Research output: Contribution to journal › Article › peer-review
Bounded-from-below conditions for A 4-symmetric 3HDM. / Ivanov, Igor P.; Buskin, N.
In: Journal of Physics A: Mathematical and Theoretical, Vol. 54, No. 32, 325401, 08.2021.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Bounded-from-below conditions for A 4-symmetric 3HDM
AU - Ivanov, Igor P.
AU - Buskin, N.
N1 - Publisher Copyright: © 2021 IOP Publishing Ltd. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2021/8
Y1 - 2021/8
N2 - Deriving necessary and sufficient conditions for a scalar potential to be bounded from below (BFB) is a difficult task beyond the simplest cases. Recently, a set of BFB conditions was proposed for the A 4-invariant three-Higgs-doublet model (3HDM). However, that set of conditions relied on numerical scan, and a complete analytic proof was lacking. Here, we fill this gap. We prove that the conjectured BFB conditions are indeed necessary and sufficient within the neutral Higgs subspace. We bypass technically challenging direct algebraic computations with a novel technique that relies on an auxiliary function, which is related to the Higgs potential but which is easier to analyze. This technique may finally be sufficient to tackle the more involved case of the original Weinberg's 3HDM model.
AB - Deriving necessary and sufficient conditions for a scalar potential to be bounded from below (BFB) is a difficult task beyond the simplest cases. Recently, a set of BFB conditions was proposed for the A 4-invariant three-Higgs-doublet model (3HDM). However, that set of conditions relied on numerical scan, and a complete analytic proof was lacking. Here, we fill this gap. We prove that the conjectured BFB conditions are indeed necessary and sufficient within the neutral Higgs subspace. We bypass technically challenging direct algebraic computations with a novel technique that relies on an auxiliary function, which is related to the Higgs potential but which is easier to analyze. This technique may finally be sufficient to tackle the more involved case of the original Weinberg's 3HDM model.
KW - boundedness from below
KW - group-invariant polynomials
KW - multi-Higgs potential
UR - http://www.scopus.com/inward/record.url?scp=85111297283&partnerID=8YFLogxK
UR - https://arxiv.org/abs/2104.11428
U2 - 10.1088/1751-8121/ac0e53
DO - 10.1088/1751-8121/ac0e53
M3 - Article
AN - SCOPUS:85111297283
VL - 54
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 32
M1 - 325401
ER -
ID: 29124097