A first estimate of triply heavy baryon masses from the pNRQCD perturbative static potential

Within pNRQCD we compute the masses of spin-averaged triply heavy baryons using the now-available NNLO pNRQCD potentials and three-body variational approach. We focus in particular on the role of the purely three-body interaction in perturbation theory. This we find to be reasonably small and of the order 25 MeV Our prediction for the Omega_ccc baryon mass is 4900(250) in keeping with other approaches. We propose to search for this hitherto unobserved state at B factories by examining the end point of the recoil spectrum against triple charm.