Physics is sometimes simple but this does not mean that is numerology - as simple minded colleague, who prefers ultraheavy numerics instead of imaginative thinking, might argue: deep principles distilled through a work of 38 years are behind this simple rule.
This 375 GeV excess might indeed represent the lightest vector meson of M89 hadron physics. ρ and ω of standard hadron physics have mass 775 MeV and the scaled up mass is about 397 GeV, which is about 5 per cent heavier than the mass of Zgamma excess.
The decay ρ→ Z+γ describable at quark level via quark exchange diagram involving emission of Z and γ. The effective action would be proportional to Tr(ρ*γ*Z), where the product and trace are for antisymmetric field tensors. This kind effective action should describe also the decay to gamma pair. By angular momentum conservation the photons of gamma pairs should be in relative L=1 state. Since Z is relativistic, L=1 is expected to be favored also for Z+γ final state. Professional could immediately tell whether this is correct view.
Similar argument applies to the decay of ω which is isospin singlet. For charged ρ also decays to Wγ and WZ are possible. Note that the next lightest vector meson would be K* with mass 892 MeV. K89 should have mass 457 GeV.
For some reason also Lubos has got interested in powers of two and notices that 375 GeV is 1/2 of the famous 750 GeV. p-Adic length scale hypothesis might allow to understand these factors if octaves or even half octaves of particles are realized.
For a summary of earlier postings see Links to the latest progress in TGD.