_{jk}) = \mathrm{Re}(g_{jk}^V y_{kj})$ and $\mathrm{Im}(g_{kj}^A \tilde{y}_{jk}) = -\mathrm{Im}(g_{jk}^A \tilde{y}_{kj})$, the combinations that appear in the total amplitude are

$$A_{1/2}(\tau_j, \lambda_j, \tau_k, \lambda_k) \equiv \frac{1}{2} [a_{1/2}(m_j, m_k, m_k) + a_{1/2}(m_k, m_j, m_j)], \quad (B.38)$$

$$B_{1/2}(\tau_j, \lambda_j, \tau_k, \lambda_k) \equiv \frac{1}{2} [b_{1/2}(m_j, m_k, m_k) - b_{1/2}(m_k, m_j, m_j)], \quad (B.39)$$

and analog definitions for the CP-odd counterparts $\tilde{A}_{1/2}$ and $\tilde{B}_{1/2}$. In figure 16 we illustrate the behaviour of these four form factors as a function of $\tau = m_h^2/(4m^2)$, where $m$ is the mass of the lightest fermion, for a fixed value of the ratio $r = m'/m$, where $m'$ is the mass of the heaviest fermion. In the limit $r = 1$ one recovers the diagonal form factors, shown in figure 15. Since $m'$ is the mass of a new charged fermion, it should be sufficiently large to comply with experimental lower bounds; requiring for example $m' > m_h$, one finds that only the region $\tau < r^2/4$ is relevant for phenomenology. Note that the behaviour of the form factors as $\tau \to 0$ is sensitive to the mass ratio: as $r$ increases from 1 to infinity, the asymptotic regime settles at larger values of $\tau$, and the asymptotic value of the form factors $A_{1/2}$ and $\tilde{A}_{1/2}$ tends to zero as $1/\sqrt{r}$. The form factors $B_{1/2}$ and $\tilde{B}_{1/2}$ are zero for $r = 1$, then become of order one as $r$ grows, then tend to zero in the large-$r$ limit.

## B.3 Experimental constraints on the Higgs couplings

Here we collect the constraints on the Higgs couplings that we use in our analysis. For a given Higgs-decay final state $\alpha$, the LHC measures the signal strength $\mu_\alpha$ defined as

$$\mu_{\alpha} \equiv \frac{\sigma(pp \to h)}{\sigma^{\mathrm{SM}}(pp \to h)} \frac{Br(h \to \alpha)}{Br^{\mathrm{SM}}(h \to \alpha)} = \frac{\sigma(pp \to h)}{\sigma^{\mathrm{SM}}(pp \to h)} \frac{\Gamma(h \to \alpha)}{\Gamma^{\mathrm{SM}}(h \to \alpha)} \frac{\Gamma_h^{\mathrm{SM}}}{\Gamma_h}, \quad (B.40)$$

where $\Gamma_h$ is the total Higgs width. In table 4 we report the present determination of $\mu_\alpha$ for $\alpha = \gamma\gamma, ZZ^*, WW^*, b\bar{b}, \tau\tau, \gamma Z, \mu\mu$ as well as on the invisible width, by the ATLAS and CMS collaborations. The expected precision for a luminosity of 300 - 3000 fb$^{-1}$ at 14 TeV [128, 129] is reported for these same channels in table 5.

From a global fit of the Higgs data, one can also extract information on the Higgs coupling to gluons. Taking a rough extrapolation from the fit in figure 16 of ref. [35], we find $0.5 \lesssim R_{gg} \lesssim 1.8$ at 99% C.L., where $R_{gg}$ is defined in eq. (3.4). In the same way we extract the analogue quantity for the diphoton channel, $0.5 \lesssim R_{\gamma\gamma} \lesssim 1.9$ at 99% C.L., that we employ throughout this paper.

