STOCKHOLM — Nearly 50 years after they came up with the theory, but little more than a year since the world’s biggest atom smasher delivered the proof, Britain’s Peter Higgs and Belgian colleague Francois Englert won the Nobel Prize in physics Tuesday for helping to explain how matter formed after the Big Bang.

Working independently in the 1960s, they came up with a theory for how the fundamental building blocks of the universe clumped together, gained mass and formed everything we see around us today. The theory hinged on the existence of a subatomic particle that came to be called the Higgs boson — or the “God particle.”

In one of the biggest breakthroughs in physics in decades, scientists at CERN, the European Organization for Nuclear Research, announced last year that they had finally found a Higgs boson using the $10 billion particle collider built in a 17-mile (27-kilometer) tunnel under the Swiss-French border.

In a statement issued by the University of Edinburgh, where he retired as a professor, the famously shy, 84-year-old Higgs said he hoped the prize would help people recognize “the value of blue-sky research.”

Englert, 80, said the award pointed to the importance of scientific freedom and the need for scientists to be allowed to do fundamental research that doesn’t have immediate practical applications.

“You don’t work thinking to get the Nobel Prize,” said Englert, a retired professor at the Free University of Brussels. Still, “we had the impression that we were doing something that was important, that would later on be used by other researchers.”

The discovery was made possible by the work of thousands of scientists worldwide, including researchers at the University of Virginia. UVA professors helped to plan the experiments in the collider, and built components of its particle detectors.

Brad Cox, a physicist at UVA, was a member of several review committees that analyzed the data coming out of the experiments. He was one of four scientists on the committee to “green light” the announcement that a particle produced in the collider may be the Higgs boson.

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