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1 Erratum to: Eur. Phys. J. C (2016) 76:324 https://doi.org/10.1140/epjc/s10052-016-4160-3
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 \(\rho = 1\), it is sufficient to consider only \(\cos \phi = \pm 1\). In fact, the solution with \(\rho = 1\), \(\cos \phi \ne \pm 1\) may exist, yielding an extra condition.
The minimisation equations for \(\phi \), \(h_{1}\), \(h_{2}\) and \(\lambda \) in the case of \(\rho = 1\) are
Their solutions with \(\cos \phi \ne \pm 1\) are given by
Altogether, the conditions for the 2HDM potential with real couplings to be bounded from below are
which includes the new condition involving \(\cos \phi _{\rho = 1}\), \(h_{1, \rho = 1}^{2}\), \(h_{2, \rho = 1}^{2}\) and \(V_{\text {min}, \rho = 1}\).
Figures 3 and 4 that present examples of the allowed parameter space for the 2HDM remain unaffected by the change.
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Kannike, K. Erratum to: Vacuum stability of a general scalar potential of a few fields. Eur. Phys. J. C 78, 355 (2018). https://doi.org/10.1140/epjc/s10052-018-5837-6
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DOI: https://doi.org/10.1140/epjc/s10052-018-5837-6