Erratum to: Vacuum stability of a general scalar potential of a few fields

The European Physical Journal C, May 2018

Kristjan Kannike

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Erratum to: Vacuum stability of a general scalar potential of a few fields

Eur. Phys. J. C Erratum to: Vacuum stability of a general scalar potential of a few fields Kristjan Kannike 0 0 NICPB , Rävala pst. 10, 10143 Tallinn , Estonia −(λ3 + λ4 − λ5)[λ5(λ3 + λ4 − λ5) - In the original, it was erroneously assumed in the derivation of the vacuum stability conditions for the two Higgs doublet model (2HDM) with real couplings that in the case of ρ = 1, it is sufficient to consider only cos φ = ±1. In fact, the solution with ρ = 1, cos φ = ±1 may exist, yielding an extra condition. The minimisation equations for φ, h1, h2 and λ in the case of ρ = 1 are 0 = h1h2 2λ5h1h2 cos φ + λ6h12 + λ7h22 sin φ, λh1 = 4λ1h13 + 2(λ3 + λ4 + λ5 cos 2φ) h1h22 + 6λ6 cos φ h12h2 + 2λ7 cos φ h23, λh2 = 4λ2h23 + 2(λ3 + λ4 + λ5 cos 2φ)h12h2 + 2λ6 cos φ h13 + 6λ7 cos φ h1h22, 2 2 1 = h1 + h2. Their solutions with cos φ = ±1 are given by cos φρ=1 = − λ6h12 + λ7h22 2λ5h1h2 (1) (2) (3) (4) (5) (6) (7) −2λ6λ7]]/[2λ5(λ1 + λ2 − λ3 − λ4 + λ5) −(λ6 − λ7)2]. Altogether, the conditions for the 2HDM potential with real couplings to be bounded from below are Vρ=0 > 0 ∧ Dcos φ=±1, ρ=1 ∧ (Qcos φ=±1, ρ=1 > 0 ∨ Rcos φ=±1, ρ=1 > 0) 2 2 ∧ (0 < h1,ρ=1 < 1 ∧ 0 < h2,ρ=1 < 1 ∧ 0 < cos2 φρ=1 < 1 ⇒ Vmin,ρ=1 > 0) ∧ (0 < h21 < 1 ∧ 0 < h22 < 1 ∧ 0 < ρ2 < 1 ⇒ Vmin > 0), which includes the new condition involving cos φρ=1, h12,ρ=1, 2 h2,ρ=1 and Vmin,ρ=1. Figures 3 and 4 that present examples of the allowed parameter space for the 2HDM remain unaffected by the change. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecomm ons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Funded by SCOAP3 (8) (9)


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Kristjan Kannike. Erratum to: Vacuum stability of a general scalar potential of a few fields, The European Physical Journal C, 2018, 355, DOI: 10.1140/epjc/s10052-018-5837-6