DISPERSION-RELATIONS IN LOOP CALCULATIONS

These lecture notes give a pedagogical introduction to the use of disp ersion relations in loop calculations. We first derive dispersion rela tions which allow us to recover the real part of a physical amplitude from the knowledge of its absorptive part along the branch cut. In per turbative calculations, the latter may be constructed by means of Cutk osky's rule, which is briefly discussed. For illustration, we apply th is procedure at one loop to the photon vacuum-polarization funct ion i nduced by leptons as well as to the <gamma f(f)over bar> vertex form f actor generated by the exchange of a massive vector boson between the two fermion legs. We also:show how the hadronic contribution to the ph oton vacuum polarization may be extracted from the total cross section of hadron production in e(+)e(-) annihilation measured as a function of energy. Finally, we outline the application of dispersive technique s at the two-loop level, considering as an example the bosonic decay w idth of a high-mass Higgs boson.