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

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 | | The~~se models~~ assume the benchmark values f,,a,,= 1 TeV, m,,a,, = 1 MeV. |

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

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

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