The new fermions may or may not affect each of the three factors on the right-hand side of eq. (B.40). Let us discuss first the Higgs production cross section. The dominant gluon fusion channel can be modified at leading order only by coloured fermions. The weak-vector-boson fusion and associated production can be modified, at tree level, only by fermions mixing with the initial state quarks: as we limit our analysis to mixing with
<figure><img src="image_17.png" /><figcaption>**Figure 16.** Form factors for the triangle loops involving two fermions of mass *m* and *m' = r m*, for *r* = 3 and *r* = 10, in the left and right-hand panels, respectively. We show the real (in blue) and imaginary (in red) parts of *A*<sub>1/2</sub>(*τ*, *λ*, *τ/r*<sup>2</sup>, *λ/r*<sup>2</sup>) (solid lines, upper panels), *A*&#773;<sub>1/2</sub>(*τ*, *λ*, *τ/r*<sup>2</sup>, *λ/r*<sup>2</sup>) (dashed, upper), *B*<sub>1/2</sub>(*τ*, *λ*, *τ/r*<sup>2</sup>, *λ/r*<sup>2</sup>) (solid, lower) and *B*&#773;<sub>1/2</sub>(*τ*, *λ*, *τ/r*<sup>2</sup>, *λ/r*<sup>2</sup>) (dashed, lower), as a function of *τ* ≡ *4m*<sub>*h*</sub><sup>2</sup>*m*<sup>2</sup>, for a fixed value of *λ* ≡ (*m*<sub>*Z*</sub>/*m*<sub>*h*</sub>)<sup>2</sup>*τ* ≃ 0.52 *τ*. The horizontal lines correspond to the asymptotic values for the case *r* = 1 (see figure 15). The vertical lines correspond to the third family masses, *τ*<sub>*t*</sub> ≃ 0.13, *τ*<sub>*b*</sub> ≃ 230 and *τ*<sub>*τ*</sub> ≃ 1300, and to the threshold values, *m* + *m*′ = *m*<sub>*h*</sub> [*τ* = (1 + *r*)<sup>2</sup>/4], and *m* + *m*′ = *m*<sub>*Z*</sub> [*τ* = (m<sub>*h*</sub>/m<sub>*Z*</sub>)<sup>2</sup>(1 + *r*)<sup>2</sup>/4].</figcaption></figure>
<table><caption>**Table 4.** Higgs signal strengths measured by the ATLAS and CMS collaborations at $\sqrt{s} = 7$ and 8 TeV and their combination. The error bars and upper limits correspond respectively to $\pm 1\sigma$ and 95% C.L.. In this paper we adopt the value of the Higgs mass and of the signal strengths from the combined fit of the ATLAS and CMS data, reported in the last column.</caption><thead><tr><th></th><th>ATLAS</th><th>CMS</th><th>ATLAS+CMS</th></tr></thead><tbody><tr><td>√s</td><td>7+8 TeV</td><td>7+8 TeV</td><td>7+8 TeV</td></tr><tr><td>Λ</td><td>4.7 + 20.3 fb<sup>-1</sup></td><td>5.1 + 19.7 fb<sup>-1</sup></td><td></td></tr><tr><td>m<sub>h</sub></td><td>125.36 ± 0.41 GeV [14]</td><td>125.02<sup>+0.29</sup><sub>-0.31</sub> GeV [12]</td><td>125.09 ± 0.24 GeV [13]</td></tr><tr><td>μ<sub>γγ</sub></td><td>1.17<sup>+0.28</sup><sub>-0.26</sub> [14]</td><td>1.12 ± 0.24 [12]</td><td>1.13<sup>+0.24</sup><sub>-0.21</sub> [35]</td></tr><tr><td>μ<sub>ZZ*</sub>→4l</td><td>1.46<sup>+0.40</sup><sub>-0.34</sub> [14]</td><td>1.00 ± 0.29 [12]</td><td>1.29<sup>+0.29</sup><sub>-0.25</sub> [35]</td></tr><tr><td>μ<sub>WW*</sub></td><td>1.18<sup>+0.24</sup><sub>-0.21</sub> [14]</td><td>0.83 ± 0.21 [12]</td><td>1.08<sup>+0.22</sup><sub>-0.19</sub> [35]</td></tr><tr><td>μ<sub>ττ</sub></td><td>1.44<sup>+0.42</sup><sub>-0.37</sub> [14]</td><td>0.91 ± 0.28 [12]</td><td>1.07<sup>+0.35</sup><sub>-0.28</sub> [35]</td></tr><tr><td>μ<sub>b<span style="text-decoration: overline">b</span></sub></td><td>0.63<sup>+0.39</sup><sub>-0.37</sub> [14]</td><td>0.84 ± 0.44 [12]</td><td>0.65<sup>+0.37</sup><sub>-0.28</sub> [35]</td></tr><tr><td>μ<sub>global</sub></td><td>1.18<sup>+0.15</sup><sub>-0.14</sub> [14]</td><td>1.00 ± 0.14 [12]</td><td>1.09<sup>+0.11</sup><sub>-0.10</sub> [35]</td></tr><tr><td>μ<sub>γZ</sub></td><td>&lt; 11.0 [130]</td><td>&lt; 9.5 [131]</td><td></td></tr><tr><td>μ<sub>μμ</sub></td><td>&lt; 7.0 [68]</td><td>&lt; 7.4 [69]</td><td></td></tr><tr><td>Γ<sub>invisible</sub>/Γ<sub>h</sub></td><td>&lt; 0.29 [132]</td><td>&lt; 0.58 [133]</td><td></td></tr></tbody></table>

the third family, we neglect these modifications. Finally, the $t\bar{t}$ associated production can be corrected by those fermions mixing with the top quark. Concerning the total Higgs decay width $\Gamma_h$, the dominant branching ratio into $b\bar{b}$ is affected by fermions mixing with the bottom quark, and the second dominant decay channel into $WW^*$ is not modified by new fermions at leading order. Finally, $\Gamma_h$ may be modified significantly by new invisible decays, that are possible in the presence of sterile neutrinos. When both $\sigma(pp \to h)$ and $\Gamma_h$ are close to their SM value, the signal strength in eq. (B.40) reduces to $\mu_\alpha \simeq R_\alpha$, where

$$R_{\alpha} \equiv \frac{\Gamma(h \to \alpha)}{\Gamma^{\text{SM}}(h \to \alpha)} = \frac{|\mathcal{A}_{\text{SM}}^{\alpha} + \mathcal{A}_{\text{new}}^{\alpha}|^2 + |\tilde{\mathcal{A}}_{\text{new}}^{\alpha}|^2}{|\mathcal{A}_{\text{SM}}^{\alpha}|^2} . \qquad (\text{B.41})$$

Here $\mathcal{A}_{\text{new}}^{\alpha}$ and $\tilde{\mathcal{A}}_{\text{new}}^{\alpha}$ are the parity-even and odd new physics amplitudes, respectively. The approximation $\mu_\alpha \simeq R_\alpha$ holds for all colourless new fermions, with the possible exception of light sterile neutrinos.

