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Phys. J. C"],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>There has been a great interest in three Higgs doublet models (3HDM) symmetric under an exact <jats:inline-formula><jats:alternatives><jats:tex-math>$$A_4$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>A<\/mml:mi>\n                    <mml:mn>4<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> symmetry. We provide the complete analytic necessary and sufficient conditions for a point to be the global minimum along the neutral directions in such models, discussing many of the subtleties involved. We also present a number of numerical examples, to highlight those issues. We then turn to the directions which break electric charge, presenting a safe analytical sufficient condition for bounded from below (BFB) potentials. Based on extensive numerical simulations, we discuss one conjecture on BFB along charge breaking directions.<\/jats:p>","DOI":"10.1140\/epjc\/s10052-022-10712-3","type":"journal-article","created":{"date-parts":[[2022,8,26]],"date-time":"2022-08-26T21:02:42Z","timestamp":1661547762000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Conditions for global minimum in the $$A_4$$ symmetric 3HDM"],"prefix":"10.1140","volume":"82","author":[{"given":"Sergio","family":"Carrolo","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9683-4055","authenticated-orcid":false,"given":"Jorge C.","family":"Rom\u00e3o","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6455-9618","authenticated-orcid":false,"given":"Jo\u00e3o P.","family":"Silva","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,8,26]]},"reference":[{"key":"10712_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physletb.2012.08.020","volume":"716","author":"G Aad","year":"2012","unstructured":"G. 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