Compositeness is an elegant way to address the hierarchy problem. In this talk, I will discuss about the phenomenology of the composite Higgs models at the LHC and beyond, in which Higgs arise as Nambu-Goldstone bosons. Under broad assumption of partial compositeness and symmetry breaking pattern, I will discuss about phenomenology of the spin-1 resonances and the top partners and the relevance of their strong interactions in the searches at the LHC.
In addition to the direct searches, the LHC has become a precision machine with accumulating enormous data at the High-Luminosity (HL) stage. I will discuss about precision measurement in the di-boson processes and their relevance in the different new physics patterns. Meanwhile, I will talk about the strong multi-pole interaction scenario, in which the transverse SM gauge bosons are also belonging to the strong sector at the multi-TeV scale. This provided a strong motivation for the precision measurement at the LHC.
Finally, I will briefly discuss about the universal relationship between the Higgs couplings predicted by the non-linearity and their phenomenological relevance.