Several groups performed global fits of the Higgs couplings to the SM particles, allowing for deviations in both the fermionic and bosonic decay channels, see e.g. refs. [134–141]. The fit of ref. [142] analyzed deviations in the Higgs couplings in the presence of new fermions only.
<table><caption>**Table 5.** Expected relative uncertainty at $1\sigma$ on the signal strengths $\mu_\alpha$ for ATLAS and CMS. The expected precisions correspond to $\sqrt{s} = 14$ TeV and $\mathcal{L} = 300$ and $3000 \text{ fb}^{-1}$. We also display the expected limit at 95% C.L. on $\Gamma_{invisible}/\Gamma_h$ for the same luminosities. For CMS the two numbers correspond to two different estimations of the future uncertainties [129].</caption><thead><tr><th></th><th colspan="2">ATLAS [128]</th><th colspan="2">CMS [129]</th></tr></thead><tbody><tr><td>Δμ<sub>α</sub>/μ<sub>α</sub></td><td>300 fb<sup>-1</sup></td><td>3000 fb<sup>-1</sup></td><td>300 fb<sup>-1</sup></td><td>3000 fb<sup>-1</sup></td></tr><tr><td>γγ</td><td>0.13</td><td>0.09</td><td>[0.06,0.12]</td><td>[0.04,0.08]</td></tr><tr><td>ZZ</td><td>0.11</td><td>0.09</td><td>[0.07,0.11]</td><td>[0.04,0.07]</td></tr><tr><td>WW</td><td>0.13</td><td>0.11</td><td>[0.06,0.11]</td><td>[0.04,0.07]</td></tr><tr><td>ττ</td><td>0.21</td><td>0.19</td><td>[0.08,0.14]</td><td>[0.05,0.08]</td></tr><tr><td>b<span style="text-decoration: overline">b</span></td><td>0.26</td><td>0.14</td><td>[0.11,0.14]</td><td>[0.05,0.07]</td></tr><tr><td>γZ</td><td>0.46</td><td>0.30</td><td>[0.62,0.62]</td><td>[0.20,0.24]</td></tr><tr><td>μμ</td><td>0.39</td><td>0.16</td><td>[0.40,0.42]</td><td>[0.20,0.24]</td></tr><tr><td>Γ<sub>invisible</sub>/Γ<sub>h</sub></td><td>&lt; 0.22</td><td>&lt; 0.14</td><td>&lt; [0.17,0.28]</td><td>&lt; [0.06,0.17]</td></tr></tbody></table>

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**References**

[1] H. Flacher, M. Goebel, J. Haller, A. Hocker, K. Monig and J. Stelzer, *Revisiting the Global Electroweak Fit of the Standard Model and Beyond with Gfitter*, Eur. Phys. J. C 60 (2009) 543 [Erratum ibid. C 71 (2011) 1718] [arXiv:0811.0009] [INSPIRE].

[2] DELPHI, OPAL, LEP ELECTROWEAK, ALEPH and L3 collaborations, S. Schael et al., *Electroweak Measurements in Electron-Positron Collisions at W-Boson-Pair Energies at LEP*, Phys. Rept. 532 (2013) 119 [arXiv:1302.3415] [INSPIRE].

[3] PARTICLE DATA GROUP collaboration, K.A. Olive et al., *Review of Particle Physics*, Chin. Phys. C 38 (2014) 090001 [INSPIRE].

[4] M. Raidal et al., *Flavour physics of leptons and dipole moments*, Eur. Phys. J. C 57 (2008) 13 [arXiv:0801.1826] [INSPIRE].

[5] G. Isidori, Y. Nir and G. Perez, *Flavor Physics Constraints for Physics Beyond the Standard Model*, Ann. Rev. Nucl. Part. Sci. 60 (2010) 355 [arXiv:1002.0900] [INSPIRE].

[6] D. Toback and L. ŽIVković, *Review of Physics Results from the Tevatron: Searches for New Particles and Interactions*, Int. J. Mod. Phys. A 30 (2015) 1541007 [arXiv:1409.4910] [INSPIRE].

[7] PARTICLE DATA GROUP collaboration, K. Nakamura et al., *Review of particle physics*, J. Phys. G 37 (2010) 075021 [INSPIRE].
[8] ATLAS collaboration, https://wiki.cern.ch/twiki/bin/view/AtlasPublic.

[9] CMS collaboration, http://cms-results.web.cern.ch/cms-results/public-results/publications/.

[10] ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 [arXiv:1207.7214] [INSPIRE].

[11] CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE].

[12] CMS collaboration, Precise determination of the mass of the Higgs boson and tests of compatibility of its couplings with the standard model predictions using proton collisions at 7 and 8 TeV, Eur. Phys. J. C 75 (2015) 212 [arXiv:1412.8662] [INSPIRE].

[13] ATLAS and CMS collaborations, Combined Measurement of the Higgs Boson Mass in pp Collisions at $\sqrt{s}$ = 7 and 8 TeV with the ATLAS and CMS Experiments, Phys. Rev. Lett. 114 (2015) 191803 [arXiv:1503.07589] [INSPIRE].

[14] ATLAS collaboration, Measurements of the Higgs boson production and decay rates and coupling strengths using pp collision data at $\sqrt{s}$ = 7 and 8 TeV in the ATLAS experiment, arXiv:1507.04548 [INSPIRE].

[15] SLD ELECTROWEAK GROUP, DELPHI, ALEPH, SLD, SLD HEAVY FLAVOUR GROUP, OPAL, LEP ELECTROWEAK WORKING GROUP and L3 collaborations, S. Schael et al., Precision electroweak measurements on the Z resonance, Phys. Rept. 427 (2006) 257 [hep-ex/0509008] [INSPIRE].

[16] D.B. Kaplan, Flavor at SSC energies: A New mechanism for dynamically generated fermion masses, Nucl. Phys. B 365 (1991) 259 [INSPIRE].

[17] R. Contino and A. Pomarol, Holography for fermions, JHEP 11 (2004) 058 [hep-th/0406257] [INSPIRE].

[18] M. Cirelli, N. Fornengo and A. Strumia, Minimal dark matter, Nucl. Phys. B 753 (2006) 178 [hep-ph/0512090] [INSPIRE].

[19] E. Del Nobile, R. Franceschini, D. Pappadopulo and A. Strumia, Minimal Matter at the Large Hadron Collider, Nucl. Phys. B 826 (2010) 217 [arXiv:0908.1567] [INSPIRE].

