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253a/SchwartzDue November 28, 2016Problem Set 111. In supersymmetry, each fermion has a scalar partner, and each gauge boson has a fermi-onic partner. For example, the partner of the electron is the selectron(e~)the partner ofthe muon is the smuon (±~) and the partner of the photon is the photino (A~). We canwrite a simpli±ed Lagrangian for this theory asLSUSY=LSM+ (@±e~¡igA±e~)(@±e~?+igA±e~?)¡me~2e~e~?+g(e~eA~+e~?A~e)(1)+A~([email protected]¡mA~)A~+ (@±±~¡igA±±~)(@±±~?+igA±±~?)¡m±~2±~±~?+g¡±~±A~+±~?A~±±±(2)The smuon and selectron have the same electric charge,¡1(we useginstead ofeforclarity:²e=g24²±1137). The size of the Yukawa couplings (cubic interactions) are ±xed tobegas well, by gauge invariance and supersymmetry.a) Calculate the contribution of 1-loop graph(s) involving the selectron to the elec-tron's magnetic dipole moment.b) The experimental value and theoretical prediction forgof the electron are listedon the door of Je²erson 463. AssumingmA~=me~, what bound onme~do you getfromg? [The experimental number is out of date now. The world's best value canbe found on pdglive.lbl.gov. It is dominated by a measurement by the Gabrielsegroup at Harvard.]c) The current best experimental value forgof the muon isg±¡22= (11659208.0²6.3)³10¡10. The current theory prediction (assuming the Standard Model only) is