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Theory Group: Interpreting LHC Data

It is unlikely that there is a single high-energy physicist in the world who is not eagerly awaiting the first results from the Large Hadron Collider (LHC). The LHC will hopefully shed light on the origin of electroweak symmetry breaking and might lead to the discovery of new physics.

However, in order to interpret the LHC data correctly, it is very important to understand expected backgrounds and signals within and beyond the Standard Model. Otherwise, interpreting LHC data would be worse than looking for a needle in a haystack.

It is particularly important to compute the rates of Standard Model processes with large numbers of final quarks and gluons, since new physics appears as excesses in very energetic events. But carrying out theoretical computations becomes quite difficult as the number of final particles increases.

Scattering amplitudes are calculated with Feynman diagrams, as an expansion in the quark-gluon interaction. However, this is not an effective way to get the answer. The number of diagrams that must be computed grows extremely quickly with the number of external particles (legs) and the number of loops. Direct analytical methods fail already at one loop with more than only five external legs. But the results of these computations are a lot less complex than the expressions at intermediate stages. This suggests that we need to look for computational methods which reflect the relative underlying simplicity of the results.

Last year, a group at Princeton developed a method by which the knowledge of amplitudes with fewer legs is "recycled" to build up amplitudes with more legs recursively. This drastically reduces the number of terms that need to be computed. However, this method was formulated only for the simplest Feynman diagrams, those with no loops.

Lance Dixon and I, of the SLAC theory group, along with our collaborators Zvi Bern at UCLA, David Kosower and Darren Forde at Saclay, France, have found a way to extend this method to the more complex diagrams with one closed loop. Our method makes use of the additional constraint that we have on scattering processes, that the total probability that something happens is 100%. By merging this additional constraint with information about the physical behavior of the scattering, we have developed a relatively simple method to compute scattering amplitudes for arbitrary numbers and configurations of quarks and gluons. For example, a certain 6-gluon one-loop configuration requires only 7 recursive graphs, a small desktop PC, and much less than a second of CPU. The previous best method required computation of 1034 Feynman diagrams, a high-performance computer, and endless nights of programming.

Since our method relies only on very general properties of scattering amplitudes, we expect that it can be straightforwardly adapted to the computation of other one-loop amplitudes relevant for the LHC. Precision calculations with top quarks, W bosons, Higgs bosons, and all of the other elements of LHC physics, seem well within our reach.

—Carola F. Berger
   SLAC Today, April 20, 2006