A smooth massless limit for supersymmetric QCD

We analyse in detail the behaviour of supersymmetric QCD with a number of flavours M smaller than the number of colours N, for quark masses smaller than the dynamically generated scale Λ. In this regime, we find it useful to move from meson superfields to Nambu–Goldstone-like variables. In particular we work out the mass spectrum and the set of decay constants that specify the interactions of the low-energy theory. We explicitly check that masses and decay constants have a consistent behaviour under decoupling and that they satisfy current algebra requirements. Finally we speculate about the massless limit. For vanishing quark masses, and only in this case, the relation between mesons and Nambu–Goldstone variables becomes singular. When analysed in terms of the Nambu–Goldstone superfields, the massless limit exhibits a spontaneous breaking of the flavour symmetry, with massless Goldstone modes embedded in an M2-dimensional complex moduli space. The symmetry-breaking order parameter is formally infinite, but this has the only effect of turning off the interactions between the chiral superfields. The massive case, for masses smaller than Λ, can be thought of as a perturbation around the massless case, with corrections that can be systematically computed in the effective theory.