Erratum to: The minimal axion minimal linear $\sigma$ model

1 Erratum to: Eur. Phys. J. C https://doi.org/10.1140/epjc/s10052-018-5892-z

In this Erratum we clarify that in contrast to the statements made in the article the bounds on the axion coupling to two W’s and to two Z’s obtained from mono-W and mono-Z searches at the LHC are the following:

$$\begin{aligned} |g_{aWW}|\lesssim 1.6\times 10^{-3}\text { GeV}^{-1},\quad |g_{aZZ}|\lesssim 8\times 10^{-4}\text { GeV}^{-1}\,. \end{aligned}$$

The corresponding limits in terms of $f_a/c_i$ are given by:

$$\begin{aligned} \dfrac{f_a}{|c_{aWW}|}\gtrsim 0.7\text { GeV},\quad \dfrac{f_a}{|c_{aZZ}|}\gtrsim 1.4\text { GeV}\,. \end{aligned}$$

This change has interesting phenomenological effects as the scale $f_s\simeq f_a$ can be as low as $1\text { TeV}$: this ML$\sigma$M ALP can then be tested both at colliders and at flavour factories. Moreover, this model does not present any fine-tuning.

Finally, a corrected version of the article is also available on the arXiv (arXiv:1710.10500).