The correction to the muon anomalous magnetic moment from the pion-pole contribution to the hadronic light-by-light scattering is considered using a description of the ${\pi }^0-{\gamma }^{*}-{\gamma }^{*}$ transition form factor based on the large-$N_C$ and short-distance properties of QCD. The resulting two-loop integrals are treated by first performing the angular integration analytically, using the method of Gegenbauer polynomials, followed by a numerical evaluation of the remaining two-dimensional integration over the moduli of the Euclidean loop momenta. The value obtained, $a_{\mu }^{\mathrm{LbyL};{\pi }^0}=+5.8\mathrm{}\left(1.0\right)\mathrm{}\times {10}^{-10},$ disagrees with other recent calculations. In the case of the vector meson dominance form factor, the result obtained by following the same procedure reads $a_{\mu }^{\mathrm{LbyL};{\pi }^0}{|}_{\mathrm{VMD}}=+5.6\mathrm{}\times {10}^{-10},$ and differs only by its overall sign from the value obtained by previous authors. The inclusion of the $\eta$ and ${\eta }^{\prime }$ poles gives a total value $a_{\mu }^{\mathrm{L}\mathrm{b}\mathrm{y}\mathrm{L};\mathrm{P}\mathrm{S}}=+8.3\mathrm{}\left(1.2\right)\mathrm{}\times {10}^{-10}$ for the three pseudoscalar states. This result substantially reduces the difference between the experimental value of $a_{\mu }$ and its theoretical counterpart in the standard model.

Following a recent suggestion by Weinberg, we use the large-$N$ expansion in QCD to discuss the decay amplitudes of tetraquarks into ordinary mesons as well as their mixing properties. We find that the flavor structure of the tetraquark is a crucial ingredient to determine both this mixing as well as the decays. Although in some cases tetraquarks should be expected to be as narrow as ordinary mesons, they may get to be even narrower, depending on this flavor structure.

Because of their small electromagnetic corrections, the isospin-breaking decays $\eta${}$\rightarrow${}3$\pi${} seem to be good candidates for extracting isospin-breaking parameters $\sim${}(md-mu). This task is unfortunately complicated by large chiral corrections and the discrepancy between the experimentally measured values of the Dalitz parameters describing the energy dependence of the amplitudes of these decays and those predicted from chiral perturbation theory. We present two methods based on an analytic dispersive representation that use the information from the NNLO chiral result and the one from the measurement of the charged $\eta${}$\rightarrow${}3$\pi${} decay by KLOE together in a harmonized way in order to determine the value of the quark mass ratio R. Our final result is R=37.7\ifmmode\pm\else\textpm\fi{}2.2. This value supplemented by values of ms/m^ or even m^ and ms from other methods (as sum-rules or lattice) enables us to obtain further quark mass characteristics. For instance the recent lattice value for ms/m^$\sim${}27.5 leads to Q=23.1\ifmmode\pm\else\textpm\fi{}0.7. We also quote the corresponding values of the current masses mu and md.

We study strongly-coupled, approximately scale-invariant gauge theories, which develop a mass gap in the infrared. We argue that a large number of fermion flavours is most suitable to provide an ultraviolet completion for the composite Higgs scenario. The holographic approach allows to describe the qualitative features of the non-perturbative dynamics in the Veneziano limit. We introduce new bottom-up holographic models, which incorporate the backreaction of flavour on the geometry, and show that this can correlate the mass gap to the scale of flavour-symmetry breaking. We compute the mass spectrum for the various composite bosonic states, and study its dependence on the scaling dimension of the symmetry-breaking operators, as well as on the number of flavours. The different regions with a light dilaton are critically surveyed. We carefully assess the domain of validity of the holographic approach, and compare it with lattice simulations and the Nambu-Jona-Lasinio model.