Uhm... I guess there is a reason that paper took so long to be made public.
That "cone cut" described on page 4 heavily biases the shape towards events near the threshold. Looking at figure 3, the peak without cone cut looks much more reliable than the one with it.
"The ##B^0_s \pi^\pm## background with a real ##B^0_s## meson is modeled using a Monte Carlo (MC) simulation [9] of events containing a ##B^0_s## meson and additional pions tuned to reproduce the ##B^0_s## transverse momentum distribution in data."
The ##B^0_s## transverse momentum distribution in data is not the critical point here. The pions are low-energetic and background comes from the poorly understood soft QCD processes in the interaction. Okay, at least they checked the ##B^0_s## sidebands.
Without cone cut, the sidebands (empty markers in figure 2) seem to have a different distribution than the peak region (figure 3b). This is also discussed in the text, but without explanation. Also, they get a lower number of events in the ##B^0_s \pi^\pm## peak without cone cut.
There is clearly something not understood, and it looks like a mass peak, so it could be a new particle, but the analysis could have been done more carefully. Also, where are checks with other decay modes of the ##B^0_s##? That particle is long-living, so the peak should look very similar in other decay modes. The purity or signal yield might be a bit lower, but ##J/\psi \phi## is not the only relevant decay channel. Also, why should it be a tetraquark? Excited states of a ##B^0## could decay to ##B^0_s \pi^\pm##. Would be odd, but not impossible. A check of the ##B^0 \pi^\pm## spectrum would help.
Anyway, I guess LHCb can quickly check this with data recorded already. They have the samples of ##B^0_s \to J/\psi \phi## for mixing studies anyway, larger than the Tevatron samples.
