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Looking for the Higgs Boson at Hadron Colliders

Diagrams for the production of a Higgs boson plus two jets. Going from calculations for the left diagram (no loops) to the right (one loop) requires a lot of work. (Click for larger image.)

The existence of the Higgs boson was predicted more than 40 years ago to solve puzzles associated with the weak interactions, very short-range forces in the Standard Model of particle physics. The Higgs still has not been discovered, nor has the possibility of its existence been excluded. Today, the search for this elusive particle is becoming intense. The Fermilab Tevatron, operating at its peak performance, is just becoming sensitive to predicted values of the Higgs' production rate. The Large Hadron Collider at CERN, which is expected to have the capability to discover the Higgs at any expected value of its mass, is just turning on.

It is not easy to discover the Higgs boson at a proton collider. Experimenters must sift through many similar reactions that mimic the production of the Higgs boson but involve only quarks, gluons and photons. To avoid these conventional background processes, it is often helpful to look for production of the Higgs in association with "jets," sprays of strongly-interacting particles that come from quarks and gluons. Reactions with jets are more likely than simpler reactions to contain a real Higgs rather than a misleading signal. But there is a price: It is more difficult to obtain accurate theoretical predictions for the rates of these reactions, compared to non-"jet" reactions.

Calculations using traditional methods quickly become too complex even for even the most powerful computers. So the SLAC Theory group is developing new methods based on carefully crafted simplifications. The results are enabling more precise predictions, and could make it easier for experimenters to spot the Higgs.

Physicists use a tool called perturbation theory to calculate such rates. The processes are expressed as a sum of terms, neatly visualized as Feynman diagrams with an ever-increasing number of closed loops. The first term in this expansion usually gives only a qualitative estimate of the rate. For accurate results, it is necessary to go further. But loop amplitudes, especially for processes with many particles, are a real challenge to compute, mainly because of the overwhelming number of Feynman diagrams. A brute-force summation of Feynman diagrams can be so complex that it renders even the most powerful computers useless. It is therefore important to use any possible insight or method that could simplify these calculations.

The SLAC Theory group has been active in developing new methods based on "looking inside" the loop diagrams. (See "Pulling QCD Predictions out of a Black Hat.") We have found that much useful information can be generated by cutting the loop open to obtain simpler "tree" diagrams. Other very powerful tricks involve evaluating the loop amplitude with different particle momenta, even unphysical sets of momenta with values that are complex instead of real numbers. These methods allow us to compute loop amplitudes by recycling simpler calculations, leading to compact final answers.

Recently, Professor Lance Dixon and I have used this method to obtain analytic results for the one-loop amplitude to produce a Higgs boson along with two quarks. This calculation should help improve the theoretical predictions for the production of the Higgs boson at the LHC. Our results will help experimenters understand better how to study the types of complex events that are expected to be enriched in Higgs bosons. We hope that this more precise theory will help experimenters recognize Higgs events over the background and assist them in extracting the most information from the collected data.

—Yorgos Sofianatos
SLAC Today, September 18, 2008