[20] L. Di Luzio, R. Gröber, J.F. Kamenik and M. Nardecchia, Accidental matter at the LHC, JHEP 07 (2015) 074 [arXiv:1504.00359] [INSPIRE].

[21] I. Picek and B. Radovcic, Nondecoupling of terascale isosinglet quark and rare K- and B-decays, Phys. Rev. D 78 (2008) 015014 [arXiv:0804.2216] [INSPIRE].

[22] G. Cacciapaglia, A. Deandrea, L. Panizzi, N. Gaur, D. Harada and Y. Okada, Heavy Vector-like Top Partners at the LHC and flavour constraints, JHEP 03 (2012) 070 [arXiv:1108.6329] [INSPIRE].

[23] C. Han, A. Kobakhidze, N. Liu, L. Wu and B. Yang, Constraining Top partner and Naturalness at the LHC and TLEP, Nucl. Phys. B 890 (2014) 388 [arXiv:1405.1498] [INSPIRE].

[24] E. Witten, An SU(2) Anomaly, Phys. Lett. B 117 (1982) 324 [INSPIRE].
[25] O. Eberhardt et al., *Impact of a Higgs boson at a mass of 126 GeV on the standard model with three and four fermion generations*, Phys. Rev. Lett. **109** (2012) 241802 [arXiv:1209.1101] [INSPIRE].

[26] A. Azatov et al., *Higgs boson production via vector-like top-partner decays: Diphoton or multilepton plus multijets channels at the LHC*, Phys. Rev. D **85** (2012) 115022 [arXiv:1204.0455] [INSPIRE].

[27] M. Montull, F. Riva, E. Salvioni and R. Torre, *Higgs Couplings in Composite Models*, Phys. Rev. D **88** (2013) 095006 [arXiv:1308.0559] [INSPIRE].

[28] T. Flacke, J.H. Kim, S.J. Lee and S.H. Lim, *Constraints on composite quark partners from Higgs searches*, JHEP **05** (2014) 123 [arXiv:1312.5316] [INSPIRE].

[29] C.-Y. Chen, S. Dawson and I.M. Lewis, *Top Partners and Higgs Boson Production*, Phys. Rev. D **90** (2014) 035016 [arXiv:1406.3349] [INSPIRE].

[30] O. Matsedonskyi, G. Panico and A. Wulzer, *On the Interpretation of Top Partners Searches*, JHEP **12** (2014) 097 [arXiv:1409.0100] [INSPIRE].

[31] ATLAS collaboration, *Searches for heavy long-lived sleptons and R-Hadrons with the ATLAS detector in pp collisions at $\sqrt{s}$ = 7 TeV*, Phys. Lett. B **720** (2013) 277 [arXiv:1211.1597] [INSPIRE].

[32] CMS collaboration, *Searches for long-lived charged particles in pp collisions at $\sqrt{s}$ = 7 and 8 TeV*, JHEP **07** (2013) 122 [arXiv:1305.0491] [INSPIRE].

[33] ATLAS collaboration, *Searches for heavy long-lived charged particles with the ATLAS detector in proton-proton collisions at $\sqrt{s}$ = 8 TeV*, JHEP **01** (2015) 068 [arXiv:1411.6795] [INSPIRE].

[34] M. Fairbairn, A.C. Kraan, D.A. Milstead, T. Sjöstrand, P.Z. Skands and T. Sloan, *Stable massive particles at colliders*, Phys. Rept. **438** (2007) 1 [hep-ph/0611040] [INSPIRE].

[35] ATLAS and CMS collaborations, *Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMS analysis of the LHC pp collision data at $\sqrt{s}$ = 7 and 8 TeV*, ATLAS-CONF-2015-044 (2015).

[36] S. Banerjee, M. Frank and S.K. Rai, *Higgs data confronts Sequential Fourth Generation Fermions in the Higgs Triplet Model*, Phys. Rev. D **89** (2014) 075005 [arXiv:1312.4249] [INSPIRE].

[37] A. Alves, E. Ramirez Barreto, D.A. Camargo and A.G. Dias, *A Model with Chiral Quarks of Electric Charges -4/3 and 5/3*, JHEP **07** (2013) 129 [arXiv:1306.1275] [INSPIRE].

[38] ATLAS collaboration, *Search for heavy long-lived multi-charged particles in pp collisions at $\sqrt{s}$ = 8 TeV using the ATLAS detector*, Eur. Phys. J. C **75** (2015) 362 [arXiv:1504.04188] [INSPIRE].

[39] ATLAS collaboration, *Search for Massive Long-lived Highly Ionising Particles with the ATLAS Detector at the LHC*, Phys. Lett. B **698** (2011) 353 [arXiv:1102.0459] [INSPIRE].

[40] D. Wyler and L. Wolfenstein, *Massless Neutrinos in Left-Right Symmetric Models*, Nucl. Phys. B **218** (1983) 205 [INSPIRE].

[41] R.N. Mohapatra and J.W.F. Valle, *Neutrino Mass and Baryon Number Nonconservation in Superstring Models*, Phys. Rev. D **34** (1986) 1642 [INSPIRE].
[42] M.C. Gonzalez-Garcia and J.W.F. Valle, *Fast Decaying Neutrinos and Observable Flavor Violation in a New Class of Majoron Models*, Phys. Lett. B 216 (1989) 360 [INSPIRE].

[43] S.S.C. Law and K.L. McDonald, *Generalized inverse seesaw mechanisms*, Phys. Rev. D 87 (2013) 113003 [arXiv:1303.4887] [INSPIRE].

