Out of more than a million million collisions between sub-nuclear particles whirling round the racetrack 'atomsmasher' at close to the speed of light, the physicists have isolated about a dozen events which, they believe, offer evidence for the existence of the 'top quark'.
Bizarrely, this sub-atomic particle, from which other particles are constructed, is more massive than many of the things that are made from it. The top quark appears to be as heavy as gold. If confirmed, the discovery of the top quark marks the fulfilment of the quest for fundamental sub-atomic particles which started at the Cavendish laboratory in Cambridge nearly a century ago with the discovery in 1897 of the electron by the English physicist J J Thomson.
But in a surprising display of modesty, the 440 scientists will say only that they have evidence for the quark, not a definitive discovery.
'We have not yet observed enough examples of top quark production to establish the particle's existence beyond question,' Melvyn Shochet, a spokesman for the Collider Detector Facility at Fermilab, said.
'Nonetheless, this points strongly to the existence of the sixth and final quark.'
The top quark is the long- sought final component which completes the picture which modern physics has build up of the innermost structure of the material world.
According to the 'standard model', everything is build up from 12 fundamental constituents - six quarks and six 'leptons'. The 'up' and 'down' quarks make up more familiar objects such as protons - which form the nuclei of hydrogen atoms.
In the early 1950s, came the discovery of 'strangeness' followed by 'charm' in 1974. The 'bottom' quark was discovered in 1977, leaving only the top to be found. Mirroring this structure are the leptons which include the electron, muon, tauon, and neutrinos.
Physicists in Europe greeted the Fermilab announcement with caution.
Dr John Ellis, head of the theory division at Cern, the European particle accelerator near Geneva, said: 'I am more convinced than I was a few months ago.'
The next step, he said, was to track down the so-called Higgs boson - 'the one remaining particle in the Standard Model'.
The Higgs holds the key to a vaster mystery still: not just why some particles are more massive than others, but why they are massive.