Deadline 23rd April 2013 This is the baisic outline of the problem but I will up

Deadline 23rd April 2013 This is the baisic outline of the problem but I will upload the actual question sheet.1) Solve the interaction Lagrangian to show the interactions between the Z boson with quarks.2) Derive expressions (in terms of the Weinberg angle) for the decay rate of Z to each type of quark and lepton.Evaluate these decay rates (in units of GeV; remember these formulae are quoted inh = c = 1 units). Add them up to show that the total decay rate of the Z (i.e. the widthof the Z resonance) is 2.5 GeV.Specific requirements:Must have step by step workings and adhere to the form of the Lagrangian in the question. No index notation to be used.Second question requires that:CL for neutrinos = 1/2CL for electrons = -1/2 + Sin^2(Theta_w)CR for electrons = Sin^2(Theta_w)