[44] A. de Gouvêa, *GeV seesaw, accidentally small neutrino masses and Higgs decays to neutrinos*, arXiv:0706.1732 [INSPIRE].

[45] J.-H. Chen, X.-G. He, J. Tandean and L.-H. Tsai, *Effect on Higgs Boson Decays from Large Light-Heavy Neutrino Mixing in Seesaw Models*, Phys. Rev. D 81 (2010) 113004 [arXiv:1001.5215] [INSPIRE].

[46] P.S. Bhupal Dev, R. Franceschini and R.N. Mohapatra, *Bounds on TeV Seesaw Models from LHC Higgs Data*, Phys. Rev. D 86 (2012) 093010 [arXiv:1207.2756] [INSPIRE].

[47] C.G. Cely, A. Ibarra, E. Molinaro and S.T. Petcov, *Higgs Decays in the Low Scale Type I See-Saw Model*, Phys. Lett. B 718 (2013) 957 [arXiv:1208.3654] [INSPIRE].

[48] S. Antusch and O. Fischer, *Testing sterile neutrino extensions of the Standard Model at future lepton colliders*, JHEP 05 (2015) 053 [arXiv:1502.05915] [INSPIRE].

[49] ATLAS collaboration, *Search for Majorana neutrino production in pp collisions at $\sqrt{s}=7$ TeV in dimuon final states with the ATLAS detector*, ATLAS-CONF-2012-139 (2012).

[50] ATLAS collaboration, *Search for heavy Majorana neutrinos with the ATLAS detector in pp collisions at $\sqrt{s}=8$ TeV*, JHEP 07 (2015) 162 [arXiv:1506.06020] [INSPIRE].

[51] CMS collaboration, *Search for heavy Majorana neutrinos in $\mu^{\pm}\mu^{\pm} + jets$ and $e^{\pm}e^{\pm} + jets$ events in pp collisions at $\sqrt{s}=7$ TeV*, Phys. Lett. B 717 (2012) 109 [arXiv:1207.6079] [INSPIRE].

[52] CMS collaboration, *Search for heavy Majorana neutrinos in $\mu^{\pm}\mu^{\pm} + jets$ events in proton-proton collisions at $\sqrt{s}=8$ TeV*, Phys. Lett. B 748 (2015) 144 [arXiv:1501.05566] [INSPIRE].

[53] A. Abada, C. Biggio, F. Bonnet, M.B. Gavela and T. Hambye, $\mu \to e\gamma$ and $\tau \to l\gamma$ decays in the fermion triplet seesaw model, Phys. Rev. D 78 (2008) 033007 [arXiv:0803.0481] [INSPIRE].

[54] A. Abada, C. Biggio, F. Bonnet, M.B. Gavela and T. Hambye, *Low energy effects of neutrino masses*, JHEP 12 (2007) 061 [arXiv:0707.4058] [INSPIRE].

[55] R. Franceschini, T. Hambye and A. Strumia, *Type-III see-saw at LHC*, Phys. Rev. D 78 (2008) 033002 [arXiv:0805.1613] [INSPIRE].

[56] L3 collaboration, P. Achard et al., *Search for heavy neutral and charged leptons in $e^{+}e^{-}$ annihilation at LEP*, Phys. Lett. B 517 (2001) 75 [hep-ex/0107015] [INSPIRE].

[57] CMS collaboration, *Search for heavy lepton partners of neutrinos in proton-proton collisions in the context of the type-III seesaw mechanism*, Phys. Lett. B 718 (2013) 348 [arXiv:1210.1797] [INSPIRE].

[58] ATLAS collaboration, *Search for type-III Seesaw heavy leptons in pp collisions at $\sqrt{s}=8$ TeV with the ATLAS Detector*, Phys. Rev. D 92 (2015) 032001 [arXiv:1506.01839] [INSPIRE].

[59] A. Falkowski, D.M. Straub and A. Vicente, *Vector-like leptons: Higgs decays and collider phenomenology*, JHEP 05 (2014) 092 [arXiv:1312.5329] [INSPIRE].
[60] W. Altmannshofer, M. Bauer and M. Carena, *Exotic Leptons: Higgs, Flavor and Collider Phenomenology*, JHEP 01 (2014) 060 [arXiv:1308.1987] [INSPIRE].

[61] T. Ma, B. Zhang and G. Cacciapaglia, *Doubly Charged Lepton from an Exotic Doublet at the LHC*, Phys. Rev. D 89 (2014) 093022 [arXiv:1404.2375] [INSPIRE].

[62] A. Delgado, C. Garcia Cely, T. Han and Z. Wang, *Phenomenology of a lepton triplet*, Phys. Rev. D 84 (2011) 073007 [arXiv:1105.5417] [INSPIRE].

[63] T. Ma, B. Zhang and G. Cacciapaglia, *Triplet with a doubly-charged lepton at the LHC*, Phys. Rev. D 89 (2014) 015020 [arXiv:1309.7396] [INSPIRE].

[64] ATLAS collaboration, *Evidence for the Higgs-boson Yukawa coupling to tau leptons with the ATLAS detector*, JHEP 04 (2015) 117 [arXiv:1501.04943] [INSPIRE].

[65] CMS collaboration, *Evidence for the 125 GeV Higgs boson decaying to a pair of $\tau$ leptons*, JHEP 05 (2014) 104 [arXiv:1401.5041] [INSPIRE].

[66] ATLAS collaboration, *Search for lepton-flavour-violating $H \to \mu\tau$ decays of the Higgs boson with the ATLAS detector*, arXiv:1508.03372 [INSPIRE].

[67] CMS collaboration, *Search for Lepton-Flavour-Violating Decays of the Higgs Boson*, Phys. Lett. B 749 (2015) 337 [arXiv:1502.07400] [INSPIRE].

