In the mid 1970s, four Soviet physicists, Batlisky, Fadin, Kuraev and Lipatov, made some predictions involving the strong nuclear force which would lead to their initials entering the lore.
“BFKL” became a shorthand for a difficult-to-understand but important physical effect which could have big implications for high energy physics. We have a good theory of the strong force, which sits proudly in our Standard Model of particle physics. BFKL proposed, or discovered, a new set of sums which could be done using the theory behind the strong force.
The scattering probability for electrons and protons is generally expressed in terms of mathematical objects called structure functions, and the BFKL predictions said that one particular structure function should rise very rapidly as the fraction of the proton’s momentum involved in the collision got smaller.
The structure function did not rise as quickly as might have been expected by BFKL. It was also possible to explain the rise using different calculations – not featuring their sums.
The qualitative impact of the BFKL sums is not now expected to be as dramatic as the initial calculations indicated, but it is still there, and still important.