6358: PHZ Standard Model I Fall Term 2011 Homework Set 4
Due Wednesday, September 28, 2011 Problem 1. Higgs production at the Tevatron. The main production process used for a discovery of a light (mh < 140 GeV) Higgs boson at the Tevatron is p W h. In this p exercise we shall calculate its cross-section using CalcHEP. (a) Start up CalcHEP and generate the diagrams for p W + h and p W - h. Without p p doing any calculations, try to guess and rank the first few dominant subprocesses according to their importance. (b) Calculate the cross-section for p W h at the Tevatron (ECM = 2 TeV) as a function p of the Higgs mass mh , for 100 < mh < 200 GeV. Hint: The cross-section is a slowly varying function of mh , so you will only need to compute it at 3-4 points. (c) Check your guesses from (a) against the numerical results from (b). Problem 2. Higgs production at the Tevatron: signal versus background. For a Higgs discovery in p W h at the Tevatron, one makes of use the decays W and h b p b. The main background is W b production, where the The final state signature is therefore bb. b b's were produced through a gluon, photon or a Z. On the same plot, show the b invariant b mass distribution Mb for the W h signal and the W b background. Notice that because of the b b very small Higgs width h , the signal will peak very sharply at Mb = mh . In reality, however, b the energy of the b-jets is not perfectly measured, which results in an uncertainty in Mb of b order 10%. An easy way to account for the poor mass resolution and thus make our plot more "realistic", is to simply inflate the Higgs width h to 0.1mh 12 GeV. Hint: You may need to use the option "regularization" to constrain Mb near the s-channel b gluon, photon, Z or H resonances. Problem 3. Higgs production at the LHC. Repeat Exercise 1, but for the case of Higgs production in vector-boson fusion at the LHC (pp collider, ECM = 7 TeV).
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