[68] ATLAS collaboration, *Search for the Standard Model Higgs boson decay to $\mu^+\mu^-$ with the ATLAS detector*, Phys. Lett. B 738 (2014) 68 [arXiv:1406.7663] [INSPIRE].

[69] CMS collaboration, *Search for a standard model-like Higgs boson in the $\mu^+\mu^-$ and $e^+e^-$ decay channels at the LHC*, Phys. Lett. B 744 (2015) 184 [arXiv:1410.6679] [INSPIRE].

[70] K. Agashe, R. Contino, L. Da Rold and A. Pomarol, *A Custodial symmetry for $Zb\bar{b}$*, Phys. Lett. B 641 (2006) 62 [hep-ph/0605341] [INSPIRE].

[71] F. del Aguila, A. Carmona and J. Santiago, *Tau Custodial searches at the LHC*, Phys. Lett. B 695 (2011) 449 [arXiv:1007.4206] [INSPIRE].

[72] A. Carmona and F. Goertz, *Custodial Leptons and Higgs Decays*, JHEP 04 (2013) 163 [arXiv:1301.5856] [INSPIRE].

[73] L.G. Almeida, E. Bertuzzo, P.A.N. Machado and R.Z. Funchal, *Does $H \to \gamma\gamma$ Taste like vanilla New Physics?*, JHEP 11 (2012) 085 [arXiv:1207.5254] [INSPIRE].

[74] J. Kearney, A. Pierce and N. Weiner, *Vectorlike Fermions and Higgs Couplings*, Phys. Rev. D 86 (2012) 113005 [arXiv:1207.7062] [INSPIRE].

[75] A. Joglekar, P. Schwaller and C.E.M. Wagner, *Dark Matter and Enhanced Higgs to Di-photon Rate from Vector-like Leptons*, JHEP 12 (2012) 064 [arXiv:1207.4235] [INSPIRE].

[76] M. Redi, *Leptons in Composite MFV*, JHEP 09 (2013) 060 [arXiv:1306.1525] [INSPIRE].

[77] S.P. Martin, *A Supersymmetry primer*, hep-ph/9709356 [INSPIRE].

[78] H.K. Dreiner, J.S. Kim and O. Lebedev, *First LHC Constraints on Neutralinos*, Phys. Lett. B 715 (2012) 199 [arXiv:1206.3096] [INSPIRE].

[79] B. Ananthanarayan, J. Lahiri, P.N. Pandita and M. Patra, *Invisible decays of the lightest Higgs boson in supersymmetric models*, Phys. Rev. D 87 (2013) 115021 [arXiv:1306.1291] [INSPIRE].
[80] J.A. Casas, J.M. Moreno, K. Rolbiecki and B. Zaldivar, *Implications of light charginos for Higgs observables, LHC searches and dark matter*, JHEP 09 (2013) 099 [arXiv:1305.3274] [INSPIRE].

[81] B. Batell, S. Jung and C.E.M. Wagner, *Very Light Charginos and Higgs Decays*, JHEP 12 (2013) 075 [arXiv:1309.2297] [INSPIRE].

[82] F. del Aguila, M. Pérez-Victoria and J. Santiago, *Observable contributions of new exotic quarks to quark mixing*, JHEP 09 (2000) 011 [hep-ph/0007316] [INSPIRE].

[83] J.A. Aguilar-Saavedra, *Identifying top partners at LHC*, JHEP 11 (2009) 030 [arXiv:0907.3155] [INSPIRE].

[84] G. Cacciapaglia, A. Deandrea, D. Harada and Y. Okada, *Bounds and Decays of New Heavy Vector-like Top Partners*, JHEP 11 (2010) 159 [arXiv:1007.2933] [INSPIRE].

[85] S. Gopalakrishna, T. Mandal, S. Mitra and R. Tibrewala, *LHC Signatures of a Vector-like b'*, Phys. Rev. D 84 (2011) 055001 [arXiv:1107.4306] [INSPIRE].

[86] Y. Okada and L. Panizzi, *LHC signatures of vector-like quarks*, Adv. High Energy Phys. 2013 (2013) 364936 [arXiv:1207.5607] [INSPIRE].

[87] J.A. Aguilar-Saavedra, R. Benbrik, S. Heinemeyer and M. Pérez-Victoria, *Handbook of vectorlike quarks: Mixing and single production*, Phys. Rev. D 88 (2013) 094010 [arXiv:1306.0572] [INSPIRE].

[88] S. Gopalakrishna, T. Mandal, S. Mitra and G. Moreau, *LHC Signatures of Warped-space Vectorlike Quarks*, JHEP 08 (2014) 079 [arXiv:1306.2656] [INSPIRE].

[89] ATLAS collaboration, *Search for production of vector-like quark pairs and of four top quarks in the lepton plus jets final state in pp collisions at $\sqrt{s}$ = 8 TeV with the ATLAS detector*, ATLAS-CONF-2015-012 (2015).

[90] CMS collaboration, *Search for vector-like T quarks decaying to top quarks and Higgs bosons in the all-hadronic channel using jet substructure*, JHEP 06 (2015) 080 [arXiv:1503.01952] [INSPIRE].

[91] ATLAS collaboration, *Search for vectorlike B quarks in events with one isolated lepton, missing transverse momentum and jets at $\sqrt{s}$ = 8 TeV with the ATLAS detector*, Phys. Rev. D 91 (2015) 112011 [arXiv:1503.05425] [INSPIRE].

[92] ATLAS collaboration, *Search for pair and single production of new heavy quarks that decay to a Z boson and a third-generation quark in pp collisions at $\sqrt{s}$ = 8 TeV with the ATLAS detector*, JHEP 11 (2014) 104 [arXiv:1409.5500] [INSPIRE].

