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@ARTICLE{Vileta:478327,
      author       = {Vileta, Victor Enguita and Gavela, Belen and Houtz, Rachel
                      and Quilez Lasanta, Pablo},
      title        = {{D}iscrete {G}oldstone {B}osons},
      reportid     = {PUBDB-2022-02540, DESY-22-082. arXiv:2205.09131.
                      IFT-UAM/CSIC-20-144. FTUAM-20-21. IPPP/22/31},
      year         = {2022},
      note         = {42 pages, 8 figures},
      abstract     = {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 in contrast
                      to non-linearly realized continuous symmetries, for which
                      the masses of pseudo-Goldstone bosons require an explicit
                      breaking mechanism. The symmetry-protected masses and
                      potentials of those discrete Goldstone bosons offer
                      promising physics avenues, both theoretically and in view of
                      the blooming experimental search for ALPs. We develop this
                      theoretical setup using invariant theory and focusing on the
                      natural minima of the potential. We show that typically a
                      subgroup of the ultraviolet discrete symmetry remains
                      explicit in the spectrum, i.e. realized 'à la Wigner',
                      which can be either abelian or non-abelian. This suggests
                      tell-tale experimental signals as a tool to disentangle that
                      explicit low-energy symmetry: at least two (three)
                      degenerate scalars produced simultaneously if abelian
                      (non-abelian), while the specific ratios of multi-scalar
                      amplitudes provide a hint of the full ultraviolet discrete
                      symmetry. Examples of exact ultraviolet $A_4$ and $A_5$
                      symmetries are explored in substantial detail.},
      keywords     = {symmetry, discrete (INSPIRE) / Goldstone particle, mass
                      (INSPIRE) / ultraviolet (INSPIRE) / abelian (INSPIRE) /
                      nonabelian (INSPIRE) / Wigner (INSPIRE) / sensitivity
                      (INSPIRE) / spontaneous symmetry breaking (INSPIRE)},
      cin          = {T},
      cid          = {I:(DE-H253)T-20120731},
      pnm          = {611 - Fundamental Particles and Forces (POF4-611)},
      pid          = {G:(DE-HGF)POF4-611},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)25},
      eprint       = {2205.09131},
      howpublished = {arXiv:2205.09131},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2205.09131;\%\%$},
      doi          = {10.3204/PUBDB-2022-02540},
      url          = {https://bib-pubdb1.desy.de/record/478327},
}