https://doi.org/10.1140/epjc/s10052-022-10712-3
Regular Article - Theoretical Physics
Conditions for global minimum in the 
symmetric 3HDM
CFTP, Departmento de Física, Instituto Superior Técnico, Avenida Rovisco Pais 1, 1049, Lisbon, Portugal
Received:
13
July
2022
Accepted:
14
August
2022
Published online:
26
August
2022
There has been a great interest in three Higgs doublet models (3HDM) symmetric under an exact 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.
Jorge C. Romão and João P. Silva contributed equally to this work.
© The Author(s) 2022
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