[93] CMS collaboration, *Search for vector-like quarks in final states with a single lepton and jets in pp collisions at $\sqrt{s}$ = 8 TeV*, CMS-PAS-B2G-12-017 (2012).

[94] CMS collaboration, *Search for pair-produced vector-like quarks of charge -1/3 decaying to bH using boosted Higgs jet-tagging in pp collisions at $\sqrt{s}$ = 8 TeV*, (2014).

[95] CMS collaboration, *Search for pair-produced vector-like quarks of charge -1/3 in lepton+jets final state in pp collisions at $\sqrt{s}$ = 8 TeV*, (2012).

[96] CMS collaboration, *Search for Vector-Like Charge 2/3 T Quarks in Proton-Proton Collisions at $\sqrt{s}$ = 8 TeV*, arXiv:1509.04177 [INSPIRE].

[97] R. Contino, L. Da Rold and A. Pomarol, *Light custodians in natural composite Higgs models*, Phys. Rev. D 75 (2007) 055014 [hep-ph/0612048] [INSPIRE].
[98] A. Pomarol and J. Serra, *Top Quark Compositeness: Feasibility and Implications*, Phys. Rev. D **78** (2008) 074026 [arXiv:0806.3247] [INSPIRE].

[99] E. Bertuzzo, P.A.N. Machado and R. Zukanovich Funchal, *Can New Colored Particles Illuminate the Higgs?*, JHEP **02** (2013) 086 [arXiv:1209.6359] [INSPIRE].

[100] O. Matsedonskyi, F. Riva and T. Vantalon, *Composite Charge 8/3 Resonances at the LHC*, JHEP **04** (2014) 059 [arXiv:1401.3740] [INSPIRE].

[101] G. Cacciapaglia, A. Deandrea, N. Gaur, D. Harada, Y. Okada and L. Panizzi, *Interplay of vector-like top partner multiplets in a realistic mixing set-up*, JHEP **09** (2015) 012 [arXiv:1502.00370] [INSPIRE].

[102] M. Gillioz, *A Light composite Higgs boson facing electroweak precision tests*, Phys. Rev. D **80** (2009) 055003 [arXiv:0806.3450] [INSPIRE].

[103] A. Azatov and J. Galloway, *Light Custodians and Higgs Physics in Composite Models*, Phys. Rev. D **85** (2012) 055013 [arXiv:1110.5646] [INSPIRE].

[104] J. Elias-Miró, J.R. Espinosa, E. Masso and A. Pomarol, *Renormalization of dimension-six operators relevant for the Higgs decays $h \to \gamma\gamma, \gamma Z$, JHEP **08** (2013) 033*, [arXiv:1302.5661] [INSPIRE].

[105] M.E. Peskin and T. Takeuchi, *A New constraint on a strongly interacting Higgs sector*, Phys. Rev. Lett. **65** (1990) 964 [INSPIRE].

[106] G. Altarelli and R. Barbieri, *Vacuum polarization effects of new physics on electroweak processes*, Phys. Lett. **B** **253** (1991) 161 [INSPIRE].

[107] M.E. Peskin and T. Takeuchi, *Estimation of oblique electroweak corrections*, Phys. Rev. D **46** (1992) 381 [INSPIRE].

[108] R. Barbieri, A. Pomarol, R. Rattazzi and A. Strumia, *Electroweak symmetry breaking after LEP-1 and LEP-2*, Nucl. Phys. **B** **703** (2004) 127 [hep-ph/0405040] [INSPIRE].

[109] GFITTER GROUP collaboration, M. Baak et al., *The global electroweak fit at NNLO and prospects for the LHC and ILC*, Eur. Phys. J. C **74** (2014) 3046 [arXiv:1407.3792] [INSPIRE].

[110] M. Ciuchini, E. Franco, S. Mishima and L. Silvestrini, *Electroweak Precision Observables*, New Physics and the Nature of a 126 GeV Higgs Boson, JHEP **08** (2013) 106 [arXiv:1306.4644] [INSPIRE].

[111] S. Gori, J. Gu and L.-T. Wang, *The Zbb Couplings at Future $e^+e^-$ Colliders*, arXiv:1508.07010 [INSPIRE].

[112] P. Bamert, C.P. Burgess, J.M. Cline, D. London and E. Nardi, *R(b) and new physics: A Comprehensive analysis*, Phys. Rev. D **54** (1996) 4275 [hep-ph/9602438] [INSPIRE].

[113] J.R. Ellis, M.K. Gaillard and D.V. Nanopoulos, *A Phenomenological Profile of the Higgs Boson*, Nucl. Phys. **B** **106** (1976) 292 [INSPIRE].

[114] M.A. Shifman, A.I. Vainshtein, M.B. Voloshin and V.I. Zakharov, *Low-Energy Theorems for Higgs Boson Couplings to Photons*, Sov. J. Nucl. Phys. **30** (1979) 711 [INSPIRE].

[115] B.A. Kniehl and M. Spira, *Low-energy theorems in Higgs physics*, Z. Phys. C **69** (1995) 77 [hep-ph/9505225] [INSPIRE].

[116] M. Carena, I. Low and C.E.M. Wagner, *Implications of a Modified Higgs to Diphoton Decay Width*, JHEP **08** (2012) 060 [arXiv:1206.1082] [INSPIRE].
[117] M. Gillioz, R. Grober, C. Grojean, M. Muhleitner and E. Salvioni, *Higgs Low-Energy Theorem (and its corrections) in Composite Models*, JHEP 10 (2012) 004 [arXiv:1206.7120] [INSPIRE].

[118] M.B. Voloshin, *CP Violation in Higgs Diphoton Decay in Models with Vectorlike Heavy Fermions*, Phys. Rev. D 86 (2012) 093016 [arXiv:1208.4303] [INSPIRE].

