  Since the discovery in 2012 of the Higgs boson at the LHC, as the last
missing piece of the Standard Model of particle physics, any hint of new
physics has been intensively searched for, with no confirmation to date. There
are however slight deviations from the SM that are worth investigating. The CMS
collaboration has reported, in a search for heavy resonances decaying in $t
\bar t$ with a 13-TeV center-of-mass energy and a luminosity of 35.9 fb$^{-1}$,
deviations from the SM predictions at the 3.5$\sigma$ level locally
(1.9$\sigma$ after the look-elsewhere effect). In addition, in the ditau final
state search performed by the ATLAS collaboration at $\sqrt{s}=13$ TeV and
$\mathcal{L}=139$ fb$^{-1}$, deviations from the SM at the 2$\sigma$ level have
been also observed. Interestingly, both slight excesses are compatible with a
new pseudoscalar boson with a mass around 400 GeV that couples at least to
fermions of the third generation and gluons. Starting from a purely
phenomenological perspective, we inspect the possibility that a 400-GeV
pseudoscalar can account for these deviations and at the same time satisfy the
constraints on the rest of the channels that it gives contributions to and that
are analyzed by the ATLAS and CMS experiments. After obtaining the range of
effective couplings compatible with all experimental measurements, we study the
gauge invariant UV completions that can give rise to this type of pseudoscalar
resonance, which can be accommodated in an $SO(6)/SO(5)$ model with consistency
at the 1$\sigma$ level and in a $SO(5)\times U(1)_{P}\times
U(1)_{X}/SO(4)\times U(1)_X$ at the 2$\sigma$ level, while exceedingly large
quartic couplings would be necessary to account for it in a general two Higgs
doublet model.
