20 | 20 | This new field is assumed to be an Axion-Like-Particle, i.e. the (pseudo) Nambu-Goldstone boson of an unspecified spontaneously broken U(1) symmetry, associated with a heavy scale f,,,a,,,. |

21 | 21 | As such, the ALP field respects an approximate shift symmetry that requires its couplings to the SM to be purely derivative and weighted by inverse powers of f,,a,,. Moreover, its mass must be much lighter than f,,a,,. |

22 | | ~~In these models the benchmark values f,,a,,= 1 TeV, m,,a,, = 1 MeV are assumed~~. |

| 22 | These models assume the benchmark values f,,a,,= 1 TeV, m,,a,, = 1 MeV. |

25 | | Two major frameworks for the electroweak sector are considered: a linear realization of electroweak symmetry breaking (EWSB), typical of weakly coupled new physics, and a non-linear one, such as those in constructions involving new strongly interacting physics. |

| 25 | Two major frameworks for the electroweak sector are considered: a linear realization of electroweak symmetry breaking (EWSB), typical of weakly coupled new physics, and a non-linear one, such as those in constructions involving new strongly interacting physics. In the first scenario, the ALP is coupled to a "linear" EFT (also called SMEFT), in which the Higgs belongs to a SU(2) doublet and the interaction terms are organized in an expansion in mass dimension. |

| 26 | In the latter scenario, instead, two independent fields are introduced for the EW Goldstone bosons and for the physical Higgs, and one constructs a "chiral" EFT (sometimes also called non-linear or HEFT), in which the effective operators are ordered according to a more complex counting that, for the Goldstone bosons sector, reduces to a derivative one. |