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# hw10 - ˜ μ 1< 5 E CM and the mass of the neutralino is...

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PHZ 6358: Standard Model I Fall Term 2011 Homework Set 10 Due Wednesday, November 23, 2011 Reading: Class notes and references linked to the class diary. Problem 1. Slepton production at a Lepton Collider. Consider the following process at a Lepton Collider with a fixed center-of-mass energy E CM (see Fig. 1). Two heavy particles, let’s call them “supermuons”, are produced and decay via two-body decays as shown. Each “supermuon” ˜ μ 1 (“smuon” for short) decays to a regular muon plus a weakly interacting massive particle (a WIMP) ˜ χ 0 1 , let’s call it a “neutralino”. The mass of the smuon is
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Unformatted text preview: ˜ μ 1 < . 5 E CM and the mass of the neutralino is M ˜ χ 1 . You can ignore the mass of the muon. e + e-γ * ,Z * ˜ μ + 1 ˜ χ 1 ˜ μ-1 ˜ χ 1 μ + μ-±igure 1: Smuon pair production and decay at an e + e-collider. (a) Show that the distribution of the muon energy E μ in the LAB frame has the shape of a rectangular box. (b) Derive the kinematic endpoints E min μ and E max μ of the E μ distribution in terms of M ˜ μ 1 , M ˜ χ 1 and E CM . (c) Solve for the unknown M ˜ μ 1 and M ˜ χ 1 in terms of the measured E min μ and E max μ . 1...
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