Speaker
Description
Exact discrete symmetries, if non-linearly realized, can protect a given theory against ultraviolet sensitivity. Quadratic divergences can cancel exactly, while the lightest scalars stemming from spontaneous symmetry breaking are massive without breaking the symmetry. This is at variance with non-linearly realized continuous symmetries, for which the masses of pseudo-Goldstone bosons require an explicit breaking mechanism and enjoy no such protection. The resulting symmetry-protected masses and potentials offer promising physics avenues, both theoretically and in view of the blooming experimental search for ALPs and other BSM particles. We develop this theoretical setup using invariant theory and focusing on the so-called natural minima of the potential. Typically, a subgroup of the ultraviolet discrete symmetry remains explicit in the spectrum, i.e. realized "à la Wigner". This suggests tell-tale experimental signals as a tool to disentangle that explicit low-energy symmetry: at least two degenerate scalars produced simultaneously, plus specific ratios of multi-scalar amplitudes which provide a hint of the full ultraviolet discrete symmetry. Theories displaying exact A4 and A5 symmetries are explored in detail, as illustrative examples.
