Softly broken N = 2 QCD with massive quark hypermultiplets, I

We present a general analysis of all possible soft breakings of N = 2 supersymmetric QCD preserving the analytic properties of the Seiberg-Witten solutions for the SU(2) group with N_f = 1, 2, 3 hypermultiplets. We obtain all the couplings of the spurion fields in terms of properties of the Seiberg-Witten periods which we express in terms of elementary elliptic functions by uniformizing the elliptic curves associated to each number of flavors. We analyze in detail the monodromy properties of the softly broken theory, and obtain them by a particular embedding into a pure gauge theory with a higher rank group. This allows us to write explicit expressions of the effective potential which are close to the exact answer for moderate values of the supersymmetry breaking parameters. The vacuum structures and phases of the broken theories will be analyzed in the forthcoming second part of this paper.