One paper considers the possibility that a Higgs boson decaying to four leptons sometimes does so via an intermediate pair of spin-0 or spin-1 bosons (or a mixed pair) with masses in the 1-60 GeV range. The abstract of the paper states: "The data are found to be consistent with Standard Model expectations." But Lubos notes that the body text shows a 2.5 sigma local excess at 28 GeV. This is a mass resonance where an earlier report from the CMS experiment at the LHC also found weak evidence for a resonance when dimuons are produced from a decaying Higgs boson.
The other paper notes a 1000 GeV mass resonance of 3 sigma significance locally, but only 2 sigma significance globally, in a search for Higgs boson pair production in events with two b-jets and two τ-leptons with the LHC at full power. The conclusion of the paper states:
The data are found to be compatible with the background-only hypothesis, with the largest deviation being found in the search for resonant H H production at mass of 1 TeV, which corresponds to a local (global) significance of 3.0 σ (2.0 +0.4 −0.2 σ).
In my view, these are both probably nothing more than statistical flukes. The LHC does an immense number of experiments looking at Higgs boson formation and decay and some of them, inevitably, are going to be further from the mean predicted result than expected simply due to random chance. This is called the "look elsewhere effect" and is the reason that there is a difference between the local significance of an experimental result and its global significance.
I am also not impressed that either resonance is particularly well motivated theoretically, although there are certainly possible beyond the Standard Model theoretical explanations for these resonances out there.
But, if there is additional stronger evidence of these resonances as more data is collected, these papers could turn out to be the first hints of beyond the Standard Model physics.