[119] M.B. Gavela, G. Girardi, C. Malleville and P. Sorba, *A Nonlinear R(xi) Gauge Condition for the Electroweak SU(2) × U(1) Model*, Nucl. Phys. B 193 (1981) 257 [INSPIRE].

[120] R.N. Cahn, M.S. Chanowitz and N. Fleishon, *Higgs Particle Production by $Z \to H\gamma$, Phys. Lett. B 82* (1979) 113 [INSPIRE].

[121] L. Bergstrom and G. Hulth, *Induced Higgs Couplings to Neutral Bosons in $e^{+}e^{-}$ Collisions*, Nucl. Phys. B 259 (1985) 137 [Erratum ibid. B 276 (1986) 744] [INSPIRE].

[122] G. Passarino and M.J.G. Veltman, *One Loop Corrections for $e^{+}e^{-}$ Annihilation Into $\mu^{+}\mu^{-}$ in the Weinberg Model*, Nucl. Phys. B 160 (1979) 151 [INSPIRE].

[123] D.Y. Bardin and G. Passarino, *International Series of Monographs on Physics. Vol. 104: The standard model in the making: Precision study of the electroweak interactions*, Clarendon Press, London U.K. (1999).

[124] A. Denner, *Techniques for calculation of electroweak radiative corrections at the one loop level and results for W physics at LEP-200*, Fortsch. Phys. 41 (1993) 307 [arXiv:0709.1075] [INSPIRE].

[125] A. Djouadi, V. Driesen, W. Hollik and J. Rosiek, *Associated production of Higgs bosons and a photon in high-energy $e^{+}e^{-}$ collisions*, Nucl. Phys. B 491 (1997) 68 [hep-ph/9609420] [INSPIRE].

[126] A. Djouadi, V. Driesen, W. Hollik and A. Kraft, *The Higgs photon — Z boson coupling revisited*, Eur. Phys. J. C 1 (1998) 163 [hep-ph/9701342] [INSPIRE].

[127] J. Cao, L. Wu, P. Wu and J.M. Yang, *The Z+photon and diphoton decays of the Higgs boson as a joint probe of low energy SUSY models*, JHEP 09 (2013) 043 [arXiv:1301.4641] [INSPIRE].

[128] ATLAS collaboration, *Projections for measurements of Higgs boson signal strengths and coupling parameters with the ATLAS detector at a HL-LHC*, ATL-PHYS-PUB-2014-016 (2014).

[129] CMS collaboration, *Projected Performance of an Upgraded CMS Detector at the LHC and HL-LHC: Contribution to the Snowmass Process*, arXiv:1307.7135 [INSPIRE].

[130] ATLAS collaboration, *Search for Higgs boson decays to a photon and a Z boson in pp collisions at $\sqrt{s}$ = 7 and 8 TeV with the ATLAS detector*, Phys. Lett. B 732 (2014) 8 [arXiv:1402.3051] [INSPIRE].

[131] CMS collaboration, *Search for a Higgs boson decaying into a Z and a photon in pp collisions at $\sqrt{s}$ = 7 and 8 TeV*, Phys. Lett. B 726 (2013) 587 [arXiv:1307.5515] [INSPIRE].

[132] ATLAS collaboration, *Search for an Invisibly Decaying Higgs Boson Produced via Vector Boson Fusion in pp Collisions at $\sqrt{s}$ = 8 TeV using the ATLAS Detector at the LHC*, ATLAS-CONF-2015-004 (2015).
[133] CMS collaboration, Search for invisible decays of Higgs bosons in the vector boson fusion and associated ZH production modes, Eur. Phys. J. C 74 (2014) 2980 [arXiv:1404.1344] [INSPIRE].

[134] J.R. Espinosa, C. Grojean, M. Muhlleitner and M. Trott, First Glimpses at Higgs' face, JHEP 12 (2012) 045 [arXiv:1207.1717] [INSPIRE].

[135] D. Carmi, A. Falkowski, E. Kuflik, T. Volansky and J. Zupan, Higgs After the Discovery: A Status Report, JHEP 10 (2012) 196 [arXiv:1207.1718] [INSPIRE].

[136] G. Cacciapaglia, A. Deandrea, G.D. La Rochelle and J.-B. Flament, Higgs couplings beyond the Standard Model, JHEP 03 (2013) 029 [arXiv:1210.8120] [INSPIRE].

[137] A. Azatov and J. Galloway, Electroweak Symmetry Breaking and the Higgs Boson: Confronting Theories at Colliders, Int. J. Mod. Phys. A 28 (2013) 1330004 [arXiv:1212.1380] [INSPIRE].

[138] A. Falkowski, F. Riva and A. Urbano, Higgs at last, JHEP 11 (2013) 111 [arXiv:1303.1812] [INSPIRE].

[139] P.P. Giardino, K. Kannike, I. Masina, M. Raidal and A. Strumia, The universal Higgs fit, JHEP 05 (2014) 046 [arXiv:1303.3570] [INSPIRE].

[140] A. Djouadi and G. Moreau, The couplings of the Higgs boson and its CP properties from fits of the signal strengths and their ratios at the 7 + 8 TeV LHC, Eur. Phys. J. C 73 (2013) 2512 [arXiv:1303.6591] [INSPIRE].

[141] G. Bélanger, B. Dumont, U. Ellwanger, J.F. Gunion and S. Kraml, Global fit to Higgs signal strengths and couplings and implications for extended Higgs sectors, Phys. Rev. D 88 (2013) 075008 [arXiv:1306.2941] [INSPIRE].

[142] G. Moreau, Constraining extra-fermion(s) from the Higgs boson data, Phys. Rev. D 87 (2013) 015027 [arXiv:1210.3977] [INSPIRE].