  We classify the complete set of dimension-5 operators relevant for the
resonant production of a singlet of spin 0 or 2 linearly coupled to the
Standard Model (SM). We compute the decay width of such states as a function of
the effective couplings, and provide the matching to various well-motivated New
Physics scenarios. We then investigate the possibility that one of these
neutral resonances be at the origin of the excess in diboson production
recently reported by the ATLAS collaboration. We perform a shape analysis of
the excess under full consideration of the systematic uncertainties to extract
the width $\Gamma_{\rm tot}$ of the hypothetical resonance, finding it to be in
the range 26 GeV $<\Gamma_{\rm tot}<$ 144 GeV at 95\% C.L. We then point out
that the three overlapping selections $WW$, $WZ$, $ZZ$ reported by ATLAS follow
a joint trivariate Poisson distribution, which opens the possibility of a
thorough likelihood analysis of the event rates. The background systematic
uncertainties are also included in our analysis. We show that the data do not
require $W\!Z$ production and could thus in principle be explained by neutral
resonances. We then use both the information on the width and the cross
section, which prove to be highly complementary, to test the effective
Lagrangians of singlet resonances. Regarding specific models, we find that
neither scalars coupled via the Higgs-portal nor the Randall-Sundrum (RS)
radion can explain the ATLAS anomaly. The RS graviton with all matter on the
infrared (IR) brane can in principle fit the observed excess, while the RS
model with matter propagating in the bulk requires the presence of IR brane
kinetic terms for the gauge fields.
