We propose a coherent explanation for the 750 GeV diphoton
anomaly and the hints of deviations from Lepton Flavor Universality in

Article funded by SCOAP3

\Lambda$ and respecting an approximate $\U(2)^5 = \U(2)_{q_L} \times \U(2)_{u_R} \times \U(2)_{d_R} \times \U(2)_{\ell_L} \times \U(2)_{\ell_R} $ flavor symmetry. The latter implies that only the third generation of SM fermions (singlets under $\U(2)^5$) can have non-vanishing Yukawa couplings in the limit of exact symmetry~\cite{Barbieri-ml-2011ci}. We assume that also the techni-quarks are $\U(2)^5$ singlets, such that only third generation SM fermions can have an effective linear mixing with the composite states in the limit of unbroken flavor symmetry (thus providing a concrete realization of the mechanism proposed in ref.~\cite{Glashow-ml-2014iga}). \begin{figure} \centering \includegraphics[width=0.4\textwidth]{VBB.pdf} ]]>

1.5$\,TeV, $m_{\rm{T}}^{\rm{tot}}$ is required to be grater than $850$\,GeV in the signal region (see table~4 in~\cite{Aad-ml-2015osa}). An appropriate recast of the analysis requires good control over $\tau$ reconstruction, which is beyond the scope of this paper. In order to qualitatively estimate the present bound on our $\rho^0$, we crudely approximate $m_{\rm{T}}^{\rm{tot}} \sim m_{\tau\tau}$ and plot in figure~\ref{Fig:rho_width} (bottom) the total $p p \to \tau^+ \tau^-$ cross section at $8$\,TeV requiring $m_{\tau \tau}^{\rm{min}}>850$\,GeV, and setting $g_\ell = g_q$. Interestingly enough, the present searches are just starting to probe the relevant parameter region as predicted by the diphoton and flavor anomalies. Clearly, future search strategies for the $\rho^0$ in this model should be optimized for a wide resonance. \begin{figure} \centering \includegraphics[width=0.445\textwidth]{rho-width} \;\; \includegraphics[width=0.465\textwidth]{rho-width-2} \includegraphics[width=0.465\textwidth]{rho-x-section} ]]>

850$\,GeV assuming $\rho^0$ contribution only and $g_q=g_\ell$ (solid blue). The preferred region from $b\to c \tau \nu$ assuming $g_q=g_\ell$ is shown in green and yellow.]]>

m_L$ they are expected to be the heaviest pNGB with $m_{\tilde \pi} \sim 1.2 \div 1.5 \TeV$, see also figure~\ref{Fig:spectrum}. It is worth stressing that the presence of such a state is a model-independent prediction of all models trying to explain the diphoton excess in terms of a singlet pNGB coupled to gluons via the anomalous coupling. Since this implies the presence of some fundamental TC fermion $Q$ charged under $\SU(3)_c$, then a color-octet pNGB, $\tilde \pi^A \sim (\overline Q T^A Q)$, will always be present in the spectrum~\cite{Bai-ml-2016czm}. While both the $\SU(2)_L$ triplet and singlet can be doubly produced in gluon fusion, the singlet also can be singly produced via its anomalous couplings to two gluons. This coupling does not depend on the details of the specific models: it is only a function of $N_{\rm TC}$ and the pion decay constant $f$, see e.g.~\cite{Redi-ml-2016kip,Bai-ml-2016czm}. In the analysis of ref.~\cite{Bai-ml-2016czm} it was shown how the present bounds from dijet searches, both at 8\,TeV~\cite{Aad-ml-2014aqa,Khachatryan-ml-2015sja} and at 13\,TeV~\cite{ATLAS-ml-2015nsi} already cast strong bounds on such a state. It was also shown that the anomalous couplings to $g \gamma$ are phenomenologically relevant and, for some models, can give comparable bounds as those from dijet searches. The main difference between our setup and those considered in previous studies is the strong coupling of this particle with a $t \bar{t}$ pair via the mixing with baryons, which we can parametrize with an analogous Lagrangian as was done for the $\eta$ in eq.~\eqref{eq:eta_ttbar_Lagr}. This term opens up the decay channel to $t \bar{t}$, which we find to be comparable in size to the one in two gluons. In figure~\ref{Fig:LHC_bounds_oct} we show the experimental bounds on such a state from the ATLAS 8\,TeV resonant search in $t\bar{t}$~\cite{Aad-ml-2015fna,CMS-ml-lhr}, as well as from the ATLAS 8\,TeV and 13\,TeV dijet searches. In order to extract the excluded cross section from the two dijet analyses, we perform a MonteCarlo simulation to estimate the acceptance of the cuts applied to be $\cA \sim 54\%$ for both analyses. The $t\bar{t}$ branching ratio isolines are shown with dashed-gray lines while the solid blue lines show the production cross section of the pseudoscalar in gluon fusion in pb.\footnote{The production cross section is computed analytically as in ref.~\cite{Redi-ml-2016kip}, which we also multiply by a QCD NLO $k$-factor $k_{\rm NLO} \simeq 2$.} In the relevant parameter space, $f\gtrsim 200 \GeV$ and $m_{\tilde{\pi}} \sim 1.5 \TeV$, the total decay width in this region is $\Gamma_{\tilde \pi} \sim O(1) \GeV$ and the decay widths in $t \bar{t}$ and $gg$ are comparable. The combination of the $t\bar{t}$ 8TeV search and the dijet 13TeV search already puts some tension in the models considered here. We expect that a future update of both searches will further improve the reach on this class of models, in particular a $t\bar{t}$ resonant search at the LHC Run-2 will have a strong exclusion (or discovery) power of this kind of state. \begin{figure} \centering \includegraphics[width=0.5\textwidth]{bounds_pi8_tt} ]]>