The Tevatron Accelerator at the U.S. government's Fermi National Laboratory in suburban Chicago once led the world in studying what happens when subatomic particles are thrown together at nearly the speed of light.  But CERN's new Large Hadron Collider in Europe has taken the lead in this exotic science.  U.S. officials took the aging Tevatron Accelerator offline in September, ending a 30-year career in particle physics.

Since it went online in 1983, Fermilab's Tevatron Accelerator fueled the study of the most fundamental building blocks of matter - sub atomic particles.  But one particle continues to elude scientists -- the Higgs Boson.

"We know a lot about where it's not, but we don't know where it is yet," said Robert Roser is a senior scientist at Fermilab who has spent much of his career looking for the so-called "God particle" which could help scientists better understand why matter has mass.

"If I look at our data right now... it's not jumping out at us," Roser said.

There's a chance the Higgs Boson will never jump out at Roser and other scientists who have been hunting it for more than 20 years.

With the Tevatron now offline, the search for the Higgs is underway at the Large Hadron Collider, or LHC, at the CERN laboratory in Geneva Switzerland.  The LHC is now the world's most advanced particle accelerator, but Roser says even it can't find the Higgs Boson.

"The fact that the LHC has ruled out the higher mass states makes the Tevatron that much more attractive at the moment, because we're good at where the remaining territory is left," Roser said.

That remaining territory is the last frontier of research for the Tevatron, despite the fact it is not operational.

Scientists are still analyzing the massive amounts of data the accelerator produced just before its shutdown.

"We hope to have the Higgs (Boson) analysis completed and ready for public consumption by February or March of 2012," Roser said.

But the final analysis could ultimately lead to the conclusion the Higgs Boson does not exist.

"Not finding the Higgs is to some people's way of thinking a lot more exciting,"  said physicist Patrick Fox. He says the absence of the Higgs particle could challenge current ideas about matter and mass.

"Finding the Higgs would be great… it would be really great to find the last piece of this puzzle.  Not finding the Higgs would actually result in us probably finding a lot more complicated stuff instead of the Higgs which would be very interesting to us to find new forces of nature, new symmetries of nature, new dimensions of space… these are all possibilities where you may or may not have a Higgs Boson but instead have something more exotic," Fox said.

Scientists at Fermilab say the discovery of nothing at all could be the greatest discovery, and the lasting legacy, of the Tevatron Accelerator.